The Io Plasma Torus During the Cassini
Encounter with Jupiter: Temporal, Radial and
Azimuthal Variations
by
Andrew Joseph Steffl
B.S., University of Wisconsin, 1999
M.S., University of Colorado, 2002
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Department of Astrophysical and Planetary Sciences
2005
This thesis entitled:
The Io Plasma Torus During the Cassini Encounter with Jupiter: Temporal, Radial
and Azimuthal Variations
written by Andrew Joseph Steffl
has been approved for the Department of Astrophysical and Planetary Sciences
Fran Bagenal
Dr. Larry Esposito
Dr. Mihaly Horányi
Dr. Nick Schneider
Dr. Ian Stewart
Date
The final copy of this thesis has been examined by the signatories, and we find that
both the content and the form meet acceptable presentation standards of scholarly
work in the above mentioned discipline.
iii
Steffl, Andrew Joseph (Ph.D., Astrophysical and Planetary Sciences)
The Io Plasma Torus During the Cassini Encounter with Jupiter: Temporal, Radial and
Azimuthal Variations
Thesis directed by Prof. Fran Bagenal
During the Cassini spacecraft’s flyby of Jupiter (1 October 2000 to 31 March
2001), the Ultraviolet Imaging Spectrograph (UVIS) produced an extensive dataset
consisting of several thousand spectrally-dispersed images of the Io plasma torus. The
temporal, radial, and azimuthal variability of the Io plasma torus during this period are
examined.
The total EUV power radiated from the torus is found to be ∼ 1.7 × 1012 W with
variations of 25%. Several events were observed during which the torus brightened by
20% over a few hours. Significant changes in the composition of the torus plasma were
observed between 1 October 2000 and 14 November 2000.
The composition and electron temperature of the torus plasma as a function of
radial distance were derived from a scan of the midnight sector of the torus. The radial
profile during the Cassini epoch shows significant differences from the Voyager era.
The Io torus is found to exhibit significant azimuthal variations in ion composition. This compositional variation is observed to have a period of 10.07 hours—1.5%
longer than the System III rotation period of Jupiter. While exhibiting many similar
characteristics, the periodicity in the UVIS data is 1.3% shorter than the “System IV”
period. The amplitude of the azimuthal variation of S II and S IV varies between 5–25%
during the observing period, while the amplitude of the variation of S III and O II remains in the range of 2–5%. The amplitude of the azimuthal compositional asymmetry
appears to be modulated by its location in System III longitude.
The observed temporal variability is reproduced by models of the torus chemistry
iv
that include a factor of 3 increase in the rate of oxygen and sulfur atoms supplied to
the extended neutral clouds that are the source of the torus plasma coupled with a
∼35% increase in the amount of hot electrons in the Io torus. The observed azimuthal
variability of the Io torus is well matched by models incorporating a primary source of
hot electrons that slips 12.2◦ /day relative to the System III coordinate system and a
secondary source of hot electrons that remains fixed in System III.
Dedication
To Carolyn, Nancy, Neil, and Katie.
vi
Acknowledgements
My profound thanks go to my advisor, Fran Bagenal, whose guidance, sense of
humor, and encouragement have been invaluable to me. Her grasp of the big picture
helped me see the forest from the trees, while her deft use of both carrot and stick
and admonishments to “Stop diddling!” provided motivation and helped me finish this
thesis in a reasonable amount of time.
Additional thanks go to: Peter Delamere and Nick Schneider for numerous discussions that expanded my knowledge of the Io torus; Ian Stewart and Bill McClintock
for sharing their knowledge of the UVIS instrument in all its detail; and Larry Esposito,
who, by funding my research assistantship, made this thesis possible.
I would also like to thank Floyd Herbert, Bill Smyth, Lori Feaga, Kurt Retherford,
Matt Burger, Paul Feldman, and the numerous other colleagues who stopped by my
posters to offer helpful suggestions and constructive criticism.
Special thanks go to Frank Scherb, for serving as my undergraduate advisor, in
spite of his recent semi-retirement. His enthusiasm for Io’s atmosphere and the plasma
torus got me hooked. Thanks to Jeff Morganthaler, Ron Oliversen, Walt Harris, Fred
Roesler, and Carey Woodward for introducing me to observing and data reduction.
My parents, Neil and Nancy Steffl, deserve special recognition for all those nights
of getting up at 2 a.m. to view meteor showers, aurora, Halley’s comet and numerous
other celestial events. Finally, my greatest thanks go to Carolyn Steffl, for all her love
and support.
Contents
Chapter
1 Introduction
1
1.1
A brief introduction to the Io plasma torus . . . . . . . . . . . . . . . .
1
1.2
The Cassini Encounter With Jupiter . . . . . . . . . . . . . . . . . . . .
4
1.3
Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.4
Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2 Initial Results From the UVIS Observations of the Io Plasma Torus
7
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
2.2
UVIS Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
2.3
2.4
2.2.1
Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
2.2.2
Instrument Calibration
. . . . . . . . . . . . . . . . . . . . . . .
15
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
2.3.1
UVIS Spectral Image . . . . . . . . . . . . . . . . . . . . . . . . .
17
2.3.2
UVIS EUV Spectrum of the Io Plasma Torus . . . . . . . . . . .
19
2.3.3
Dawn/Dusk Brightness Asymmetry . . . . . . . . . . . . . . . .
19
2.3.4
Radial Brightness Profiles . . . . . . . . . . . . . . . . . . . . . .
22
2.3.5
Temporal Variations . . . . . . . . . . . . . . . . . . . . . . . . .
26
2.3.6
System III Variations . . . . . . . . . . . . . . . . . . . . . . . .
35
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
viii
3 Radial Variation in the Io Torus
38
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
3.2
UVIS Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
3.2.1
Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
3.2.2
Data Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
3.3
3.4
3.5
Torus Spectral Emissions Model
. . . . . . . . . . . . . . . . . . . . . .
46
3.3.1
Thermal and Non-Thermal Electron Distributions . . . . . . . .
47
3.3.2
Line of Sight Assumptions . . . . . . . . . . . . . . . . . . . . . .
51
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
3.4.1
Electron Temperature and Densities . . . . . . . . . . . . . . . .
55
3.4.2
Ion Mixing Ratios . . . . . . . . . . . . . . . . . . . . . . . . . .
59
3.4.3
Uncertainties in Derived Model Parameters . . . . . . . . . . . .
63
3.4.4
κ-Distribution Results . . . . . . . . . . . . . . . . . . . . . . . .
65
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
4 Temporal and Azimuthal Variability
4.1
70
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
4.1.1
Jovian Coordinate Systems . . . . . . . . . . . . . . . . . . . . .
72
4.1.2
Variations with System III Longitude . . . . . . . . . . . . . . .
73
4.1.3
Subcorotating Torus Phenomena and “System IV” . . . . . . . .
77
4.2
Observations and Data Analysis
. . . . . . . . . . . . . . . . . . . . . .
82
4.3
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
4.3.1
Temporal Variation in Torus Composition . . . . . . . . . . . . .
84
4.3.2
Azimuthal Variations in Torus Composition
. . . . . . . . . . .
84
4.3.3
Torus Periodicities . . . . . . . . . . . . . . . . . . . . . . . . . .
89
4.3.4
Amplitude Variations and System III Modulation . . . . . . . . .
96
4.4
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
ix
4.5
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5 Modeling
5.1
5.2
108
Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.1.1
Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.1.2
Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.1.3
Reaction Rate Coefficients . . . . . . . . . . . . . . . . . . . . . . 114
5.1.4
Latitudinal Averaging . . . . . . . . . . . . . . . . . . . . . . . . 116
5.1.5
Addition of the Azimuthal Dimension . . . . . . . . . . . . . . . 121
Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.2.1
Comparison to Steady-State Model Results . . . . . . . . . . . . 123
5.2.2
Comparison to Time-Variable Model Results . . . . . . . . . . . 133
5.2.3
Azimuthal Model Results . . . . . . . . . . . . . . . . . . . . . . 146
5.3
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5.4
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6 Conclusions
159
6.1
Temporal Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.2
Radial Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
6.3
Azimuthal Variations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.4
Outstanding Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
6.5
6.4.1
Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
6.4.2
Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
6.4.3
Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
6.4.4
Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Future Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
x
Bibliography
167
Appendix
A Flatfielding
178
A.1 Definitions and Instrumental Details . . . . . . . . . . . . . . . . . . . . 179
A.2 Methods for Obtaining Flatfield Corrections . . . . . . . . . . . . . . . . 181
A.2.1 Spica Flatfields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
A.2.2 LISM Flatfields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
A.2.3 Solar Flatfields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
A.3 Temporal Changes in the Flatfield . . . . . . . . . . . . . . . . . . . . . 192
A.4 Bad Pixels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
A.5 Comparison of Spica and LISM Flatfields . . . . . . . . . . . . . . . . . 194
Tables
Table
2.1
Observed values of the dusk/dawn brightness ratio . . . . . . . . . . . .
22
3.1
Observational parameters . . . . . . . . . . . . . . . . . . . . . . . . . .
41
4.1
Peak periodogram values and uncertainties . . . . . . . . . . . . . . . .
93
4.2
Peak periodogram values of subdivided data
97
5.1
Charge exchange reactions . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.2
Comparison of UVIS data and steady state model results for 14 January
. . . . . . . . . . . . . . .
2001 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.3
Source and Loss Mechanisms for S I; 14 January 2001 equilibrium conditions125
5.4
Source and Loss Mechanisms for O I; 14 January 2001 equilibrium conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.5
Source and Loss Mechanisms for S II; 14 January 2001 equilibrium conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.6
Source and Loss Mechanisms for S III; 14 January 2001 equilibrium conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.7
Source and Loss Mechanisms for S IV; 14 January 2001 equilibrium conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.8
Source and Loss Mechanisms for O II; 14 January 2001 equilibrium conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
xii
5.9
Source and Loss Mechanisms for O III; 14 January 2001 equilibrium conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
5.10 Source and Loss Mechanisms for e− ; 14 January 2001 equilibrium conditions132
5.11 Best-fit time-variable lat-az model parameters . . . . . . . . . . . . . . . 136
5.12 Source and Loss Mechanisms for S I; 1 October 2000 non-equilibrium
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.13 Source and Loss Mechanisms for O I; 1 October 2000 non-equilibrium
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
5.14 Source and Loss Mechanisms for S II; 1 October 2000 non-equilibrium
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.15 Source and Loss Mechanisms for S III; 1 October 2000 non-equilibrium
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.16 Source and Loss Mechanisms for S IV; 1 October 2000 non-equilibrium
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.17 Source and Loss Mechanisms for O II; 1 October 2000 non-equilibrium
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.18 Source and Loss Mechanisms for O III; 1 October 2000 non-equilibrium
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.19 Source and Loss Mechanisms for e− ; 1 October 2000 non-equilibrium
conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5.20 Best fit parameters for the time-variable, azimuthally-varying model . . 155
A.1 Description of Flatfield Method . . . . . . . . . . . . . . . . . . . . . . . 188
A.2 Quantitative comparison of flatfielding methods (χ2ν ) . . . . . . . . . . . 198
Figures
Figure
2.1
UVIS Observing Geometry . . . . . . . . . . . . . . . . . . . . . . . . .
10
2.2
Raw Image of the Io Plasma Torus From the UVIS EUV Channel . . . .
13
2.3
UVIS Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
2.4
Calibrated Spectral Images of the Io Plasma Torus at Four Central Meridian Longitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
2.5
Composite EUV Spectrum of the Io Plasma Torus . . . . . . . . . . . .
20
2.6
UVIS EUV channel Radial Profile of the Io Torus . . . . . . . . . . . . .
23
2.7
Comparison of Cassini, Voyager, and EUVE Radial Profiles of the S III680Å
Feature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8
25
Total EUV Luminosity of the Io Plasma Torus During the Cassini Encounter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
Io torus EUV Luminosity event of Day 280 Year 2000 . . . . . . . . . .
29
2.10 Io torus EUV Luminosity event of Day 307 Year 2000 . . . . . . . . . .
31
2.11 Torus Luminosity in Four Spectral Features . . . . . . . . . . . . . . . .
32
2.9
2.12 Comparison of Io Torus EUV Spectra from 1 October 2000 and 14 November 2000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
2.13 Io Torus Ansa EUV Luminosity versus System III Longitude . . . . . .
36
3.1
43
Observing Geometry for 14 Januray 2001 . . . . . . . . . . . . . . . . .
xiv
3.2
Calibrated Spectral Image of the Io Torus at 6.5 RJ . . . . . . . . . . .
44
3.3
Composite EUV/FUV Spectrum of the Io Plasma Torus . . . . . . . . .
45
3.4
Spectral fit to UVIS data . . . . . . . . . . . . . . . . . . . . . . . . . .
54
3.5
Electon Temperature and Column Density Versus Radial Distance . . .
56
3.6
Derived local electron density versus radial distance . . . . . . . . . . .
57
3.7
Ion mixing ratios versus radial distance . . . . . . . . . . . . . . . . . .
60
3.8
Selected 2-D model confidence intervals . . . . . . . . . . . . . . . . . .
64
3.9
Normalized Maxwellian and κ electron distribution functions at 7.4 RJ .
66
3.10 Values of κ versus radial distance . . . . . . . . . . . . . . . . . . . . . .
67
4.1
Electron temperature and ion mixing ratios versus time . . . . . . . . .
85
4.2
Relative torus electron density and electron temperature versus System
III longitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3
86
Ion mixing ratios, electron temperature, and electron column density with
best-fit sinusoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
4.4
Phase of azimuthal variation versus time . . . . . . . . . . . . . . . . . .
90
4.5
Best-fit lines to phase increase with time . . . . . . . . . . . . . . . . . .
91
4.6
Lomb-Scargle periodogram of dusk ansa S II . . . . . . . . . . . . . . . .
92
4.7
Comparison of real and synthetic S IIdata . . . . . . . . . . . . . . . . .
95
4.8
Lomb-Scargle periodogram of synthetic S IIdata . . . . . . . . . . . . . .
96
4.9
Amplitude of azimuthal variation versus time . . . . . . . . . . . . . . .
98
4.10 Phase-colored amplitude of azimuthal variations versus time . . . . . . . 100
4.11 Graphic representation of the System III modulation of amplitude . . . 101
5.1
Model ion mixing ratios versus time and comparison to UVIS data . . . 137
5.2
Azimuthally-averaged ion parameters vs. time . . . . . . . . . . . . . . . 139
5.3
Azimuthally-averaged electron parameters vs. time . . . . . . . . . . . . 140
5.4
Comparison of model phase with UVIS data . . . . . . . . . . . . . . . . 154
xv
5.5
Comparison of model amplitude with UVIS data . . . . . . . . . . . . . 154
A.1 Orientation of the Cassini UVIS
. . . . . . . . . . . . . . . . . . . . . . 180
A.2 Example of columns affected by bad pixels . . . . . . . . . . . . . . . . . 194
A.3 Number of bad pixels per FUV detector row . . . . . . . . . . . . . . . . 194
A.4 Comparison of raw and flatfielded H2 lamp spectra . . . . . . . . . . . . 199
A.5 Comparison of raw and flatfielded spectra of Spica . . . . . . . . . . . . 200
A.6 Comparison of raw and flatfielded spectra of the LISM . . . . . . . . . . 202
A.7 Comparison of raw and flatfielded spectra of the Jovian aurora . . . . . 203
A.8 Comparison of raw and flatfielded reflectance spectra from Jupiter . . . 204
Chapter 1
Introduction
Since its discovery in 1976 (Kupo et al., 1976), the Io plasma torus has been an
enigmatic object. Nearly 30 years later, after numerous observations by ground and
space-based instruments, five spacecraft encounters, dozens of theoretical models, and
numerous Ph.D. theses, fundamental questions about the torus remain unanswered. In
this chapter, I provide a very basic introduction to the Io plasma torus and list four
broad questions about the Io torus that will be addressed in this thesis.
A more comprehensive review of the Io plasma torus is given by Thomas et al.
(2004) and references therein. Additionally, summaries of prior observations of the Io
torus can be found in Chapters 2–4.
1.1
A brief introduction to the Io plasma torus
Io, the innermost of the four large Galilean satellites of Jupiter, is locked in
a Laplace orbital resonance with two of the other Galilean satellites: Europa and
Ganymede. This resonance pumps the eccentricity of Io’s orbit which results in the
tidal heating of Io’s interior. The immense amount of energy dissipated in the interior
of Io (up to 3x1015 W (Segatz et al., 1988)) drives active volcanism, making Io the
most volcanically-active body in the solar system. Volcanic plumes and interactions
with the surface form a tenuous, primarily SO2 atmosphere. Material is lost from this
atmosphere, mostly in the form of neutral oxygen and sulfur atoms. These escaping
2
neutrals circle Jupiter on Keplerian orbits and form extended clouds.
Eventually, the neutrals become ionized, at a rate of approximately 1 ton/s,
primarily through electron impact and charge exchange reactions. Once ionized, they
interact with Jupiter’s magnetic field, which at distance of 6–9 RJ from the planet is
effectively a dipole field offset slightly from the center of the planet and tilted 9.6◦ from
the rotational axis toward a System III longitude of 200◦ (Connerney et al., 1998). The
freshly created ions are rapidly accelerated from their Keplerian velocities (17 km/s at
6 RJ ) to nearly the corotation velocity of Jupiter’s magnetic field. Since Jupiter rotates
once every 9.925 hours (Riddle and Warwick , 1976), the corotational velocity at 6 RJ
is 75 km/s. These ions form a dense (∼ 2000 cm−3 ) ring-shaped cloud known as the Io
plasma torus.
The corotating plasma in the Io torus will experience a significant centrifugal
force due to the rapid rotation of Jupiter. Since magnetic mirror forces on the torus
plasma are generally not important (Bagenal and Sullivan, 1981), the plasma will find
an equilibrium about the position on a given magnetic field line that is most distant
from Jupiter’s rotation axis. This position is known as the centrifugal equator, and it
is located 1/3 of the way between the magnetic equator and the rotational equator, or
alternatively, 6.4◦ from the rotational equator (Hill et al., 1974; Cummings et al., 1980).
The balance of centrifugal and pressure forces will cause the torus plasma to spread out
along magnetic field lines with a scale height determined by the mass and temperature
of the ions.
The tilt between the centrifugal equator plane and the rotational equator plane
cause the Io torus, when viewed from a distance, to appear to wobble. Since the tilt of
Jupiter’s magnetic field is toward a System III longitude of 200◦ , the torus will appear
in a face-on, or open, configuration for an observer near on the rotational equator
at λIII =20◦ and λIII =20◦ , and edge-on, or closed, configuration for an observer at
λIII =110◦ and λIII =290◦ , the longitudes at which the rotational equator and centrifugal
3
equator planes intersect.
The pickup process, whereby fresh ions are accelerated to nearly the corotational
speed of the ambient torus plasma, imparts a significant amount of kinetic energy to the
picked-up ions (380 eV for sulfur ions and 190 eV for oxygen ions at 6 RJ , assuming an
isotropic distribution. See Eq. 5.1). Typical ion temperatures in the Io plasma torus are
∼100 eV, implying that torus ions have lost much of their original pickup energy. The
primary means by which the ions cool are Coulomb interactions with torus electrons.
Because of their low mass, electrons gain very little energy in the pickup process and
are therefore heated primarily through Coulomb interactions. Typical electron temperatures in the torus are ∼5 eV.
The electrons in the torus lose energy by collisional excitation of radiative transitions in the torus ions.
In total, the Io plasma torus radiates roughly ∼2 TW
(1 TW=1012 W) of power. This constitutes the principal means by which energy is
removed from the torus. Roughly 60% of the total radiated energy is emitted in the
EUV region of the spectrum (500–1200Å).
Shemansky (1988) and Smith et al. (1988) noted that the power radiated from the
Io torus (primarily in the UV) exceeds the power supplied to the torus by the ion pickup
process. This deficit became known as the “energy crisis”. Without an additional source
of energy, the torus can neither radiate enough energy to match observations (Shemansky, 1980; Hall et al., 1994b; Steffl et al., 2004a) nor support an electron temperature
of ∼5 eV (Shemansky, 1988; Barbosa, 1994; Schreier et al., 1998; Lichtenberg, 2001;
Delamere and Bagenal , 2003). One possible source of this extra energy is through the
addition of a small population (a few tenths of a percent of the total electron density) of
high temperature (∼50–100 eV) electrons. These relatively hot electrons efficiently heat
the thermal electrons through Coulomb interactions. Evidence for such a high-energy
population of electrons was found by the Voyager 1 Plasma Science instrument (Sittler
and Strobel , 1987).
4
Plasma is removed from the Io torus in two ways: fast neutrals and outward
radial transport. When a corotating torus ion becomes neutralized (through either
charge exchange reactions or recombination), it is no longer bound by Jupiter’s magnetic field. Since the velocity of particles moving at corotation (75.4 km/s at 6.0 RJ )
exceeds Jupiter’s escape velocity (59.5 km/s), these neutrals (and the energy associated
with them) are removed from the system and have been detected to a distance of 500 RJ
from Jupiter (Mendillo et al., 1990). Plasma that does not leave the torus as a fast neutral is eventually transported radially outwards into the middle Jovian magnetosphere.
Although the details of this process are not well understood, flux tube interchange is
generally agreed to be the mechanism responsible for the outward transport of torus
plasma. In flux tube tube interchange, flux tubes filled with torus plasma feel a strong
centrifugal force due to Jupiter’s rapid rotation and exchange with relatively empty flux
tubes from the middle magnetosphere. This process is similar to the Raleigh-Taylor instability, which occurs when a higher-density dense fluid overlays a less dense fluid. The
timescale for radial transport is ∼40–80 days.
1.2
The Cassini Encounter With Jupiter
On its way to Saturn, the Cassini spacecraft flew past Jupiter on 30 December
2000. For three months before and after the closest approach, the Ultraviolet Imaging
Spectrograph (UVIS) observed the Io plasma torus. In all, nearly 3400 spectrallydispersed images of the torus were acquired—an enormous dataset. The 3Å spectral
resolution and imaging capabilities of UVIS coupled with the excellent time coverage
(e.g. UVIS observed the Io torus for more than 50% of the time between 1 October
2000 and 14 November 2000) make this dataset uniquely suited to answer questions
about the nature of the Io torus. Particular attention has been paid to two subsets of
this data: the inbound staring observations made from 1 October 2000 to 14 November
2000 and the radial scan observation of 14 January 2001.
5
1.3
Goals
The goal of this thesis is to use data from the Cassini Ultraviolet Imaging Spec-
trometer and theoretical models of the physical processes underlying the torus to provide
answers to the following broad questions about the Io plasma torus:
(1) What was the torus composition during the Cassini epoch and how does this
compare to previously observations?
(2) How do the properties of the Io plasma torus vary on timescales of minutes,
days, and months?
(3) What is the spatial structure of the Io torus, and how do torus properties
like composition, temperature, and density change with radial distance and
azimuthal position?
(4) What are the underlying physical processes responsible for the observed temporal and azimuthal variability of the torus?
1.4
Layout
This thesis is divided into six chapters and one appendix. Chapter 2 presents
results from the initial analysis of the UVIS Io torus observations. Much of the chapter
focuses on the changes in the brightness of torus emissions during the observing period.
This chapter was published in the journal, Icarus, as: Steffl, A. J., A. I. F. Stewart, and
F. Bagenal, Cassini UVIS observations of the Io plasma torus. I. Initial results, Icarus,
172, 78–90, 2004.
Chapter 3 introduces the model used to fit the UVIS spectra of the Io torus. The
composition, temperature and density of the torus, as derived from spectra obtained
during the torus radial scan of 14 January 2001, are presented. This chapter was
6
published as: Steffl, A. J., F. Bagenal, and A. I. F. Stewart, Cassini UVIS observations
of the Io plasma torus. II. Radial variations, Icarus, 172, 91–103, 2004.
Chapter 4 presents the temporal and azimuthal variability in the composition
of the Io torus during the period of 1 October 2000 to 14 November 2000. Particular
emphasis is placed on the non-System III periodicity observed in the torus mixing
composition. This chapter has been submitted to Icarus as: Steffl, A. J., P. A. Delamere,
and F. Bagenal, Cassini UVIS observations of the Io plasma torus. III. Temporal and
azimuthal variability.
Chapter 5 presents models of the physics and chemistry of the Io plasma torus
with the goal of reproducing, ab initio, the temporal and azimuthal variability observed
by UVIS.
A summary of the individual chapters and the conclusions of this thesis are presented in Chapter 6.
The appendix presents a detailed review of the data and techniques used to make
the Spica-derived UVIS flatfield correction and comparison of this flatfield to the LISMderived UVIS flatfield correction. As such, it is useful primarily to those interested in
the details of UVIS data analysis.
Chapter 2
Initial Results From the UVIS Observations of the Io Plasma Torus
During the Cassini spacecraft’s flyby of Jupiter (01 October 2000 to 31 March
2001), the Ultraviolet Imaging Spectrograph (UVIS) produced an extensive dataset consisting of 3349 spectrally dispersed images of the Io plasma torus1 . Here we present an
example of the raw data and representative EUV spectra (561 Å–1181 Å) of the torus,
obtained on 1 October 2000 and 14 November 2000. For most of the flyby period, the
entire Io torus fit within the UVIS field of view, enabling the measurement of the total
power radiated from the torus in the extreme ultraviolet. A typical value for the total
power radiated in the wavelength range of 580 Å–1181 Å is 1.7 × 1012 W, with observed
variations of up to 25%. Several brightening events were observed. These events lasted
for roughly 20 hours, during which time the emitted power increased rapidly by ∼20%
before slowly returning to the pre-event level. Observed variations in the relative intensities of torus spectral features provide strong evidence for compositional changes in
the torus plasma with time. Spatial profiles of the EUV emission show no evidence for
a sharply peaked “ribbon” feature. The ratio of the brightness of the dusk ansa to the
brightness of the dawn ansa is observed to be highly variable, with an average value of
1.30. Weak longitudinal variations in the brightness of the torus ansae were observed
at the 2% level.
1
This chapter published as: Steffl, A. J., A. I. F. Stewart, and F. Bagenal, Cassini UVIS observations
of the Io plasma torus. I. Initial results, Icarus, 172, 78–90, 2004
8
2.1
Introduction
The ionization of ∼1 ton per second of neutral material from Io’s atmosphere
produces a dense (∼2000 cm−3 ) torus of electrons, sulfur and oxygen ions, trapped in
Jupiter’s strong magnetic field. While in situ, measurements of the Io plasma torus from
the Voyager and Galileo spacecraft and remote sensing observations from the ground
and from space-based UV telescopes have characterized the density, temperature and
composition of the plasma as well as the basic spatial structure (see review by Thomas
et al. (2004)), the temporal variability of the torus remains poorly determined.
On its way to Saturn, the Cassini spacecraft flew past Jupiter on the dusk side of
the planet with a closest approach distance of 137 RJ which occurred on 30 December
2000. The optical design of the Ultraviolet Imaging Spectrograph (UVIS) enabled observations of the jovian system from 01 October 2000 to 31 March 2001. In this paper
we present an analysis of the extreme ultraviolet (EUV) emissions from the Io torus
obtained by UVIS during the six-month Jupiter flyby. The 3349 spectral images used
in this analysis reveal torus variability on time scales ranging from minutes to months.
The UVIS instrument consists of two independent, but co-aligned, spectrographs:
one optimized for the extreme ultraviolet (EUV), covering a wavelength range of 561 Å
to 1181 Å and the other optimized for the far ultraviolet (FUV), covering a wavelength
range of 1140 Å to 1913 Å (McClintock et al., 1993; Esposito et al., 1998; Esposito
et al., 2004). Each spectrograph is equipped with a CODACON 102464 pixel imaging
microchannel plate detector (Lawrence and McClintock , 1996). Images are obtained
of UV-emitting targets with a spectral resolution of 3 Å FWHM (as measured by the
point-spread function) and a spatial resolution of 1 milliradian. The broad spectral
range, high spectral resolution (compared to Voyager), and temporal coverage of UVIS
resulted in the creation of a unique and rich dataset of the Io plasma torus in the
ultraviolet.
9
In this paper, we show examples of the dataset of the Io plasma torus obtained by
UVIS. Additionally, we present the temporal variability of the brightness of EUV torus
emissions observed during the flyby period. In an accompanying paper, we present an
analysis of observations of the midnight ansa of the Io torus made shortly after closest
approach, when UVIS obtained data at highest spatial resolution.
2.2
UVIS Observations
The vast majority of UVIS observations of the Io torus were obtained while the
Cassini spacecraft was oriented such that the spacecraft −Y axis (which points in the
nominal direction of the UVIS boresight) was pointed towards Jupiter while the +X axis
was pointed at the north ecliptic pole. The long axis of the UVIS entrance slit is parallel
to the spacecraft Z axis and was therefore approximately parallel to Jupiter’s equator.
Figure 2.1 shows the viewing geometry for the UVIS data taken on 01 October 2000
and 04 December 2000. The viewing geometry for these observations is representative
of the UVIS Io torus dataset.
For the purposes of analyzing the UVIS Io torus observations, the Jupiter flyby
period can be subdivided into three separate phases, based on the location of the Cassini
spacecraft and the mode of observation during that phase: the inbound staring phase,
which lasted from 01 October 2000 to 14 November 2000; the inbound mosaic phase,
which lasted from 15 November 2000 to 04 December 2000; and the outbound mosaic
phase, which lasted from 22 January 2001 to 31 March 2001. In the period between the
inbound mosaic phase and the outbound mosaic phase, the angular size of the Io torus
exceeded the field of view of UVIS, so measurements of the total radiated power were
not possible.
During the inbound staring phase, the boresight of the instrument was pointed
at the center of Jupiter, where it remained for the entirety of the observation. Spectral
images of the Io torus were obtained with integration times of 1000 seconds. Due to the
10
G
+
Jupiter
+ +I
E
+
C
UVIS EUV Occultation Slit Field-of-View October 4, 2000
Jupiter
+
I
+
E
UVIS EUV Occultation Slit Field-of-View December 4, 2000
Figure 2.1: Observing geometry for UVIS observations of the Io torus on 4 October
2000 and 4 December 2000. The projection of the UVIS EUV occultation slit is shown
relative to the locations of Jupiter and the galilean satellites and their orbits.
11
required spacecraft downlink time and other observations requiring a different spacecraft
orientation, spectra of the Io plasma torus were not acquired continuously during this
period. Rather, observations were made in a cycle lasting 12 jovian rotations (5 days).
UVIS obtained data during rotations 1, 3, 5, 6, 7, 9, and 11; this cycle was repeated
nine times. We analyzed a total of 1904 spectral images of the Io torus obtained in this
mode. Since data obtained during the inbound staring phase is easier to interpret than
data obtained during other phases of the Jupiter flyby, much of our initial analysis has
focused on this period.
On 15 November 2000, the Cassini spacecraft entered the inbound mosaic phase
of the Jupiter flyby. Prior to this date, the pointing of the spacecraft had remained fixed
on Jupiter for the length of a given observation. After this time, however, the spacecraft
pointing was changed in order to ensure that the Orbiter Remote Sensing instruments
would be able to observe the whole of Jupiter. During this inbound mosaic phase,
the spacecraft pointing moved in a 22 mosaic pattern, centered on Jupiter, followed by
a gradual north-to-south scan through the middle of the planet. The motion of the
spacecraft makes the interpretation of this data significantly more difficult, as the 1000second UVIS integrations were not synchronized with the changes in spacecraft pointing.
As a result, data taken during this mode of operation are smeared along the spectral
and/or the spatial directions. In addition, the motion of the spacecraft occasionally
caused parts of the torus to drift in and out of the UVIS field-of-view. Therefore, we
have limited our analysis of the mosaic phase data to those spectral images that contain
the entire torus within the instrument field-of-view for the entire 1000-second integration
period. All spectral images meeting this criterion, (roughly one out of every five UVIS
images taken after 15 November 2000) were obtained while the spacecraft was executing
a gradual, north-to-south scan through the center of Jupiter, resulting in a degradation
of the spectral resolution of these images. Since there was no east-west motion during
this scan, the spatial resolution along the length of the slit, i.e., in the radial direction,
12
is unaffected.
The observations made during the outbound mosaic phase are very similar to
those made during the inbound mosaic phase, with the exception that different mosaic
patterns were used (22, 21, etc.). The same selection criterion was used to reduce the
data analyzed to only those images containing the whole torus for the entire integration
period, which varied from 250–1000 seconds.
2.2.1
Data Reduction
Proper analysis of the UVIS dataset requires careful background subtraction. In
addition to the expected sources of background counts from the spacecraft’s radioisotope
thermal generators (RTGs) and the detector electronics, there is a pinhole light-leak in
the EUV channel, that allows Lyman alpha radiation from the interplanetary medium
(IPM) to fall undispersed onto the detector. The FUV channel has no such light leak,
and is unaffected by the EUV channel light leak. The undispersed light falling on the
EUV channel detector creates a spatially non-uniform background pattern, known as the
“mesa” feature, which varies in intensity depending on the pointing of the spacecraft.
The mesa feature primarily affects the short wavelength end of the detector, with an
intensity that slowly increases with increasing wavelength until around 950 Å (column
630), where it suddenly falls off to nominal background levels. The exact location of
this drop-off is row-dependent (near column 610 for row 48 and near column 660 for row
16) and is the result of the shadow of the cylindrical shade which surrounds the detector
projected onto the detector surface. The effect of the mesa pattern on the quality of
the Io torus data can be seen in Figure 2.2, which shows a raw spectral image of the Io
torus and the various background sources.
In order to determine the spatial variation of the mesa feature across the EUV
detector, a composite background image was created by averaging together 75 660second observations of the IPM. These observations are well-suited to diagnose the
1
16
24
32
40
48
0
200
400
600
Column Number
10
800
100
1000
200
Figure 2.2: Unprocessed image of the Io torus. This image illustrates the signal-to-noise of the UVIS data and the various background
effects. The dusk ansa of the torus is at the top half of the image, and jovian north is to the left. The background level in the “mesa”
feature is a factor of ∼ 2 higher than the nominal background. The faint, diamond-shaped pattern present in the mesa feature is caused
by the shadow of a wire grid positioned above the detector. Scattered Lyman alpha can also be seen at the long wavelength end (right)
of the EUV detector.
Row Number
Counts / 1000s
13
14
nature of the mesa feature since they contain only two bright spectral lines: Lyman-β at
1025 Å and He II 584 Å. Since the intensity of the mesa feature varies with the spacecraft
pointing, the composite background image must be scaled to the level of background
present in a given observation. Inspection of the data reveals that no detectable signal
from the Io torus is present at distances greater than 10 RJ from Jupiter. Therefore,
this region provides an estimate of the intensity of the background level. To improve the
signal-to-noise ratio of the data background, a 55 pixel smoothing filter was passed over
the image. The smoothed data image was then divided by the composite background
image, after it had been likewise smoothed, to create a scaling image. Each pixel in the
scaling image represents the factor by which the corresponding pixel in the composite
background image must be multiplied before it is subtracted off from the data. For each
column of the detector, a line was fit to the two regions of the scaling image lying at a
projected radial distance of greater than 10RJ . For a given column, the values of the
scaling image inside of 10RJ were replaced with values interpolated from the best-fit
line for that column. This produced a scaling image valid for all regions of the detector.
The unsmoothed composite background image was then multiplied by the scaling image
before subtracting it from the unsmoothed data image. This method effectively removes
the mesa feature from the data and does not introduce any significant residuals.
During the inbound staring phase of observations, i.e., for data obtained before
15 November 2000, only the central 32 rows of the detector were read out, necessitating
a slightly different method to scale the composite background image to the data image.
For these data, the baseline level of background, i.e., that due to sources other than the
mesa feature, was calculated by averaging together pixels longward of the mesa feature
drop-off in a spectral region containing no significant emission from the Io torus. This
constant value was subtracted from the data image, and a similar procedure was applied
to the composite background image. After removing the constant basal background
value from the two images, the data image was divided by the composite background
15
image. Pixels in the resulting scaling image lying in wavelength regions containing no
significant emissions from the torus were then averaged together to determine a constant
background scaling factor. Once the scaling factor has been determined, the original
composite background image, minus its baseline background value, was multiplied by
the constant scaling factor. Finally, the scaled background image was subtracted from
the data image (after the baseline level of background had been subtracted from the data
image). For data to which both methods of background subtraction could be applied,
the differences between the two methods were minimal.
2.2.2
Instrument Calibration
One of the challenges of working in the far-to-extreme ultraviolet region of the
spectrum is obtaining an accurate detector calibration. For UVIS, this was accomplished with the use of two calibrated photodiodes, provided by the National Institute
of Standards and Technology (NIST). These two photodiodes are the primary standards
for the radiometric sensitivity calibration of UVIS. Due to laboratory constraints and
the count rates of the photodiodes, it was not possible to use the NIST photodiodes
directly measure the UVIS detector effective area. Rather, the NIST photodiodes were
used to calibrate two secondary standards which were then used to measure the UVIS
effective area. Results from the calibration standards were compared to instrumental
sensitivities derived from theoretical and laboratory spectra of H2 , N2 , Ne, and Ar.
A lack of available—and suitably bright—calibration sources in the wavelength
range of 580 Å to 925 Å hindered the absolute calibration of this region of the EUV
channel. However, Ajello et al. (1988) present the integrated intensities of four narrow
features in the spectrum of Ar between 576 Å and 722 Å and a fifth feature centered on
925 Å. The observed intensities of these emissions relative to the feature at 925 Å, which
was calibrated by the secondary standard, were used to scale the instrument effective
area below 900 Å.
16
0.04
Effective Area (cm2)
EUV Channel
FUV channel
0.03
0.02
0.01
0.00
600
800
1000
1200
1400
Wavelength (Å)
1600
1800
Figure 2.3: Effective area (cm2 ) of the EUV and FUV channels of UVIS. The error bars
represent the 1-σ error from the quadrature sum of the errors from the NIST diode
formal error, the transfer of calibration to a secondary calibration standard, and the
measurement precision. Data provided by Bill McClintock (personal communication).
Subsequent calibration work after Cassini flew past earth in 1999 revealed that
the original estimate of the EUV detector sensitivity (i.e., the lab calibration) was systematically 25% too low. The 1999 post-Earth correction of the laboratory calibration
was used in the analysis of all data presented in this paper and can be seen in Fig. 2.3.
Between 900 Å and 730 Å, the instrument effective area rapidly declines by about a
factor of three, which is consistent with pre-calibration models of the EUV channel effective area based on the reflectivity of the boron carbide coatings of the grating and
the telescope (Bill McClintock, personal communication).
Work on the UVIS calibration is ongoing. Coordinated observations of the Sun
with UVIS and the Solar EUV Experiment (SEE) (Woods et al., 1998) aboard the
Thermosphere, Ionosphere, Mesosphere, Energetics, and Dynamics (TIMED) spacecraft
were obtained in July and December 2002. These observations will be used to cross-
17
calibrate the EUV channel, especially in the region below 900 Å, where the shape of the
EUV effective area curve is poorly constrained due to paucity of laboratory calibration
measurements.
2.3
Results
2.3.1
UVIS Spectral Image
Spectrally dispersed images of the Io torus are presented in Fig. 2.4. These images
are from the EUV channel of UVIS and are typical of the quality of data obtained during
the Jupiter flyby. The data were obtained during 46-hour period beginning on 03:06
UT 11 November 2000. Individual images, acquired when the sub-Cassini System III
longitude (λIII ) was within ± 15◦ of 20◦ , 110◦ , 200◦ , and 290◦ , were averaged together to
increase the signal-to-noise ratio. Jovian north is toward the left, while the dusk ansa of
the torus is toward the top of the figure. The longitudes of 110◦ and 290◦ show the torus
in an edge-on orientation. The Cassini spacecraft was located at 4◦ north latitude during
these observations, and the centrifugal equator of the Io torus is inclined approximately
6◦ to the rotational equator. Therefore, when the Cassini spacecraft is located near
λIII =20◦ , the opening angle of the torus is approximately 2◦ and the torus appears
close to edge-on, while at λIII =200◦ , the opening angle is approximately 10◦ , resulting
in a torus that appears somewhat face-on. A movie—created by summing the major
torus emissions—showing the rotation of the Io torus from 10–14 November 2000 can
be found at:
http://lasp.colorado.edu/cassini/whats_new/whats_newarchives.htm
Roughly 20 spectral features due to the Io plasma torus can be seen in the EUV
channel image. Several of these features overlap as a result of the latitudinal extent
of the Io torus and the spectral resolution of UVIS (3 Å FWHM, as determined by
the point-spread function). Emission from the jovian aurora can be clearly seen in the
λIII=110° λIII=200° λIII=290°
Distance from Jupiter (RJ)
0
−5
−10
−15
0
−5
−10
−15
0
−5
−10
−15
0
−5
−10
−15
1
600
600
700
700
10
900
800
900
Wavelength (Å)
800
1000
1000
1100
100
1100
>200
Figure 2.4: UVIS EUV channel spectral images showing the Io torus in open and edge-on configurations. As in Fig. 2.2, the dusk ansa is
up, and Jovian north is to the left. The central meridian longitude (CML) of the Cassini spacecraft during the observation is given to the
left of the spectral images. To increase signal-to-noise, observations obtained over a 46-hour period beginning on 03:06 UT 11-Nov-2000
with a CML ± 15 ◦ of the nominal value were averaged together. Cassini was located at 4◦ north latitude during the observations, causing
the image taken at CML λIII =20◦ to appear near edge-on. Auroral emissions from Jupiter are visible in the central rows. Shortward of
∼845Å, Jupiter becomes absorber. The narrow, vertical features near 600Å are instrumental artifacts.
λIII=20°
Rayleighs/Ångstrom
18
19
central rows, longward of 845 Å. At wavelengths below this point, Jupiter becomes an
absorber rather than an emitter, and these rows appear darkened.
2.3.2
UVIS EUV Spectrum of the Io Plasma Torus
The spectrum of the dusk ansa of the Io plasma torus at the beginning of the flyby
period, as observed by the EUV channel of UVIS, is shown in Fig. 2.5. This spectrum is
the average of a single row from each of 164 individual spectral images, obtained during
a 67-hour period beginning at 08:43 UT 01 October 2000. Cassini was 1160 RJ from
Jupiter at the time of these observations, so that single row covers the dusk ansa of the
torus from 6.0–7.2 RJ in projected radial distance. The features in the spectrum are
labeled by the ion species responsible for the majority of emission in the feature and
the central wavelength of the feature. Since the Io torus is clearly not a point source,
the effective resolution of the spectrum is limited by the angular size of the torus in
the latitudinal direction, and, as such, is proportional to the spacecraft’s distance from
Jupiter. The highest resolution spectrum of the Io torus obtained by UVIS, which also
includes the FUV channel, is presented in the accompanying paper (Steffl et al., 2004b)
(Chapter 3).
2.3.3
Dawn/Dusk Brightness Asymmetry
The dawn/dusk brightness asymmetry of the Io torus, discovered in Voyager
UVS data by Sandel and Broadfoot (1982a), has been seen by a variety of observers and
instruments in wavelengths ranging from the ultraviolet to the infrared (Morgan, 1985;
Oliversen et al., 1991; Dessler and Sandel , 1992; Hall et al., 1994a; Hall et al., 1994b;
Schneider and Trauger , 1995; Gladstone and Hall , 1998; Herbert and Sandel , 2000;
Herbert et al., 2001; Lichtenberg et al., 2001)). The dawn/dusk asymmetry is readily
seen in the UVIS data, with the dusk ansa being, on average, 1.3 times as bright as
the dawn ansa (integrated over the full EUV channel wavelength range). However, this
20
120
__ S III 1126Å
__
__ S IV 1099 & S II 1102Å
__ S II 1047Å
__ S IV 1063Å
__
__ S IV 1073 & S III 1077Å
__ S II 995Å
__ S II 1006Å
__
__ S III 1015Å & S III 1021Å
__ S II 938Å
20
__ S II 906Å
40
__ S II 875Å
60
__ S III 729Å
__ S IV 748Å
__ S II 765Å
__ S V 786Å
__ S III 797Å
__ S IV 809Å
__ S III 822Å
__ S III 700Å
80
__ S II 642Å
__ S IV 657Å
Brightness of Dusk Ansa (R/Å)
100
__ O II 833Å & O III 834Å
__ S III 680Å
0
600
700
800
900
Wavelength (Å)
1000
1100
Figure 2.5: Composite EUV (561Å-1181Å) spectrum of the Io plasma torus dusk ansa.
This spectrum is the average of 164 1000-second integrations obtained during a 67-hour
period beginning at 08:43 UT 1 October 2000. Cassini was ∼1,160 RJ from Jupiter at
the time of these observations, so the spectrum was extracted from 6.0 RJ –7.2 RJ in
projected radial distance. The spectral features are labeled by wavelength and the ion
species that makes the dominant contribution to the feature.
21
ratio was observed to be highly variable. During the inbound staring phase (01 October
2000 to 14 November 2000), this ratio varied from 0.73–2.29, with a mean value of 1.30
and a standard deviation of 0.25.
If there are longitudinal variations in the torus, then the instantaneous ratio of
dusk ansa brightness to dawn ansa brightness will be a combination of the effects of
the dawn-to-dusk electric field and the longitudinal asymmetry. The relatively short
integration time (≤ 1000 seconds), imaging capability, and temporal coverage of UVIS,
make it possible to directly compare the spectrum of a particular blob of plasma located
at the dawn ansa to the spectrum from the same blob of plasma (i.e., at the same
longitude) when it is located at the dusk ansa, slightly less than 5 hours later. Likewise,
a spectrum of the dusk ansa can be directly compared to the spectrum of the dawn
ansa 5 hours later. Since we are observing the same blob of plasma as it rotates from
dawn to dusk and back again, this method of obtaining a dusk-to-dawn brightness ratio
will be independent of any longitudinal asymmetries. Perhaps surprisingly, this method
yields results that are virtually identical to those obtained by taking the instantaneous
ratio of the two ansa brightnesses. Values of the EUV dusk/dawn brightness ratio,
as observed by the Cassini UVIS, Voyager 2 Ultraviolet Spectrograph (UVS), and the
Extreme Ultraviolet Explorer (EUVE), are presented in Table 2.1.
Analysis of Voyager UVS data by Shemansky and Sandel (1982) determined that
the dawn/dusk brightness asymmetry was caused by a 10–30% increase in the electron
temperature on the dusk side of the torus, as opposed to an increase in plasma density.
Observations of the Io torus at the dawn and dusk ansae by the Hopkins Ultraviolet
Telescope (HUT) indicated an electron temperature difference of ∼10% (Hall et al.,
1994a). However, the most recent analysis of EUVE observations of the Io torus determined that the dusk ansa was actually 2% cooler than the dawn ansa in 1996 and 4%
cooler in 1999 (Herbert et al., 2001). The uncertainty in these values is 7% for 1996 and
9% for 1999. Preliminary analyses of the UVIS spectra are consistent with an electron
22
Table 2.1: Observed values of the dusk/dawn brightness ratio
Instrument
Mean
Std. dev.
Min.
Max.
] Percent of time
dawn > dusk
Cassini UVISa
1.30
0.25
0.73
2.29
10%
Cassini UVISb
1.31
0.24
0.66
2.16
7%
Voyager 2 UVSc
1.22
0.33
0.64
2.17
22%
EUVEd
1.24
2.30
Not observed
a
44 days of observations from Cassini inbound staring phase in 2000 instantaneous ratio of dusk
ansa brightness/dawn ansa brightness.
b
Dusk ansa brightness/dawn ansa brightness (1/2 rotation later) combined with dusk ansa brightness (1/2 rotation later)/dawn ansa brightness.
c
8 days of observations from Voyager 2 inbound leg in 1979 (Sandel and Broadfoot, 1982a).
d
2 days of observation in 1993 (Hall et al., 1994a), 5 days in 1996 (Gladstone and Hall , 1998), and
15 days in 1999 (Herbert et al., 2001).
temperature increase of ∼15% on the dusk side.
2.3.4
Radial Brightness Profiles
Each of the 1904 spectral images obtained during the inbound staring phase of
observations were summed along the spectral dimension to produce a 32 pixel-wide
spatial profile of the torus EUV emissions. During the inbound staring phase, the
distance of the Cassini spacecraft to Jupiter decreased by almost a factor of two, causing
a corresponding factor of two increase in spatial resolution. In order to correct for errors
caused by the changes in spatial scale caused by the decreasing jovicentric distance, the
individual spatial profiles were rebinned, using linear interpolation, and realigned to
correct for minor pointing variations. The resulting profiles were averaged together to
produce the radial profile seen in Fig. 2.6.
The error bars in Fig. 2.6 represent the 1-σ level of the intrinsic variability of the
torus radial profile, rather than the statistical uncertainty in the data. The brightness
peak of both the dawn and dusk sides of the torus are located near 5.8 RJ . However, the
spatial resolution of UVIS (∼0.6 RJ ) is insufficient to resolve the small (a few hundredths
to a few tenths of an RJ ) radial offset between the locations of the brightness peaks
23
1.0
Dawn Ansa
Dusk Ansa
Relative Brightness
0.8
0.6
0.4
0.2
0.0
-10
-5
0
Distance from Jupiter (RJ)
5
10
Figure 2.6: Total UVIS EUV channel (561Å-1181Å) spatial profile. The dawn ansa is
to the left while the dusk ansa is to the right. The error bars represent the intrinsic 1-σ
variance of the Io torus i.e. the instantaneous observed spatial profile lies within the
error bars 68% of the time.
of the dawn and dusk ansa that is predicted by the cross-tail electric field proposed
by Barbosa and Kivelson (1983) and Ip and Goertz (1983) to explain the dawn/dusk
brightness asymmetry. Once scaled to the height of the dusk side, the shape of the
dawn-side radial profile is nearly identical to the dusk side, outside 5.5 RJ . Inside of
this distance, however, the dawn-side profile falls off much more slowly.
Working independently to explain the increased temperature of the dusk ansa,
as reported by Shemansky and Sandel (1982); Ip and Goertz (1983) and Barbosa and
Kivelson (1983) proposed the existence of an electric field extending from dawn to dusk
across the jovian magnetosphere. Such a field might be created by the anti-sunward flow
of plasma down the magnetotail. This electric field would result in higher temperatures
on the dusk side via adiabatic compression of the plasma, and a radial shift in the
24
location of the torus by a few tenths of an RJ in the direction of the dawn ansa.
Observations by Morgan (1985); Oliversen et al. (1991); Schneider and Trauger (1995)
and Dessler and Sandel (1992), and others have confirmed the existence of such a radial
offset. Due to the relatively coarse spatial resolution of UVIS, no radial offset of the
torus was detected.
Radial profiles of the S III 680 Å feature were also obtained by the Voyager 1
UVS (Sandel and Broadfoot, 1982a; Dessler and Sandel , 1993) and the Extreme Ultraviolet Explorer (EUVE) spacecraft (Hall et al., 1994b). The radial profile of Sandel
and Broadfoot (1982a) was obtained from many observations during the post-encounter
period. The profile of Dessler and Sandel (1993) was made from a single, high-spatialresolution observation that also occurred during the post-encounter period. The EUVE
radial profile of Hall et al. (1994b) was obtained during a 2-day period beginning on
30 March 1993. These profiles, along with the UVIS radial for sub-region lying with ±
10 Å of 680 Å, are shown, after normalization to the peak of the dusk ansa, in Fig. 2.7.
The general shape of the profile observed by EUVE is fairly similar to the UVIS
profile. However, the ratio of the brightness of the dawn ansa to the brightness of the
dusk ansa is much higher in the EUVE profile. On the dawn side of the torus, both
UVIS and UVS show a section whose brightness is nearly independent of radial distance.
The minimum energy required to produce a photon observable by the EUV channel of UVIS is 11 eV. Since the electron temperature of the torus inside 6 RJ is significantly less than this (∼5 eV) (Sittler and Strobel, 1987), observations of this region are
particularly susceptible to viewing geometry effects caused by the superposition of the
warm, outer torus on the cold, inner torus. For this reason, and because the peaks in
the spatial profile are asymmetrical, we believe that the half-width at half-maximum
(HWHM), measured radially outward from the peak, is a more accurate measure of
the intrinsic width of the torus emitting region than the full-width at half-maximum
(FWHM) that has been reported in previous studies. The outward HWHM of the dusk
25
Figure 2.7: Spatial profiles of the S III 680Å feature. The thick black line is the UVIS
profile, averaged over 41 days. The connected grey dots are the Voyager 1 UVS profile
of Sandel and Broadfoot (1982a). The connected black dots is the high-resolution UVS
profile of Dessler and Sandel (1993). The histogram is the EUVE profile of Hall et al.
(1994b). All three instruments observe the brightness of the dawn side to fall off more
slowly inside of the peak on the dawn side than on the dusk side.
ansa of the UVIS spatial profile is 1.3 RJ . The outward HWHM of the UVS dusk ansa,
as presented by Sandel and Broadfoot (1982a), is 1.0 RJ , while the outward HWHM for
EUVE is 1.3 RJ —the same as measured by UVIS. The outward HWHM for the dawn
ansa is 1.4 RJ for UVIS, 1.1 RJ for UVS, and 1.5 for EUVE.
Analysis of high spatial resolution Voyager 1 and Voyager 2 UVS radial scans by
Dessler and Sandel (1993) and Volwerk et al. (1997) suggested that roughly 80–85% of
the EUV emission comes from a narrow “ribbon” feature with a FWHM of 0.22 RJ .
Such an extremely narrow peak in the EUV emitting region of the torus is not consistent
with the observations of UVIS. This result is confirmed by the highest spatial resolution
observations of the torus obtained by UVIS on 14 January 2001 (Steffl et al., 2004b)
26
(Chapter 3).
2.3.5
Temporal Variations
One of the greatest strengths of the UVIS dataset is that observations of the
Io torus in the EUV were made regularly over a period of six months by the same
instrument. This allows us to separate phenomena that are intrinsically time-variable
from those that vary with either local time (i.e., the dawn/dusk asymmetry) or System
III longitude.
2.3.5.1
EUV Radiated Power
Measurements of the torus luminosity provide important constraints on the energy
available to the torus. For typical conditions (i.e., the densities and temperatures found
by Bagenal (1994); Oliversen et al. (2001); Steffl et al. (2004b) observed in the Io
torus, the CHIANTI atomic physics database (Dere et al., 1997; Young et al., 2003)
predicts that roughly 60% of the total power radiated by the torus is emitted in the
wavelength region covered by the EUV channel of UVIS. The first measurements of the
torus EUV luminosity were made by the Voyager 1 UVS. Based on these measurements,
Shemansky (1980) estimated a total torus luminosity of 2.5–3.5 TW. The Voyager 2 UVS
measured a total luminosity approximately twice as large Shemansky (1987). After the
Voyager flybys in 1979, no further measurements of the EUV luminosity were made until
1993, when the EUVE spacecraft made its first observations of the Io torus. EUVE
covered a wavelength range of 370 Å to 735 Å, and the observed torus luminosity in
this wavelength range was ∼0.4 TW (Hall et al., 1994b). Subsequent observations of
the torus by EUVE measured the power output at 0.25–0.30 TW in 1994 (Hall et al.,
1994b), and 0.375 and 0.245 TW in 1996 and 1999, respectively (Herbert et al., 2001).
Hall et al. (1994b) estimated that 8–27% of the power emitted by the torus was observed
by EUVE, implying that the total luminosity during the EUVE observation period was
27
roughly 1–5 TW and consistent with measurements by Voyager.
The torus EUV luminosity, as observed by UVIS, is shown in Fig. 2.8. At the
beginning of the UVIS observation period, the total radiated power was approximately
2.0 TW. The long-term trend in the first half of the data is of decreasing power output with time, although there are several short-term events during which the radiated
power temporarily increases. The total torus EUV luminosity falls to 1.4 TW by midNovember 2000, a decrease of more than 25% in 35 days. The increase in the scatter of
the data points after 14 November 2000 is the result of the switch to the “mosaic” mode
of data collection, and the subsequent degradation of the quality of the data. Before
this date, however, the scatter in the observed luminosity is indicative of the intrinsic
short-term variations (sometimes referred to as “twinkling”) of the torus. Between consecutive 1000-second integrations, the torus EUV power output is observed to vary by
±6%. This variation is an order of magnitude greater than the statistical uncertainty
in the data.
The trend of decreasing luminosity with time continues until the beginning of the
observation gap. This gap, extending from 4 December 2000 to 27 January 2001, results
from the fact that during this period, the angular size of the torus, as seen from Cassini,
is greater than the angle subtended by the widest UVIS entrance slit, thus preventing
UVIS from observing the whole torus simultaneously. Observations of the torus were
made during this period; however, these observations were designed to take advantage of
the Cassini spacecraft’s relative proximity to Jupiter to obtain higher spatial resolution
images and are therefore not well-suited for determining the luminosity of the torus as
a whole.
2.3.5.2
EUV Luminosity Events
Superimposed on the long-term trends and the short-term “twinkling,” are several
events where the torus luminosity increases significantly on timescales of a few hours.
28
Torus EUV Luminosity (Terawatts)
Oct 1, 2000
2.2
Nov 1
Dec 1
Jan 1, 2001
Feb 1
Mar 1
2.0
1.8
1.6
1.4
1.2
270
300
330
360 1
Day of Year
30
60
Figure 2.8: Total torus EUV luminosity during the UVIS observation period. The vertical spread of the data points before 14 November 2000 is due to the intrinsic variability
of the torus. After this date, the spread is a combination of intrinsic variability and
uncertainty introduced by the “mosaic” mode of UVIS operation. The observation gap
in the middle of the plot is a result of angular size of the torus exceeding the UVIS
occultation slit field of view.
29
2.2
Torus EUV Luminosity (TW)
2.1
2.0
1.9
1.8
1.7
1.6
280
281
Day of Year 2000
282
283
Figure 2.9: Total torus EUV luminosity versus time for the Day 280 event. The total
torus luminosity increases sharply around DOY 280.6. The decay back to “normal”
torus levels is less rapid. The observed scatter in the data points greatly exceeds the
statistical noise in the data and is intrinsic to the torus (i.e. twinkling).
The most intense event occurred on 6 October 2000 (DOY 280). This event is shown in
Fig. 2.9.
During this event, the torus EUV luminosity increased from 1.8 to 2.2 TW in
just 5 hours—an increase of 22%. The torus luminosity continued to increase until the
end of the UVIS observation cycle. Since the observations ended before the luminosity
reached a clear maximum, it is possible that the increase was even greater. When
the UVIS observations resume, eleven hours later, the power output is observed to be
steadily returning to its original value of ∼1.8 TW. From start to finish, this event lasted
roughly 20 hours, or two jovian rotations. This event appears to have been immediately
preceded by a smaller luminosity event, whose peak intensity was also not observed.
At least five similar luminosity events were observed throughout the UVIS dataset,
30
although none are quite as dramatic as the event on 6 October 2000 (DOY 280).
One problem associated with interpreting these events is that the duty cycle of UVIS
observations—9 hours of data collection followed by a break of 11 hours—is comparable to the timescale of these brightening events. The best-sampled brightening event
occurred on 2 November 2000 (DOY 307). For this event, which is shown in Fig. 2.10,
the radiated power begins at an initial level of 1.62 TW. The morphology of this event
is as follows: a potential minor brightening and decay back to the initial levels lasting
∼10 hours followed by a larger brightening that peaked and was still decaying at the
end of the observation period. During the main event, the luminosity steadily increases
to peak value of 1.84 TW in 10.8 hours. After reaching this peak value, the radiated
power decays continuously for 4.4 hours, when the observation sequence ends. When
observations resume 12 hours later, the torus has returned to its pre-event level. It
appears that in all of these events, the decay back to the pre-event level of radiated
power occurs more slowly than the increase from the pre-event level to the peak value.
31
Torus EUV Luminosity (TW)
1.9
1.8
1.7
1.6
1.5
306
307
308
Day of Year 2000
309
310
Figure 2.10: Total torus EUV luminosity versus time for the Day 307 event.
32
1-Oct-2000 1-Nov-20001-Dec-2000 1-Jan-2001 1-Feb-20011-Mar-2001 1-Apr-2001
Radiated power (TW)
0.5
0.4
0.3
S III 680Å
0.2
O II 834Å
0.1
0.0
270
S IV 748Å
S II 765Å
300
330
3601
Day of Year
30
60
90
Figure 2.11: Total power radiated in four spectral features. The thick line is the power
emitted in the S IV 748Å feature. The data have been averaged over one Jovian rotation
period. Changes in the S II765Å to S IV 748Å ratio are evidence of compositional
changes in the Io torus.
Interestingly, four of the six torus events observed are preceded by a sudden
brightening of the jovian aurora roughly 10–20 hours prior to the onset of torus brightening (Pryor et al., 2001; Steffl et al., 2002). However, given the time sampling of UVIS
observations and the small number of observed events, it is difficult to make a definitive statement about the correlation of torus and auroral brightenings. As of yet, no
mechanism is obvious that could correlate the brightness of the Io torus and the jovian
aurora on such relatively short timescales.
2.3.5.3
Luminosity of Individual Spectral Features
The spectral resolution of UVIS enables us to determine the contribution to the
total emitted power from individual spectral features. Figure 2.11 shows the luminosity
of the brightest spectral feature for each of the four major ion species present in the
torus.
For clarity, the running 4-hour average of emitted power has been plotted, rather
33
than the instantaneous power. This has the effect of smoothing out the short-term
“twinkling,” while preserving the longer-term trends. The S III line at 680 Å is by
far the most energetic feature in the EUV spectrum of the torus. This single feature,
composed of some 16 individual spectral transitions, is responsible for fully 20% of the
total EUV radiated power.
Significant changes in the EUV spectrum of the torus are observed during the
Jupiter flyby. At the start of the UVIS observation period ∼0.10 TW of power are
radiated in the S II 765 Å line, while ∼0.06 TW are radiated in the S IV 748 Å line.
After a brief jump, associated with the brightening event of 6 October 2000, the intensity
of the S II line steadily decreases until it reaches a value of 0.04 TW around day 323
(18 November 2000), where it remains until the data gap. The S IV line, on the other
hand, begins near 0.06 TW—fainter than the S II line. However, whereas the intensity
of the S II line decreases with time, the intensity of the S IV line initially increases with
time, reaching a maximum value of 0.10 TW on day 323. After this point, it fades
gradually to a value of 0.07 TW at the beginning of the data gap. When the wholetorus observations resume after closest approach, the behavior of the S II and S IV lines
has settled down. The S II line intensity remains near 0.05 TW until shortly after day
60 of year 2001, after which it decreases to 0.04 TW. During this time, the S IV line
exhibits variations about 0.07 TW, but shows no similar decrease after day 60 of year
2001. These trends are confirmed in the intensities of other observed spectral features
resulting from S II and S IV emission. Spectra from the dusk half of the torus from the
beginning and end of the inbound staring phase are presented in Fig. 2.12.
The observed changes in the torus EUV spectrum strongly suggest that significant
compositional changes occurred during the UVIS observing period. For example, the
ratio of S II 765 Å to S IV 748 Å decreased by more than a factor of three from 1 October
2000 to 14 November 2000. Since spectral features primarily result from transitions to
the ground state and are close to each other in wavelength their ratio is relatively
Dusk emission rate (1027 photons s−1)
34
12
October 1
November 14
10
8
6
4
2
0
600
700
800
900
1000
Wavelength (Å)
1100
Figure 2.12: EUV spectra from the dusk ansa of the torus on 1 October 2000 and 14
November 2000. Since the effective spectral resolution is determined by the angular size
of the torus, the resolution decreases as Cassini approaches Jupiter. Note the dramatic
change in the S II 765Å to S IV 748Å ratio, indicative of compositional change in the
torus during this period.
insensitive to changes in the electron temperature in the torus, i.e., if the composition
of the torus remained constant, the electron temperature would have to increase by
more than two orders of magnitude to account for the factor of three decrease in the
brightness ratio. Such a temperature increase is clearly not physical, so the change in
the brightness ratio must be caused by changes in the S II and S IV ion densities in the
torus.
There are over 400 individual radiative transitions from the major ion species
present in the torus that lie in the wavelength region covered by the EUV channel of
UVIS, according to the CHIANTI atomic physics database. With the spectral resolution
of UVIS almost all of the observed spectral features are blends of several individual
radiative transitions. Therefore, it is necessary to develop a detailed model of the torus
35
emissions in order to extract the electron temperature and ion mixing ratios from the
UVIS data. Such a model, based on the CHIANTI atomic physics database has been
developed and is described in Steffl et al. (2004b) (Chapter 3). Applying this model to
the full UVIS dataset will be the focus of future work.
2.3.6
System III Variations
Nearly all temporally extended observations of the Io plasma torus have looked
for a correlation between torus brightness and System III longitude. Some of the most
dramatic System III variations were reported by Schneider and Trauger (1995), who
observed the intensity of the [S II] 6731 Å feature over six nights in 1992. They reported
that the longitudes λIII = 150◦ –210◦ were consistently 3–4 times as bright as longitudes
λIII = 0◦ –70◦ . Other observers have either not detected any consistent variation with
System III longitude or reported variations with lower amplitudes (Sandel and Broadfoot, 1982a; Morgan, 1985; Brown, 1995; Woodward et al., 1997; Herbert and Sandel ,
2000; Lichtenberg, 2001). Initial examination of the Cassini UVIS Io torus dataset yields
a small ( 5%) variation in the ansa brightness with System III longitude, over the 44
days of the UVIS inbound staring phase. This variation is shown in Fig 2.13.
To correct for the dawn/dusk brightness asymmetry and long-term variations in
torus luminosity, each individual measurement of the ansa luminosity has been divided
by the ansa luminosity averaged over a 9.925-hour period, centered on the measurement
time. In contrast to previously observed System III variations, the peak in ansa brightness occurs near λ=110◦ . It should be noted that the scatter in the data is considerably
larger than the amplitude of the variation, and therefore, the physical significance of
the variation is uncertain.
36
Relative Ansa EUV luminosity
1.4
1.3
Ansa Luminosity
10° Average
1.2
1.1
1.05
1.0
0.95
0.9
0.8
0.7
0.6
0
100
200
System III longitude
300
Figure 2.13: Relative EUV luminosity of the torus ansae versus System III longitude.
Both dawn and dusk ansae are included in this plot. The thick line is the average of all
data points in 10◦ longitude bins.
2.4
Conclusions
The broad spectral range and high spectral resolution of UVIS combined with
roughly six months of observations made during the Cassini Jupiter flyby resulted in a
rich and unique dataset of EUV emissions from the Io plasma torus. In this paper we
have presented initial results from the analysis of this dataset. Our main conclusions
are:
(1) The total power emitted by the torus in the EUV region of the spectrum (561 Å
–1182 Å) is highly variable. Variations of 5% were observed on timescales of
∼15 minutes, and long-term variations of 25% were observed on timescales of
∼40 days. Intermediate-length events, lasting roughly 20 hours from start to
finish, change the total torus EUV luminosity by ∼20%.
37
(2) The composition of the torus changes on timescales of a few tens of days. The
observed factor of 3 variation in the ratio of S II 765 Å /S IV 748 Å is too great
to be explained solely by a change in electron temperature.
(3) The dawn/dusk brightness asymmetry of the torus ansae is highly variable.
Observed values of the dusk ansa brightness divided by the dawn ansa brightness
range from 0.74–2.29, with a mean value of 1.32 and a standard deviation of
0.25.
(4) The profile of the brightness of the S III 680 Å feature versus distance from
Jupiter has a half-width at half-maximum, as measured radially outward from
the peak, of 1.3RJ . This width is comparable to that measured by Voyager
UVS and EUVE. We find no evidence for an extremely narrow ribbon feature,
such as that described by Dessler and Sandel (1993).
(5) The EUV power emitted by the torus ansae over a 44-day period was observed
to vary with System III longitude at the 5% level, with a peak occurring near
λIII =110◦ . However, given the large scatter in the data points, the physical
significance of this variation is uncertain.
The UVIS Io plasma torus dataset holds substantial scientific potential. Future
work will include modeling the EUV emissions to derive parameters such as electron
temperature and ion mixing ratios as a function of time, local time (i.e., dawn vs.
dusk), and System III longitude. These parameters will provide important constraints
for torus chemistry models, such as that presented by Delamere and Bagenal (2003),
used to determine the plasma conditions underlying the EUV emissions.
Chapter 3
Radial Variation in the Io Torus
On January 14, 2001, shortly after the Cassini spacecraft’s closest approach to
Jupiter, the Ultraviolet Imaging Spectrometer (UVIS) made a radial scan through the
midnight sector of Io plasma torus1 . The Io torus has not been previously observed
at this local time. The UVIS data consist of 2-D spectrally dispersed images of the Io
plasma torus in the wavelength range of 561 Å–1912 Å. We developed a spectral emissions model that incorporates the latest atomic physics data contained in the CHIANTI
database in order to derive the composition of the torus plasma as a function of radial
distance. Electron temperatures derived from the UVIS torus spectra are generally less
than those observed during the Voyager era. We find the torus ion composition derived
from the UVIS spectra to be significantly different from the composition during the
Voyager era. Notably, the torus contains substantially less oxygen, with a total oxygento-sulfur ion ratio of 0.9. The average ion charge state has increased to 1.7. We detect
S V in the Io torus at the 3σ level. S V has a mixing ratio of 0.5%. The spectral emission
model used can approximate the effects of a non-thermal distribution of electrons. The
ion composition derived using a κ distribution of electrons is identical to that derived
using a Maxwellian electron distribution; however, the κ distribution model requires a
higher electron column density to match the observed brightness of the spectra. The
derived value of the κ parameter decreases with radial distance and is consistent with
1
This chapter published as: Steffl, A. J., F. Bagenal, and A. I. F. Stewart, Cassini UVIS observations
of the Io plasma torus. II. Radial variations, Icarus, 172, 91–103, 2004.
39
the value of κ=2.4 at 8 RJ derived by the Ulysses URAP instrument (Meyer-Vernet
et al., 1995). The observed radial profile of electron column density is consistent with
a flux tube content, NL2 , that is proportional to r−2 .
3.1
Introduction
The Io plasma torus is a dense (∼2000 cm−3 ) ring of electrons and sulfur and
oxygen ions trapped in Jupiter’s strong magnetic field, produced by the ionization of ∼1
ton per second of neutral material from Io’s atmosphere. In situ measurements of the Io
plasma torus from the Voyager and Galileo spacecrafts and remote sensing observations
from the ground and from space-based UV telescopes have characterized the density,
temperature and composition of the plasma as well as the basic spatial structure (see
review by Thomas et al. (2004)). Extensive measurements of torus emissions made by
the Ultraviolet Imaging Spectrograph on the Cassini spacecraft as it flew past Jupiter
on its way to Saturn allow us to further examine the spatial and temporal structure of
the plasma torus.
On ionization, fresh ions tap the rotational energy of Jupiter (to which they are
coupled by the magnetic field). Much of the torus thermal energy is radiated as intense
(∼1012 W) EUV emissions. The ∼100 eV temperature of the torus ions indicates that
they have lost more than half of their initial pick-up energy. Electrons, on the other
hand, have very little energy at the time of ionization and gain thermal energy from
collisions with the ions (as well as through other plasma processes) while losing energy
via the EUV emissions that they excite. As a result, the torus electrons have an average
thermal energy of ∼5 eV, although in situ measurements indicate that the velocity
distribution of the torus electrons has a supra-thermal tail (Smith and Strobel, 1985;
Frank and Paterson, 2000b; Meyer-Vernet et al., 1995).
Analysis of torus emissions provides estimates of plasma density, composition and
temperature (Brown et al., 1983). Models of mass and energy flow through the torus
40
can then be used to derive plasma properties such as source strength, source composition, and radial transport timescale (Thomas et al., 2004; Delamere and Bagenal , 2003;
Lichtenberg et al., 2001; Schreier et al., 1998). Thus, one aims to relate observations
of spatial and temporal variations in torus emissions to the underlying sources, losses
and transport processes. Towards this ultimate goal, we present an analysis of observations of the Io torus made by the Cassini spacecraft’s Ultraviolet Imaging Spectrograph
(UVIS) on 14 January 2001, with emphasis on determining the radial structure. In
a companion paper (Steffl et al., 2004a) (Chapter 2), hereafter referred to as paper I,
we present examples of the EUV spectra of the torus and its temporal variability as
observed during the full 6-month encounter period. Analysis of the temporal structure
of the torus is presented in Delamere et al. (2004).
3.2
UVIS Data
UVIS consists of two independent, but co-aligned, spectrographs: one optimized
for the extreme ultraviolet (EUV), which covers a wavelength range of 561 Å–118 Å and
the other optimized for the far ultraviolet (FUV), which covers a wavelength range of
1140 Å–1913 Å(McClintock et al., 1993; Esposito et al., 1998; Esposito et al., 2004). Each
spectrograph is equipped with a 1024×64 pixel imaging microchannel plate detector.
UVIS pixels are rectangular, and subtend an angle of 1 mrad in the spatial dimension
(i.e., along the length of the slit) and 0.25 mrad long in the spectral dimension (i.e.,
along the dispersion direction). Images are obtained of UV-emitting targets with a
spectral resolution of ∼3 Å FWHM, roughly a factor of ten increase in resolution over
previous UV spectrographs sent to Jupiter. The spectral range and resolution of the
instrument and the extended observation period resulted in the creation of a unique
and rich dataset of the Io plasma torus in the extreme and far ultraviolet.
41
Table 3.1: Observational parameters
Date
14 JAN
14 JAN
14 JAN
14 JAN
14 JAN
14 JAN
] 14 JAN
14 JAN
14 JAN
14 JAN
14 JAN
14 JAN
2001
2001
2001
2001
2001
2001
2001
2001
2001
2001
2001
2001
Timea
16:31:04
17:04:24
17:37:44
18:02:44
18:19:24
18:36:04
18:52:44
19:09:24
19:26:04
19:42:44
19:59:24
20:16:04
Rb
8.84
8.51
8.14
7.85
7.66
7.46
7.25
7.03
6.82
6.60
6.38
6.16
λcIII
252
272
292
308
318
328
338
348
358
8
18
28
a
UTC on spacecraft at exposure midpoint.
b
Projected radial distance to center of UVIS entrance slit, in RJ .
c
System III longitude of torus ansa.
3.2.1
Observations
The data used in this analysis were obtained from a single observational sequence
that began at 12:04:25 UT 14 January 2001. This data represents only a small fraction
of the total observations of the Io plasma torus made by UVIS; a general summary of
the UVIS Jupiter encounter dataset can be found in paper I (Chapter 2). The data
consist of 39 spectrally-dispersed images of the Io torus, each with an integration time
of 1000 seconds. During the observation period, Io moved from near western elongation
to 0.4 RJ (jovian radii, 1 RJ =71,492 km) east of the planet, as seen from Cassini. By
maintaining a constant angular offset of 21.1 mrad from Io, the center of the UVIS field
of view was scanned radially inwards from 10.4 to 4.3 RJ . A listing of observational
parameters for the data analyzed in this paper is provided in Table 3.1.
Cassini’s closest approach to Jupiter occurred on 30 December 2000, so the spacecraft was well within the dusk sector when it made these observations. The local time of
the observed torus ansa was approximately 01:50, i.e., nearly two hours past midnight.
This region of local time cannot be seen from earth and was not well observed by either
42
of the Voyager spacecraft.
In contrast to the vast majority of the UVIS observations of the Io torus, the data
used in this paper were obtained with the long axis of the UVIS entrance slits oriented
approximately perpendicular to Jupiter’s rotational equator. The low-resolution slit
was used for both channels. This slit has an angular width, as seen from the detector,
of 2 mrad for the EUV channel and 1.5 mrad for the FUV channel. At the time, Cassini
was 244 RJ from Jupiter, resulting in a field of view 0.48 RJ wide for the EUV channel
and 0.36 RJ wide for the FUV channel.
In addition to the difference in slit width, there is a small pointing offset between
the EUV and FUV channels such that, in this configuration, the fields of view of the
two channels do not overlap. The sense of this offset is such that the FUV channel
views a section of the torus at a greater radial distance from Jupiter than that viewed
by the EUV channel. Fortuitously, the field of view of the FUV channel at a given time
lies completely within the field of view of the EUV channel one integration time earlier.
Therefore, we have excluded from our analysis the first image from the FUV channel
and used the second FUV image in conjunction with the first EUV channel image.
Likewise, the third FUV image is used in conjunction with the second EUV image, and
so on for the rest of the dataset. Since the two channels view the same radial distance
1000 seconds apart, systematic errors will be introduced if there are strong longitudinal
or temporal variations in torus properties. However, since the integration period less
than 3% of Jupiter’s rotation period, these systematic effects should be relatively minor.
The projection of the UVIS EUV slit field-of-view and the positions of Io and Europa
relative to Jupiter are shown in Fig. 3.1.
3.2.2
Data Reduction
The data were reduced and calibrated using techniques similar to those described
in greater detail in paper I (Chapter 2). To summarize this procedure: the background is
43
Initial Slit Position
Europa Initial
+
+
Io Initial
+ Europa Final
Jupiter
Io Final
(behind Jupiter)
Final Slit Position
Figure 3.1: Observing geometry for the UVIS observation of the Io torus on 14-January2000. The initial and final positions of the projected field of view of the UVIS EUV
channel entrance slit, Io, and Europa are shown. Jovian north is up. The local solar
time of the spacecraft is 19:40. The Cassini spacecraft is south of the Jovian equator,
so the far side of the obits appear below the near side.
subtracted from the raw data, a flat-field correction is applied, and the data are divided
by the effective area curve of the instrument to convert it from counts to physical units.
Figure 3.2 shows a calibrated, background-subtracted sample of the data.
To increase signal-to-noise in the data, each 2-D spectral image was averaged over
the latitudinal extent of the Io torus (i.e., in the vertical direction on the detector) to
create a 1-D spectrum. This was accomplished by first summing along the rows of the
detector (the spectral direction) to create a latitudinal emission profile. A Gaussian plus
quadratic background was fit to the latitudinal emission profile and all rows lying within
2σ of the centroid of the Gaussian fit were averaged together to create the final spectrum.
This corresponds to those rows lying within 1.2 RJ of the centrifugal equator. Spectra
created in this fashion were averaged together to produce the spectrum in Fig. 3.3.
1
1200
600
1300
700
900
1400 1500 1600
Wavelength (Å)
800
10
1700
1000
1800
1100
100
1900
200
Figure 3.2: Spectral image of the Io torus at 6.5 RJ . The EUV channel appears above the FUV channel. For the observations presented
in this paper, the long axis of the slit was oriented roughly perpendicular to Jupiter’s equator. North is up and Jupiter is to the left.
The data have been background-subtracted, flatfielded, and calibrated to physical units (Rayleighs). The region from 1210Å–1230Å in
the FUV channel is dominated by Lyman-α from the interplanetary medium. The spatial scale is 0.24 RJ /pixel in the vertical (spatial)
direction and 0.06 RJ /pixel in the horizontal (spectral) direction.
4
2
0
−2
−4
4
2
0
−2
−4
Distance from Equator (RJ)
Rayleighs/Ångstrom
44
Rayleighs/Å
−20
0
20
40
60
−20
0
600
_ S III 702Å
1200
800
900
_ S III 901Å
_
S II 906Å
_ S II 875Å
1400
1500
1600
Wavelength (Å)
_ S III 729Å
_ S IV 748Å
_ S II 765Å
1300
− H I 1216Å
700
_ S II 938Å
1000
1700
1800
1100
1900
Figure 3.3: Composite spectrum of the Io plasma torus from 561Å-1913Å. 1-D spectra of the Io torus were created by averaging the rows
of the 2-D spectral images lying within 1.2 RJ of the latitudinal center of the torus. The composite spectrum was created by averaging
together 17 individual 1-D spectra of the torus covering a radial range of 4 RJ –8 RJ . The spectral features are labeled and color-coded by
the ion species that makes the dominant contribution to the feature. Locations (as contained in the CHIANTI database) of the individual
spectral lines of the five major ion species in the torus are plotted beneath the spectrum.
Rayleighs/Å
20
_ S II 1253Å
_
S II 1260Å
40
_ S II 1167Å
_ S III 1191Å
_
S III 1201Å
_ S II 642Å
_ S IV 657Å
S III 680Å
_ O III 1661Å
_
O III 1666Å
_S V 786Å & S III 789Å
_
_ S III 797Å
_ S IV 809Å
_ S III 822Å
_ O II 833Å
& O III 834Å
_ S IV 1405Å
_ _ S IV 1417Å
S IV 1424Å
_ S II 995Å
_ S II 1006Å
_
_ S III 1012Å
S III 1021Å
_ S II 1047Å
_ S IV 1063Å
_
_ S IV 1073Å
S III 1077Å
__ S IV 1099Å
S II 1102Å
_ S III 1126Å
_ S III 1713Å
_ S III 1729Å
60
45
46
This spectrum, which contains data from both EUV and FUV channels, covers
a wavelength range of 561 Å–1912 Å. It is the average of 17 individual 1000-s images
covering a range of projected radial distances from 4 RJ –8 RJ . The major spectral
features are labeled by approximate wavelength and the ion species responsible for the
majority of the emission in each feature. Below the spectrum are plotted the wavelengths
of the radiative transitions produced by the five major ion species of the Io torus: O II,
S III, S II, S IV, and O III, as contained in the CHIANTI atomic physics database,
version 4.2 (Dere et al., 1997; Young et al., 2003). The wavelength region covered
by UVIS contains over 500 individual radiative transitions from these five ion species.
The high density of emission lines, coupled with the ∼3 Å spectral resolution of UVIS,
means that with only three exceptions—the S IV line at 1063 Å and the S III multiplet
at 1713 Å and 1729 Å—all the features observed in the UVIS spectra are blends of the
multiplet structure within a particular ion species, blends of radiative transitions from
two or more different ion species, or some combination thereof. This spectral complexity
necessitates a detailed, multispecies model to properly interpret the data.
3.3
Torus Spectral Emissions Model
In order to model the torus spectra, we developed a homogeneous, 0-D “cubic
centimeter” spectral emission model. Such a model calculates the volume emission rate
for a given spectral line, i.e., the number of photons at a specific wavelength produced
by a single cubic centimeter of plasma in one second, and integrates this over the line
of sight to produce a synthetic spectrum. The technique is similar to that used by
(Shemansky, 1980; Shemansky and Smith, 1981). The brightness, B of a given spectral
line is given by:
Z
−6
B = 10
Aji fj (Te , ne )nion dl
Rayleighs
(3.1)
47
where Aji is the Einstein coefficient for spontaneous emission, fj is the fraction of ions
in state j, Te is the electron temperature, ne is the electron number density, nion is the
number density of the ion species responsible for the emission, and the integral is over
the line of sight. The level populations, fj , are determined by solving the level balance
equations for each ion species in matrix form:
Cf = b
(3.2)
where f is a vector containing the fraction of ions in a particular energy state, relative
to the ground state; b is a vector whose elements are all zero except for the first element,
which is equal to one; and C is a matrix containing the rates for collisional excitation
and deexcitation and radiative deexcitation. The elements of this matrix are given by:
C[i, j] = Aij + ne qij
(3.3)
where Aij is the Einstein coefficient for spontaneous emission if state i is at a higher
energy than state j and zero otherwise. qij is the rate coefficient for collisional excitation
(or deexcitation) from state i to state j and is given by:
Z
qij =
0
∞
ĝe vσij dv
(3.4)
ĝe is the normalized distribution function, v is the electron velocity, and σij is the crosssection for the transition from state i to state j. Once Eq. 3.2 has been solved, the level
populations vector, f , is renormalized so that the sum of its elements is equal to one.
3.3.1
Thermal and Non-Thermal Electron Distributions
If the electrons are distributed according to Maxwell-Boltzmann statistics:
4
ĝe (v) = √
π
µ
me
2kTe
¶3/2
µ
2
v exp
−me v 2
2kTe
¶
(3.5)
48
where me is the mass of an electron and k is the Boltzmann constant. With this equation
for the electron distribution function, Eq. 3.4 reduces to:
µ
¶r
µ
¶
√
Eij
2 πa0 h
1
I∞
qij =
Υij exp
me
we wi
kTe
kTe
where
√
2 πa0 h
−8
me =2.1716×10
(3.6)
cm3 s−1 ; wi is the statistical weight of state i; I∞ =13.6086 eV;
and Eij is the transition energy between states i and j. Υij is the thermally-averaged
collision strength, as defined by Seaton (1953) and is given by:
Z
Υij =
µ
∞
0
Ωij exp
−Ej
kTe
¶ µ
¶
Ej
d
kTe
(3.7)
where Ej is the electron energy after the collision and Ωij is the collision strength, which
is related to the collision cross-section, σij , by:
σij =
πh2 Ωij
m2e v 2 wi
(3.8)
In the basic form of our spectral emissions model, the electron distribution is
Maxwellian and therefore defined by a single parameter, Te . However, in situ measurements of the electron distribution in the Io plasma torus made by the Voyager
and Galileo spacecrafts suggest that the electron distribution function in the Io torus
may actually be non-thermal or at least have a non-thermal, high-energy tail (Sittler
and Strobel , 1987; Frank and Paterson, 2000b)). Rather than examining the changes
in the torus spectrum due to an arbitrary, non-thermal electron distribution, we have
focused our efforts on modeling the effects of a κ electron distribution function (Vasyliunas, 1968). κ distributions have been invoked to explain discrepancies between spectra
from the Voyager Ultraviolet Spectrometer (UVS) and model spectra based on emission
rates generated by the Collisional and Radiative Equilibrium code (COREQ) (Taylor
et al., 1995; Taylor , 1996), differences in the in situ plasma measurements made by the
Voyager and Ulysses spacecrafts (Meyer-Vernet et al., 1995; Moncuquet et al., 2002),
49
latitudinal changes in torus ion temperature in ground-based observations of the torus
(Thomas and Lichtenberg, 1997),and features of Io’s ultraviolet limb-glow (Retherford
et al., 2003). A review of κ distributions and their effect on astrophysical plasmas is
given by Meyer-Vernet (2001).
A κ distribution, defined by the equation:
4
ĝe (v) = √
π
µ
me
2κkTe
¶3/2 Ã
Γ(κ + 1)
¡
¢
Γ κ − 12
!
¶−(κ+1)
µ
mv 2
v 1+
2κkTe
2
(3.9)
is quasi-Maxwellian at low temperatures but falls off as a power law at high temperatures. From a computational perspective, a κ distribution has an additional advantage
over other types of non-thermal distributions in that it is fully defined by only two
parameters: the characteristic temperature of the distribution, Tc , and the parameter,
κ. The characteristic temperature, Tc , of a κ distribution is related to the energy at the
peak of the distribution function. Unlike a Maxwellian distribution, the characteristic
temperature in a κ distribution is not the same as the effective temperature, Te , which
is related to the mean energy per particle of the distribution. Instead, Tc and Te are
related by the equation:
Ã
Te = Tc
κ
κ−
!
3
2
(3.10)
As can be seen from Eq. 3.10, the κ-parameter determines the degree to which the
distribution is non-Maxwellian. The larger the value of κ, the closer the distribution is
to a Maxwellian, and in the limit of κ=∞, the distribution is equivalent to a Maxwellian.
The atomic data required for these calculations (wavelengths, energy levels, A coefficients, thermally-averaged collision strengths, etc.) are obtained from the CHIANTI
database (Dere et al., 1997; Young et al., 2003). CHIANTI consists of a set of critically
evaluated atomic data together with a set of routines written in the Interactive Data
Language (IDL) to calculate emission spectra from astrophysical plasmas. The database
50
is a compilation of both experimental and theoretical values and is periodically updated.
Version 4.2 of CHIANTI was used for all modeling in this paper. The CHIANTI database implicitly assumes a Maxwellian distribution and contains only thermally-averaged
collision strengths, Υij , stored according to the method of Burgess and Tully (1992).
The cross-sections, σij , are required to evaluate Eq. 3.4 if the distribution function, ĝe ,
is non-Maxwellian. When using a κ distribution, we must therefore approximate the
integral in Eq. 3.4 as the linear combination of five thermally-averaged rate coefficients,
qij :
0
qij
=
5
X
wk qij (Tk )
(3.11)
k=1
where qij (Tk ) is the rate coefficient, given by Eq. 3.6 with Te =Tk and wk is the relative
weighting of the rate coefficient. The weights, wk , are determined by logarithmically
fitting the linear combination of five Maxwellians to a κ distribution over the energy
range of 0.01–500 eV. The resulting fit is within 10% of the value of the κ distribution
over the entire energy range. It is worth reiterating that when we fit the spectra, we
solve only for two parameters, Tc and κ, that fully describe the κ distribution; the wk ’s
and Tk ’s in Eq. 3.11 are completely determined by the values of Tc and κ.
The decision to use the CHIANTI database over other means of determining radiative emission rates, namely the Collisional and Radiative Equilibrium (COREQ) code
that is an extension of the work of Shemansky and Smith (1981), was made based on the
public availability, documentation, periodic updating, and ease of use of the CHIANTI
database. For most spectral features in the UVIS wavelength range, the differences
between models using CHIANTI and models using COREQ are at the 10% level, with
COREQ generally predicting more emission than CHIANTI (D.E. Shemansky, personal
communication). However, for several spectral features (e.g., S III 1021 Å, S IV 1063 Å),
and S II 1260 Å) there exist large (factors of several) differences between the emissions
51
predicted by the two databases. One notable weakness of the CHIANTI database—at
least as it exists in version 4.2—is that it does not include radiative transitions from
singly ionized sulfur (S II) at wavelengths less than 765 Å. As a result, the S II features
at 642 Å and 700 Å are absent from our model.
3.3.2
Line of Sight Assumptions
Evaluating the integral in Eq. 3.1 requires knowledge of how Te , nion , and ne
vary over the line of sight. Since these are the very quantities we are trying to derive
from the spectra, certain assumptions must be made. As indicated by Eq. 3.1, the
level populations of the ions, fj , are a function of the electron density. In theory, this
dependence can be used as a diagnostic of the local torus electron density (Feldman
et al., 2001; Feldman et al., 2004) In practice, however, the spectral resolution of UVIS
is insufficient to resolve the density-sensitive multiplet structure present in the torus
spectra, and therefore, the torus spectra observed by UVIS are effectively independent
of the local electron density.
We have chosen to use a relatively simple treatment of projection effects. We make
the assumption that the electron distribution function of the torus, be it Maxwellian
or κ, is uniform over the line of sight. This assumption should not significantly affect
our results for two reasons. First, the observed brightness of the torus falls off sharply
with radial distance outside of 6 RJ (Brown, 1994a; Steffl et al., 2004a) (Chapter 2).
Second, because we are observing the torus at its ansa, the pathlength of the line of
sight through regions of the torus lying exterior to the region of interest is minimized.
The combination of lower brightness and smaller pathlengths mean that the spectral
contributions from regions of the torus lying exterior to the region we are interested in
will be relatively small. Inside of 6 RJ , however, the local electron temperature is too
low to excite much emission in the EUV/FUV. In this region, line of sight projection
effects become much more important as the majority of observed EUV/FUV photons
52
are actually emitted from regions of the torus lying at greater radial distances than the
ansa, and the validity of our assumption breaks down. Therefore, we have limited our
analysis to those regions lying outside of 6 RJ .
With the assumption of a uniform electron distribution over the line of sight,
Eq. 3.1 reduces to:
B = 10−6 Aji fj (Te )Nion
Rayleighs
(3.12)
R
where Nion = ni on dl is the ion column density. The ion column densities, Ni , needed to
match the observed torus brightness depend on the level populations of the ion species,
fj , which, in turn, depend on the shape of the electron distribution function.
The plasma composition of our model is specified by six parameters, one for the
column density of each of six ion species: S II, S III, S IV, S V, O II, and O III. For
computational reasons, as well as to reduce correlations between parameters, we have
found it advantageous to use five parameters for the ion column densities relative to
the column density of S III (NS III /NS III , NS II /NS III , NS V /NS III , NO II /NS III ,
NO III /NS III ) and a sixth parameter for the electron column density, Ne . The column
density of S III is then derived from the charge neutrality condition:
X
qion Nion = Ne
(3.13)
ions
where qi on is the charge on each ion. Protons are included in the calculation of charge
neutrality at the 0.1 Ne level (Bagenal , 1994). In addition to the six parameters for
the plasma composition, the model requires one parameter (Te ) to specify the electron
distribution if we are using a thermal distribution, or two parameters (Tc and κ) for a
κ distribution.
With these parameters and the above equations we produce model spectra and
fit them to the data by minimizing the χ2 statistic using a combination of Levenberg-
53
Marquardt least squares and downhill simplex (amoeba) algorithms (Moré, 1977; Nelder
and Mead , 1965; Press et al., 1992). This combined approach was necessary because
the Levenberg-Marquardt method, while computationally efficient, tended to get stuck
in small, local χ2 minima of the seven-dimensional parameter space. The downhill
simplex method was more successful at finding the global minimum value for χ2 , at
the expense of greatly increased computation time. Therefore, we began the fitting
procedure using the Levenberg-Marquardt algorithm. Once the algorithm had settled
in to a local minimum in parameter space we used the fit parameters to specify one
point in the initial input simplex. The remaining points of the simplex consisted of the
Levenberg-Marquardt algorithm fit parameters plus a random deviation. With these
inputs, the downhill simplex algorithm was generally able to climb out of local minima
in parameter space and find a lower overall value of the χ2 statistic.
3.4
Results
A typical fit of the spectral model to an individual UVIS spectrum of the Io torus
can be seen in Fig. 3.4. This spectrum of the ansa at 6.3 RJ is typical of the quality
of the data and quality of the model fit There is generally good agreement between the
model and the data. However, the S IV 657 Å, S III 702 Å, S II 910 Å, and S III 1729 Å
features are consistently underfit by the model. The discrepancies between the spectral
emissions model and the UVIS spectra are likely caused, at least in part, by inaccuracies
in the atomic data contained in the CHIANTI database. Herbert et al. (2001) report
similar discrepancies in their analysis of EUVE spectra of the Io plasma torus.
Preliminary work on the in-flight calibration of the EUV channel of UVIS suggests
that the true instrumental effective area below 740 Å may be greater than what was
measured in the laboratory by as much as a factor of two (D.E. Shemansky and W.E.
McClintock, personal communication). If the true instrumental effective area below
740 Å has been underestimated then the brightness of the spectral features in this
Rayleighs/Ångstrom
54
70
60
50
40
30
20
10
0
UVIS Spectrum
Model Fit
700
800
900
1000
1100
70
60
50
40
30
20
10
0
1200
1300
1400 1500 1600
Wavelength (Å)
1700
Figure 3.4: Sample fit of the model to a UVIS spectrum of the Io torus at 6.3 RJ . The
model generally fits well to the spectrum with the exception of the three features at
657Å, 702Å, and 729Å, which are consistently underfit. The region from 1210Å-1230Åis
dominated by Lyman-α emission from the interplanetary medium and has been set to
zero.
55
region has been overestimated, which would bring the features at 657 Å and 702 Å
into better agreement with the model. However, given the relatively good fit of the
S III features at 680Å and 729 Å, the shape of the instrumental effective area curve
(see Figure 2.3 on page 16) would have to change dramatically to fully reconcile the
differences between model and spectra at 657 Å and 702 Å while preserving the quality
of the fit elsewhere. It therefore seems most likely that these discrepancies are primarily
caused by inaccuracies in the atomic physics data.
3.4.1
Electron Temperature and Densities
The electron temperature, Te , and column density, Ne , derived from the Cassini
UVIS torus spectra are shown in Fig. 3.5.
For comparison to the Voyager era, we also plot these quantities as obtained by
the model of Bagenal (1994), hereafter referred to as B94, which is based on an analysis
of Voyager 1 Plasma Science (PLS) data coupled with the ion composition derived
from analysis of the Voyager 1 UVS spectra by D.E. Shemansky. Independent analysis
of Voyager 1 UVS spectra of the torus was conducted by Herbert and Sandel (2000),
which is hereafter referred to as HS00. The electron temperatures derived from the UVIS
spectra are somewhat lower than those from the models of B94 and HS00. Although
it is not plotted, HS00 generally has a slightly higher electron temperature than B94.
The sharp increase in electron temperature between 7.4 RJ and 8.5 RJ present in the
B94 model is not seen in the UVIS spectra, nor was it seen by HS00. Our results
support the claim made by HS00 that this sudden increase in electron temperature is
not representative of “typical” conditions in the Io torus. Curiously, the UVIS electron
temperature profile reaches a minimum value of 4.43 eV at 6.6 RJ . A similar dip is seen
in the electron temperature profile of HS00, but not in B94.
The derived electron column density, Ne , is plotted in the lower panel of Fig. 3.5.
The column density falls off monotonically with increasing radial distance from a max-
Ne (cm−2)
Te (eV)
56
10
1014
1013
6.0 6.5 7.0 7.5 8.0 8.5 9.0
Radial Distance (RJ)
Figure 3.5: Best-fit electron parameters as a function of radial distance. The electrons
distribution is assumed to be a single Maxwellian. The solid lines are the UVIS results,
while the dotted lines are the parameters from the Voyager-based model of Bagenal
(1994). The error bars are the formal 1-σ errors obtained from the fitting algorithm.
The electron column density is derived from the ion column densities using the chargeneutrality condition.
imum value of just under 1014 electrons cm−2 to 5 × 1012 electrons cm−2 near 9 RJ .
Inside of 7.5 RJ , the UVIS values generally lie within one error bar of the values derived
from B94. Outside of 7.7 RJ the column density falls off more rapidly with distance
than the B94 model.
Although the electron column density is the quantity that is actually measured
by remote sensing instruments, often we would like to know the local electron number
density. In order to extract this information from the integrated column density, we
must make additional assumptions about how the torus plasma is distributed along
the line of sight. The first additional assumption we make is that the relative plasma
composition is uniform over the line of sight (previously we had assumed only that the
Local Electron Density (cm-3)
Voyager 1
1000
2200(r/6)
1013
-5.4
400(r/8)
100
6.
-1 2
1012
9.
7.
8.
Distance From Jupiter (RJ)
57
Electron Column Density (cm-2)
1014
10000
Figure 3.6: The derived electron column density (points with error bars) plotted versus
radial distance. To match the observed electron column density profile, we have fit the
local electron density profile as two power laws joined at 7.8 RJ (solid line). The Voyager
1 electron density profile of Bagenal (1994) (dotted line) is shown for comparison. The
local density profile integrated over the sight (dot-dash line) closely matches the observed
electron column density profile.
electron distribution function was uniform over the line of sight). We then assume that
the local electron density as a function of radial distance is reasonably well described
as a power law:
ne (r) =


¡ ¢


α r −β1
6
6

¡ ¢−β2


α8 8r
if r ≤ r0 ;
if r >
(3.14)
r0
where r is the radial distance, measured in RJ . We then varied the parameters α6 ,
β1 , α8 , β2 , and r0 to fit the integral of ne (r) over the line of sight to the derived values
of the electron column density, subject to the constraint that ne (r) be continuous at
r = r0 . The resulting fit to the integrated column density is show in Figure 3.6.
Also shown are the function ne (r) and the electron density profile of B94. Al-
58
though the value of the curve itself is slightly less than the B94 value, between 6 RJ
and 7.4 RJ , the slope of the electron density curve derived from the UVIS spectra is
almost identical to the slope of the B94 model. The UVIS electron density is less than
the electron density derived by HS00 and a factor of ∼2 less than the electron density
derived by the Galileo Plasma Wave Subsystem during the J0 flyby (Kurth et al., 1996).
We derive the number of electrons per shell of magnetic flux using the equation:
Z
N L2 = 4πRJ3 L4
≈ 2π
3/2
θmax
0
RJ3 ne (θ
ne (θ) cos7 (θ)dθ
= 0)HL3
(3.15)
where L is the radial distance of a magnetic field line at the magnetic equator, θ is the
magnetic latitude, ne (θ = 0) is given by Eq. 3.14, and H is the scale height given by:
v
³
´
u
u 2k T̄ion 1 + Z̄ion Te
t
T̄ion
H =
3mΩ2J
v³
´
u
u 1 + Z̄ion Te
t
T̄ion
= 0.64
RJ
Aion
(3.16)
where T̄ion is the average ion temperature, Z̄ion is the average charge per ion, and Āion
is the average ion mass number. The average ion temperature, T̄ion , cannot be directly
determined from our analysis of the UVIS spectra so we use the values from B94 (60
eV from 6.0 RJ –7.5 RJ , and increasing roughly linearly from 7.5 RJ to a value of 228
p
eV at 9.0 RJ ). Since the scale height, H, varies as T̄ion , this assumption should not
significantly affect our calculation of flux tube content. The derived values for N L2 as
a function of radial distance are fit well by a single power law:
N L2 (r) = 2.0 × 1036
³ r ´−2.1
6
(3.17)
The index of the power law for the UVIS-derived value of flux tube content, 2.1±0.4, is
59
statistically identical to the value derived by B94, and significantly less than the value
of 3.5 derived by Herbert and Sandel (1995). An index of 2 is consistent with flux tube
interchange as the mechanism for radial transport of plasma (see review by Thomas
et al. (2004) and references therein). There is some evidence to suggest that the index
of the power law fit to the UVIS-derived flux tube content, NL2 , is greater than two
outside of 7.5 RJ . However, this finding is only marginally statistically significant.
3.4.2
Ion Mixing Ratios
The torus composition derived from the UVIS spectra obtained from the 14 January 2001 radial scan is plotted in Figure 3.7.
We have plotted the derived composition information as ion mixing ratios, (i.e.,
ion densities divided by the electron density). For comparison to the Voyager era, we
have also plotted the mixing ratios from B94. The UVIS-derived composition is significantly different than the Voyager values, implying a fundamental change in torus
composition between the two epochs. This is hardly surprising, given that substantial
compositional changes were observed during the six months of the Cassini Jupiter flyby
(Steffl et al., 2004a) (Chapter 2). It is important, then, to remember that the compositional information presented in this paper comes from observations made during single
day, 14 January 2001.
The torus observed by UVIS contains substantially less oxygen than the torus of
the Voyager epoch. The total O/S ion ratio,
2
P
i=1
3
P
Oi+
S i+
i=1
averaged between 6 RJ and 8 RJ , is 0.9, compared to 1.6 in B94. The sharp decrease
in the amount of oxygen in the torus relative to the Voyager 1 conditions supports the
findings of ground-based optical observations of the Io torus (Morgan, 1985; Thomas
60
S++
0.10
0.10
+++
4+
NS IV/Ne
S
0.01
0.100
S
0.10
0.010
0.01
1.00
0.001
1.00
O+
O++
0.10
0.01
6.0
0.10
6.5
7.0
7.5
8.0
8.5
6.0
6.5
7.0
7.5
8.0
8.5
NS V/Ne
0.01
1.00
NO II/Ne
1.00
NS III/Ne
S+
NO III/Ne
NS II/Ne
1.00
0.01
9.0
Radial Distance (RJ)
Figure 3.7: Model derived mixing ratios as a function of radial distance. The solid lines
are the UVIS results, while the dotted lines are the parameters from the Voyager-based
model of Bagenal (1994). The error bars are the formal 1-σ errors obtained from the
fitting algorithm.
61
et al., 2001) and is opposite to the higher oxygen levels found by Galileo PLS on the
J0 flyby (Crary et al., 1998) and EUVE (Herbert et al., 2001). The UVIS composition
shows a trend toward higher ionization states: the mixing ratios of S II and O II derived
from the UVIS spectra are both lower than the B94 values, while the mixing ratios of
S III, S IV, and O III are generally higher. This results in an increase in the average
charge per torus ion, hZi i, to 1.7 compared with a value of 1.4 in the B94 model.
Determination of the relative ion abundance of O II and O III from EUV spectra
has been historically difficult (Brown et al., 1983). This is due primarily to the paucity
of bright emission lines from these ions in the EUV/FUV region of the spectrum. In
marked contrast to the sulfur ion species present in the torus, O III has just three
relatively bright spectral features in the wavelength range covered by UVIS: the brightest
centered at 834 Å and the other two at 703 and 1666 Å. Singly ionized oxygen has but
one bright spectral feature, located at 833 Å. Initial analysis of the Voyager UVS spectra
focused on determining the abundance of O III by fitting to the multiplet at 703 Å. The
O II abundance was then derived by determining the extra emission required to fit
the feature at 833 Å. Unfortunately, the O III multiplet at 703 Å is heavily blended
with significantly brighter emissions from S III centered on 702 Å. Thus, this approach
requires knowledge of the amount of S III along the line of sight and accurate atomic
data for O II, O III, and S III. These difficulties led to the initial analyses of Voyager
UVS spectra concluding that the ratio of O II to O III in the Io torus was less than 1
(Shemansky, 1980; Shemansky and Smith, 1981; Broadfoot et al., 1981). Since that time,
numerous additional analyses of torus observations at UV and optical wavelengths have
confirmed that O II is actually the dominant ionization state of oxygen, with O III being
a relatively minor constituent (Brown et al., 1983; Smith and Strobel, 1985; Shemansky,
1987; McGrath et al., 1993; Thomas, 1993a; Hall et al., 1994b; Herbert et al., 2001).
If we consider only the EUV channel of UVIS, the spectral emissions model concludes that O III is the dominant ionization state of oxygen in the Io torus. This
62
unphysical result occurs because the model maximizes the amount of O III in order to
minimize the model/spectrum discrepancy at 702 Å (see Figure 3.4 on page 54). With
the inclusion of the FUV channel, there are two additional O III spectral lines located at
1661 and 1666 Å. These lines, first detected in the Io torus by Moos et al. (1991), place
a strong constraint on the amount of O III present in the torus. Unfortunately, they
are relatively faint and barely above the level of noise in the UVIS spectra. Therefore,
the values we derive for the mixing ratio of O III (O II) as a function of radial distance
should more properly be thought of as an upper (lower) limit on the actual value. With
this caveat in mind, there is still significantly more O III and less O II compared to the
Voyager model of B94. The [O II] / [O III] ratio, averaged over 6.2–8.8 RJ , is 3.7—less
than half the corresponding value of 8.8 from B94. The value of this ratio generally
decreases with increasing radial distance, which is consistent with the observed increase
in electron temperature. The upper limit on the amount of O III seen in the UVIS
spectra is still significantly less than the lower limit reported by Crary et al. (1998),
during the Galileo spacecraft’s flythrough of the Io torus in 1995.
In the EUV/FUV region of the spectrum, the brightest emission feature (by
over two orders of magnitude) due to S V, occurs at 786 Å. Since the 786 Å S V
feature lies between several nearby spectral features from S II and S III it has proven
difficult to detect. The initial analysis of Voyager UVS spectra of the Io torus placed
an upper limit of 11 cm−3 on the mean ion number density of S V (Shemansky and
Smith, 1981). The factor-of-ten increase in spectral resolution of the Cassini UVIS over
the Voyager UVS us to make what we believe to be the first spectroscopic detection
of S V in the Io torus. Near 6 RJ , where the signal-to-noise ratio is highest, S V is
detected at the 3-σ level. S V is a trace component of the torus, present at a mixing
ratio of 0.003 at 6 RJ and rising to maximum of 0.01 at 8.5 RJ . Another instrument
aboard the Cassini spacecraft, the Charge-Energy-Mass Spectrometer (CHEMS) of the
Magnetospheric Imaging Instrument (MIMI), detected S V ions on 10 January 2001 and
63
23 January 2001—periods when the spacecraft was within the magnetosphere of Jupiter
(Hamilton et al., 2001; Krimigis et al., 2001). While the MIMI result does not directly
confirm the detection of S V ions in the Io torus, it does confirm that S V is present
within the jovian magnetosphere.
3.4.3
Uncertainties in Derived Model Parameters
The error bars presented in Figure 3.5 (page 56) and Figure 3.7 (page 60) represent
the formal 1-σ error bars of the least-squares fit, i.e., they are the square roots of the
diagonal elements of the covariance matrix. This method of estimating errors implicitly
assumes that the model parameters are independent of each other. However, many of
the model parameters are correlated (or anticorrelated), e.g., electron column density
and electron temperature. In order to assess the effect of parameter correlations on
the actual uncertainty in the model parameters, a series of two-dimensional confidence
intervals was generated following the method of (Press et al., 1992). Four of these
confidence intervals for the spectrum at 6.2 RJ can be found in Fig. 3.8.
The cross in the center of the ∆χ2 ? contours represents the size of the formal
error bar. The top two panels, NS IV /NS III vs NS II /NS III and Ne vs NS IV /NS III ,
provide examples of parameters that are minimally correlated, while the bottom two
panels show pairs of parameters that are strongly anticorrelated. The 1-D confidence
interval for a single parameter is defined by the projection of the contour of desired
probability onto that parameter’s axis. For example, the probability that the “true”
value of NO III /NS III lies in the interval 0.065–0.255 is 68%. The formal error bars
almost always underestimate the full extent of the parameter confidence intervals, so
the error bars in Figure 3.5 (page 56) and Figure 3.7 (page 60) should be used with
some caution.
64
8.6x10 13
3-
0.17
0.16
1-s
2-s -s
3
0.15
0.14
0.26
0.28
0.30
NS II /NS III
0.32
8.2x10 13
4- s
2-s
8.0x10 13
0.14 0.15 0.16 0.17 0.18
NS IV /NS III
5.0
0.2 4-s3-s
4s
3s
T e (eV)
4-
s
2s
1-
NO III /NS III
1- s
8.4x10 13
0.3
0.1
3-s 4-s
s
Ne (cm-2)
NS IV /NS III
0.18
s
4.8
1-
4.6
s 2 4-s
-s
4.4
0.0
0.9 1.0 1.1 1.2 1.3 1.4
NO II/NS III
8.0x10 13
8.4x10 13
Ne (cm-2)
8.8x10 13
Figure 3.8: Four selected 2-D confidence intervals of the model parameters. The contours represent the value of δχ2 corresponding to the probability of finding the pair of
parameters within the contour. The cross in the center of the panels represents the formal 1-σ errors (i.e. the square root of the diagonal elements of the covariance matrix)
obtained from the fitting algorithm. The formal 1-σ bars often, though not always,
underestimate the true range of possible parameter values. The upper panels show examples of two pairs of parameters that are only weakly correlated, while the bottom
panels show pairs of parameters that are highly anti-correlated.
65
3.4.4
κ-Distribution Results
As described above, the spectral emissions model used to fit the UVIS spectra
can accommodate either a thermal, Maxwellian electron distribution function or an
approximation to a non-thermal, κ electron distribution function. Fits of the spectra
were made using both distribution functions. The models that used a Maxwellian
distribution and the models that used a κ distribution both produced fits to the data
qualitatively similar to Figure 3.4. However, the value of the χ2 statistic was marginally
lower (∼2%) for the models using a κ distribution, indicating a somewhat better fit. The
torus ion composition derived by the two models was statistically identical—a surprising
result. It appears that the derived ion mixing ratios are nearly independent of the shape
of the electron distribution function for most “reasonable” distribution functions. This
effect can also be seen in the relatively large error bars for the electron parameters
derived from the κ distribution model.
Although the ion composition between the two models was indistinguishable,
the models using the κ approximation required an electron column density ∼1.7 times
greater than the models that used a Maxwellian to fit the spectra. The reason for this
can be understood by examining the shape of the distribution functions. Figure 3.9
shows the two best-fit distribution functions for the spectrum of the torus obtained at
7.4 RJ .
From Eq. 3.12 we see that the observed brightness of the torus spectrum is dependent on the level populations of the ions, which from Eqs. 3.2 and 3.3 will depend
on the shape of the electron distribution function. For the example shown in Figure 3.9,
the κ distribution function is greater than the Maxwellian distribution function below 5
eV and above 60 eV. However, electrons with energies of 5 eV or less are generally incapable of collisionally exciting ions to the states that produce EUV/FUV photons. As a
result these electrons have little effect on the observed EUV/FUV spectrum. Electrons
Normalized Distribution Function (s m−1)
66
10−6
10−7
10−8
10−9
10−10
10−11
0.01
Maxwellian Te=7.3 eV
Kappa TC=1.3 eV κ=2.5
0.10
1.00
10.00
Electron Energy (eV)
100.00
Figure 3.9: Normalized distribution functions for the Maxwellian and kappa distributions fit to the spectrum at 7.4 RJ . The Maxwellian distribution contains more particles
than the kappa in the energy range of 5–40 eV. Consequently, model fits using a kappa
distribution require a higher electron column density than those using a Maxwellian
distribution.
in the high-energy tail of the κ distribution are certainly capable of exciting EUV/FUV
transitions, but there are far fewer of these electrons than there are electrons in the
5–60 eV range. In this critical middle energy range, the Maxwellian distribution has
more electrons than the κ distribution. As a result, the κ distribution model requires
higher ion column densities than the Maxwellian distribution model in order to match
the observed brightness of the spectrum. The similar χ2 statistic of models using the
two different distribution functions (Maxwellian and κ) implies that the shape of the
electron distribution cannot be tightly constrained by EUV/FUV observations of the
torus alone. The electron distribution function could be better constrained by either obtaining an independent measure of the ion column densities or extending the wavelength
range of the analysis into the optical.
In February 1992, the Ulysses spacecraft flew through the Io torus. This pass
through the torus is unique in that the spacecraft trajectory was basically north-to-
67
7
6
k-Parameter
5
4
M-V 95
3
2
1
0
6.0
6.5
7.0
7.5
8.0
Radial Distance (R J)
8.5
9.0
Figure 3.10: Best-fit values of the κ parameter versus radial distance. The solid diagonal
line is the best-fit line through the values of κ. The labeled M-V 95 is the value of κ
determined from the Ulysses URAP instrument during the Io torus flythrough in 1992
(Meyer-Vernet et al., 1995). The decrease of κ inside of 6.5 RJ may be due to line of
sight projection effects.
south, as opposed to lying close to the equatorial plane. For the period when Ulysses was
within 15◦ of the jovian equator, it sampled the region from approximately 7.1–8.2 RJ in
radial distance. Although the particle detector instruments were not turned on for this
encounter, in situ measurements of the electron density and temperature were made
by the Unified Radio and Plasma (URAP) wave experiment (Stone et al., 1992a,b).
Analysis of this data revealed that the bulk electron temperature was not constant
along magnetic field lines, but rather varied with latitude in anticorrelation with density
(Meyer-Vernet et al., 1995; Moncuquet et al., 2002). The authors proposed that this
effect could be explained if the electron distribution approximated a κ distribution with
κ = 2.4 ± 0.2. The values for κ derived from the UVIS spectra are shown in Figure 3.10.
Outside 6.6 RJ , the values for κ show a steady decrease with radial distance. The
Ulysses URAP value of κ = 2.4 ± 0.2, which was measured at ∼8 RJ , fits nicely between
68
the UVIS values derived at 7.9 and 8.1 RJ . The decrease of kappa inside 6.6 RJ may
result from a projection of the outer regions of the torus into the line of sight.
3.5
Conclusions
We have analyzed a radial scan of the midnight sector of the Io plasma torus
obtained by the Ultraviolet Imaging spectrograph on 14 January 2001. These observations record the radial structure of Io torus at a local time of 01:50, which has not been
previously observed. Two-dimensional spectrally dispersed images of the torus are obtained from the UVIS instrument, although to increase the signal-to-noise, we average
over the latitudinal structure of the torus. Features from six different ion species are
readily apparent in the torus spectra.
In order to derive information about the plasma composition from the spectra,
we developed a spectral emissions model, similar to that used by Shemansky and Smith
(1981), which incorporates the latest atomic physics data from the CHIANTI database
(Dere et al., 1997; Young et al., 2003). In order to deal with line of sight projection
effects, we assume that the electron distribution function is uniform over the column
through the torus, an assumption that should not significantly affect our results. We
find that the electron temperature is less than that predicted by the Voyager-era model
of Bagenal (1994). We find that the observed radial profile of electron column density is
well matched by assuming that the local electron number density profile is proportional
to r−5.4 from 6.0 RJ -7.8 RJ and r−12 outside of 7.8 RJ . If we use this profile for
electron density and the ion temperatures derived by Bagenal (1994) we find that the
flux tube content of the Io torus is proportional to r−2 , which is consistent with flux
tube interchange acting to transport plasma radially outward.
The plasma composition derived from the UVIS spectra of 14 January 2001 is
significantly different that the torus composition during the Voyager era. However,
Steffl et al. (2004a) (Chapter 2) has shown significant temporal variations over the six-
69
month flyby of Jupiter. Both O II and S II are depleted compared to the Voyager values,
while S III and S IV show enhancements. The O/S ion ratio of 0.9, obtained from the
UVIS spectra, is much lower than the Voyager value of 1.6. Ground-based observations
of the torus have also found less oxygen than predicted by the Voyager models. In
addition to the lower O/S ratio, we find that the charge per ion has increased to 1.7
from 1.4. The spectral resolution of UVIS allows us to report the 3-σ detection of S V.
S V, which has not previously been detected in the Io torus, is present in the torus at
a mixing level of ∼0.5%.
Our spectral emissions model has the ability to approximate the effects of an
arbitrary, non-thermal electron distribution as the linear combination of Maxwellian
components. We explored the effects of using a non-thermal κ-distribution, which is
quasi-Maxwellian at low energies and a power law at high energies, to analyze the
torus spectra. Models using a κ-distribution of electrons had a marginally lower value
of the χ2 statistic, although the actual spectral fits were qualitatively very similar to
those produced by the Maxwellian model. We found that the ion composition derived
using the κ-distribution model was identical to the ion composition derived using a
Maxwellian model. However, as a result of the shape of the distribution function in
the 5–60 eV range of energy, the κ models required a higher electron column density to
match the brightness of the UVIS torus spectra. The value of the κ-parameter, which
determines the index of the power law, high-energy tail of the distribution, was found
to generally decrease with radial distance. The derived radial profile value of the κparameter is consistent with the measurement of κ = 2.4 at 8 RJ made by the Ulysses
URAP instrument (Meyer-Vernet et al., 1995).
The analysis presented this data set has focused on the radial variations of torus
parameters. However, the orientation of the UVIS entrance slits parallel to the jovian
rotational axis also make these data well suited to analyze the latitudinal structure of
the torus. Such a latitudinal analysis will be the focus of future work.
Chapter 4
Temporal and Azimuthal Variability
We present analysis of the observations of the Io plasma torus obtained with
the Cassini Ultraviolet Imaging Spectrometer (UVIS) between 1 October 2000 and 14
November 20001 . The Io torus is found to exhibit significant azimuthal variations in
ion composition. This compositional variation is observed to have a period of 10.07
hours—1.5% longer than the System III rotation period of Jupiter. While exhibiting
many similar characteristics, the periodicity in the UVIS data is 1.3% shorter than the
“System IV” period. The mixing ratio of S II is found to be correlated with electron
density and anti-correlated with both the mixing ratio of S IV and electron temperature.
The amplitude of the azimuthal variation of S II and S IV varies between 5–25% during
the observing period, while the amplitude of the variation of S III and O II remains in
the range of 2–5%. The amplitude of the azimuthal compositional asymmetry appears
to be modulated by its location in System III longitude, such that when the region of
maximum S II mixing ratio (minimum S IV mixing ratio) is aligned with a System III
longitude of ∼200◦ , the amplitude is a factor of ∼4 greater than when the variation is
anti-aligned.
1
This chapter has been submitted to Icarus as: Steffl, A. J., P. A. Delamere, and F. Bagenal, Cassini
UVIS observations of the Io plasma torus. III. Temporal and azimuthal variability
71
4.1
Introduction
The Io plasma torus is a dense (∼2000 cm−3 ) ring of electrons and sulfur and
oxygen ions trapped in Jupiter’s strong magnetic field, produced by the ionization of
∼1 ton per second of neutral material from Io’s extended neutral clouds. On ionization, fresh ions tap the rotational energy of Jupiter (to which they are coupled by the
magnetic field). Much of the torus thermal energy is radiated as intense (∼1012 W)
EUV emissions. The ∼100 eV temperature of the torus ions indicates that they have
lost more than half of their initial pick-up energy. Electrons, on the other hand, have
very little energy at the time of ionization and gain thermal energy from collisions with
the ions (as well as through other plasma processes) while losing energy via the EUV
emissions that they excite.
In situ measurements of the Io plasma torus from the Voyager, Ulysses, and
Galileo spacecrafts and remote sensing observations from the ground and from spacebased UV telescopes have characterized the density, temperature and composition of
the plasma as well as the basic spatial structure (see review by Thomas et al. (2004)).
However, the azimuthal and temporal variability of the torus remains poorly determined. Extensive measurements of torus emissions made by the Ultraviolet Imaging
Spectrograph (UVIS) on the Cassini spacecraft as it flew past Jupiter on its way to
Saturn allow us to further examine the azimuthal structure of the plasma torus and its
changes with time.
Analysis of torus spectral emissions provides estimates of plasma composition,
temperature, and density, which can then be used to constrain models of mass and
energy flow through the torus. Such models can be used to derive plasma properties such
as source strength, source composition, and radial transport timescale (Delamere and
Bagenal , 2003; Lichtenberg et al., 2001; Schreier et al., 1998). Thus, one aims to relate
observations of spatial and temporal variations in torus emissions to the underlying
72
source, loss and transport processes. Towards this ultimate goal, we present an analysis
of UVIS observations of the Io torus from 1 October 2000 to 14 November 2000.
4.1.1
Jovian Coordinate Systems
In order to understand the UVIS observations of azimuthal variability and periodicity, it is useful to briefly review the various Jovian coordinate systems (see also
Dessler (1983) and Higgins et al. (1997)). Jupiter has no fixed surface features on which
measurements of its rotation period can be based. Observations of the transits of Jovian
cloud features by several late 19th century astronomers, among whom were Marth (1875)
and Williams (1896), led to the adoption of the “System I” and “System II” rotation
periods. The System I period, based on the rate of rotation of equatorial cloud features,
was defined as 9h 50m 30.0034s , while the System II period, based on the more slowly
rotating cloud features at high latitudes, was defined as 9h 55m 40.6322s (Dessler , 1983).
The prime meridians of the associated longitude grids for both coordinate systems were
defined to be the Central Meridian Longitude at Greenwich noon on July 14, 1897.
Attempts to derive a rotation period based on the motion of the interior of the
planet, rather than the cloud tops, met with little success until the discovery of decametric (DAM; ∼20 MHz) radio emissions from Jupiter by Burke and Franklin (1955).
From this radio emission, Shain (1956) obtained the first measurement of the Jovian
rotation period based on the rotation of the magnetosphere. Subsequent observations
improved the accuracy of the rotation period derived from radio emissions, and a period
of 9h 55m 29.37s —the weighted average of several radio observations—was defined as the
“System III” (1957) rotation period (Burke et al., 1962). With further observations,
it gradually became clear that this period was in need of a slight revision. Riddle and
Warwick (1976) reported the weighted average of radio observations obtained since the
System III (1957) period was defined; their published value of 9h 55m 29.71s became
known as System III (1965) and was adopted by the International Astronomical Union
73
(IAU) as the standard rotation period of Jupiter (Seidelman and Devine, 1977). Recently, Higgins et al. (1997) reported that the System III (1965) rotation period should
be further revised to 9h 55m 29.6854s , based on 35 years of radio observations of Jupiter.
This difference results in a shift of ∼1◦ in longitude every four years relative to System
III (1965). Since this shift in longitude is far less than can be measured by UVIS during
the Jupiter encounter and since the proposed revision to the System III period has not
yet been uniformly adopted (Russell et al., 2001), all subsequent references to “System
III”, corotation, or rotation with the magnetic field, will refer to the IAU accepted
Jovian rotation period: System III (1965).
4.1.2
Variations with System III Longitude
For the purposes of modeling, the Io plasma torus is often assumed to be azimuthally symmetric. However there have been numerous observations of the Io torus
that suggest that the torus exhibits significant variation with System III longitude.
Here, we present a brief review of some of these observations. An additional discussion
of observations of longitudinal asymmetries can be found in Thomas (1993b).
Some of the earliest observations of the Io plasma torus found that the brightness
of the [S II] 6716Å/6731Å doublet was correlated with System III longitude. Trauger
et al. (1980) observed this [S II] doublet using the 5 m Hale telescope on the nights of
7–11 October 1976. They found that a region extending 90◦ in longitude and centered
on λIII = 280◦ was consistently fainter than the rest of the torus. The [S II] brightness
peaked at λIII ≈ 180◦ , although given the relatively large scatter in the data, this value
is poorly constrained.
Using the 2.2 m telescope of the Mauna Kea observatory, Pilcher and Morgan
(1980) observed the [S II] 6716Å/6731Å doublet over a three month interval that began
in December 1977. The brightness of the [S II] doublet was found to vary with longitude
by as much as a factor of 4. The peak brightness was observed in the longitude range
74
of 160◦ < λIII < 340◦ . At other times, Pilcher and Morgan (1980) found the [S II]
brightness to be more azimuthally uniform, with the transition between these two states
taking approximately two weeks.
Trafton (1980) reported a similar azimuthal variation in the brightness of the
[S II] 6716Å/6731Å doublet in widely-spaced observations between 19 January 1976
and 19 June 1979 using the McDonald Observatory’s 2.7 m telescope. The brightness
was found to vary by about a factor of 5, with a peak located at λIII =260◦ .
Extensive observations of the Io plasma torus were made by the ultraviolet spectrometers (UVS) aboard the Voyager 1 and Voyager 2 spacecraft (Broadfoot et al., 1977,
1981). The initial search for variations in the UV brightness of the torus with System
III longitude focused on the pre-encounter period of the Voyager 2 spacecraft, which
took place from days 116–144 of 1979 (Sandel and Broadfoot, 1982a). During the period
of day 121/16:20 UT to day 123/14:00 UT, a weak (<10%) azimuthal variation in the
brightness of the S III 685Å feature was observed. This variation had a peak brightness
located in the range of 330◦ < λIII < 40◦ and a minimum brightness in the range of
140◦ < λIII < 200◦ and was seen only in the dusk ansa of the torus. Roughly two
days later, during the period of day 123/18:00 UT to day 125/12:00 UT, a stronger
azimuthal variation was seen in both the dawn and dusk ansae. However, the phase of
the variation had shifted by ∼60◦ in longitude, such that the peak in brightness was
located between 40◦ < λIII < 100◦ and the minimum between 180◦ < λIII < 240◦ .
A short-term variation with System III longitude similar to that reported by
Sandel and Broadfoot (1982a) has been found in spectra from the Voyager 1 UVS (Herbert and Sandel , 2000). After analyzing 47 hours of Voyager 1 UVS spectra of the Io
torus, Herbert and Sandel (2000) found that both the electron density and electron
temperature vary with System III longitude. The electron density variation had an
amplitude of about 12% with a peak near λIII =150◦ and a minimum near λIII =320◦ .
the electron temperature variation had an amplitude of about 7% with a a peak near
75
λIII =270◦ and a minimum near λIII =80◦ .
Although Sandel and Broadfoot (1982a) found evidence for short-term azimuthal
variations in the brightness of the S III 685Å feature, they reported no significant longlived variation of torus brightness with System III longitude during the 44-day Voyager
2 pre-encounter period. However, such a long-lived System III variation was found
by Sandel and Dessler (1988), who used a Lomb-Scargle periodogram analysis (Lomb,
1976; Scargle, 1982; Horne and Baliunas, 1986) to search for periodicities in the Voyager
2 pre-encounter data. Using similar analysis techniques (Lomb-Scargle periodograms)
Woodward et al. (1994) and Brown (1995) also discovered System III periodicities in
their observations of the torus [S II] 6731Å emission.
Imaging observations of the torus in 1981 by Pilcher et al. (1985) showed that
the brightness of the [S II] 6731Å line varied by a factor of 6 as a function of System III
longitude. The peak brightness was found to be at λIII ≈ 170◦ , although a secondary
peak at λIII ≈ 280◦ was also evident.
Also in 1981, Morgan (1985) was able to simultaneously image the [S II] 6716Å/6731Å
doublet, the [S II] 4069Å/4076Å doublet, and the [O II] 3726Å/3729Å doublet, using
the Mauna Kea Observatory 2.2 m telescope. On observing runs that took place from
14–17 February 1981 and 20–23 March 1981, Morgan (1985) found the brightness of
both [S II] doublets varied with System III longitude, with a peak at λIII ≈ 180◦ . However, no correlation of the brightness of the [O II] doublet with System III longitude was
apparent. Brown and Shemansky (1982) made spectroscopic observations of the Io torus
[S II] 6716Å/6731Å doublet on 23–24 February 1981—six days after the observations of
Morgan (1985)—and found no obvious correlation of [S II] brightness with System III
longitude.
Additional imaging of the Io plasma torus at the [S II] 6731Å emission was conducted by Schneider and Trauger (1995) over six nights from 31 January 1991 to 6
February 1991. They found the longitudes 150◦ < λIII < 210◦ to be consistently ∼3–
76
4 times brighter than the longitudes 0◦ < λIII < 170◦ . More detailed examination
revealed that the variation of brightness with longitude was weakest on 31 January
1991 with a poorly-constrained maximum near ∼120◦ . Three nights later, the variation
with longitude was significantly stronger, and the peak had shifted to a longitude of
∼170◦ . Finally, on the last night of observation (5 February 1991), the amplitude of
the longitudinal variation remained relatively large, and the peak had shifted further to
a longitude of ∼210◦ . Schneider and Trauger (1995) interpreted the shift in phase of
∼18◦ /day as evidence for a possible 2.1% subcorotation (relative to rigid corotation) of
a torus feature. Additionally, Schneider and Trauger (1995) proposed that the modulation of the amplitude of the longitudinal variation might explain why numerous previous
observations had detected an enhanced brightness of S II in the “active sector” (a sector
spanning roughly 90◦ in longitude centered around λIII ≈ 180◦ ): the amplitude of the
variation is greatest when the peak lies within this region and is diminished when it lies
outside.
Spectra of the Io torus obtained on 10–11 February 1992 showed that the brightness of the [S II] 6716Å/6731Å doublet and the S III 6312Å line were correlated. These
spectral features peaked in brightness at a System III longitude of ≈ 180◦ (Rauer et al.,
1993).
In contrast to observations of the S III 685Å feature by the Voyager 1 and Voyager
2 UVS (Sandel and Broadfoot, 1982a; Herbert and Sandel , 2000), Gladstone and Hall
(1998) found no correlation between the brightness of torus emission between 70–760Å
and System III longitude.
Emission from the [S IV] 10.51 µm line was discovered in observations of the Io
plasma torus on 25 May 1997 using the Infrared Space Observatory (Lichtenberg et al.,
2001). The brightness of this feature was found to vary by ∼20% with System III
longitude with a poorly-constrained peak near λIII ≈ 120◦ .
77
4.1.3
Subcorotating Torus Phenomena and “System IV”
In the 29 years since its discovery by Kupo et al. (1976), there have been numerous
observations of phenomena occurring in the Io plasma torus having a period longer than
the System III rotation period. There have also been several direct measurements of
the torus plasma lagging corotation with System III. To place our results into proper
context, we present a brief review of these observations.
4.1.3.1
Radio Emissions
The first indications that plasma in the Io torus might not be rigidly corotating with Jupiter’s magnetic field came from the Planetary Radio Astronomy (PRA)
experiments aboard the two Voyager spacecrafts. The Jovian narrow-band kilometric
radiation (nKOM), first described by Kaiser and Desch (1980), is emitted from source
regions lying in the outer Io plasma torus at radial distances of ∼8–9 RJ . Kaiser and
Desch (1980) found that the rotation period of Jovian narrow-band kilometric radiation
(nKOM) source regions was 3.3% slower than the System III rotation period during the
Voyager 1 encounter and 5.5% slower during the Voyager 2 encounter.
The initial analysis by Kaiser and Desch (1980) of the Jovian nKOM emissions
observed by the Voyager PRA experiments covered only a relatively short period (∼45
Jovian rotations) during each spacecraft encounter. A statistical analysis of all detections of nKOM by both Voyager PRA experiments between 14 January 1979 and 31
December 1979 (the period when the spacecrafts were within 900 RJ of Jupiter) found
that the rotation period of the nKOM sources was not constant (Daigne and Leblanc,
1986). Rather, the rotation periods for individual nKOM sources varied between 0–8%
longer than the System III rotation period with average values of 3.2% and 2.7% for Voyager 1 and Voyager 2, respectively. The large range of values reflects intrinsic variability
in the rotation period of the nKOM sources rather than errors in measurement, which
78
are estimated to be ∼1%. Although the rotation period of individual nKOM sources
generally lagged the System III rotation period, the probability of observing nKOM
emission was found to be significantly greater when the spacecrafts were at System III
longitudes of 40◦ and 300◦ .
The order of magnitude greater sensitivity and direction-finding capabilities of
the Unified Radio and Plasma Wave instrument (URAP) on the Ulysses spacecraft
allowed the detection of six distinct nKOM source regions during the Ulysses encounter
with Jupiter in February, 1992 (Reiner et al., 1993). These source regions were found
to lie at radial distances of 7.0–10.0 RJ and to have a rotation periods ranging from
3.0–8.6% greater than the System III period (again the range in values represents the
variability of the individual nKOM sources, rather than measurement uncertainty). In
addition, to the subcorotation period of nKOM source regions, URAP also detected a
new component of the Jovian hectometer radiation (HOM) that recurs with a period
2–4% longer than the System III rotation period (Kaiser et al., 1996). Reexamination
of Voyager 1 and Voyager 2 PRA data found similar results. Based partly on the
spectroscopic observations of Brown (1995), which were concurrent with the Ulysses
encounter, Kaiser et al. (1996) conclude that the new HOM component is the result of
an HOM source region in the high-latitude regions of Jupiter being periodically blocked
by a high-density region in the Io torus.
4.1.3.2
In Situ Plasma Measurements
In situ measurements of the bulk rotation velocity of the torus plasma have been
made by the Plasma Science (PLS) instruments aboard the Voyager 1 and Galileo
spacecrafts and the URAP instrument aboard the Ulysses spacecraft. The Voyager 1
PLS found that the torus plasma was within a couple percent of rigid corotation inside
of 5.7 RJ , but between 5.9–10 RJ , deviations from corotation of up to 10% could not be
ruled out (Bagenal , 1985). The Ulysses URAP instrument measured two components
79
of the dc electric field during its flythrough of the outer Io torus, and from this derived
the flow speed of torus plasma (Kellogg et al., 1993). URAP found the plasma flow
speeds to be generally close to corotation but with significant deviations having an rms
value of 5.3 km/s. Finally, on five passes through the Io torus, the Galileo PLS observed
that the bulk plasma flow lagged the corotation velocity by 2–10 km/s, with an average
deviation of ∼2–3 km/s (Frank and Paterson, 2001).
4.1.3.3
Spectroscopic Measurements
The first direct observation of a corotational lag in the Io torus plasma came from
analysis of the Doppler shift of the [S II] 6716 Å/6731 Å doublet (Brown, 1983). Using
observations from two nights in February, 1981 and three nights in April, 1981, Brown
(1983) found that the radial velocity of S II deviated from rigid corotation by 6%±4%,
where the ±4% represents the variability of the derived corotation lag, rather than the
measurement uncertainty.
Observations of [S III] 9531 Å emitted from the dusk side of the torus between 12
April 1982 and 30 April 1982 found that the torus brightness was not correlated with
the System III rotation period, but rather with a period of 10.2±0.1 hours, 2.8% longer
than the System III period (Roesler et al., 1984). These observations were obtained
between 12 April 1982 and 30 April 1982 using a scanning Fabry-Perot spectrometer
that had a field of view 2 RJ in diameter centered at a radial distance of 6 RJ . This was
the first detection of a long-lived (roughly 43 rotations of Jupiter) periodic phenomenon
in the Io torus at a period other than System III. A reanalysis of this data by Woodward et al. (1994) confirmed the existence of a 10.20 hour periodicity in the data and
found a statistically significant secondary periodicity at the System III rotation period.
Additional ground-based observations of [S III] 9531 Åand [S II] 6731 Å emission from
the Io torus in March and April, 1981 by Pilcher and Morgan (1985) and Pilcher et al.
(1985) were interpreted as requiring a torus rotation period a few percent longer than
80
System III, consistent with Roesler et al. (1984).
The reported subcorotation of the nKOM source regions (Kaiser and Desch,
1980), the 10.2-hour periodicity in the brightness of [S III] 9531Å (Roesler et al., 1984),
and analysis of Voyager Ultraviolet Spectrometer (UVS) data (Sandel , 1983), led Dessler
(1985) to propose a new Jovian coordinate system known as “System IV” that rotates
3.1% slower than System III. The proposed System IV coordinate system was further
refined by Sandel and Dessler (1988). Using a Lomb-Scargle periodogram analysis of
the brightness of the Voyager 2 UVS 685 Å feature, (a feature dominated by three
multiplets of S III though also containing emissions from S IV and O III), Sandel and
Dessler (1988) found evidence for periodicity at both the System III period, and at a
period of 10.224 hours, 3.0% longer than System III. In addition, Sandel and Dessler
(1988) noted that the azimuthal variation in brightness was greatest when these two
periods were aligned. The observed period of 10.224 was used to define the System
IV (1979) coordinate system. The prime meridian of the System IV (1979) coordinate
system was defined such that the peak of the 685 Å emissions occurred near λIV =180◦ .
Recent analysis of 47 hours of Voyager 1 UVS spectra of the Io torus by Herbert and
Sandel (2000) found both electron density and electron temperature to be organized in
System IV longitude. However, the uncertainty in these quantities is larger than the
observed System IV modulation.
The first observational program designed specifically to look for periodicities in
the Io torus was undertaken in 1988 (Woodward et al., 1994). Woodward et al. (1994)
observed emission of [S II] 6731Å from the Io torus over a 35 day period using a FabryPerot spectrometer similar to that used by Roesler et al. (1984). After careful analysis
of their data using weighted Lomb-Scargle periodograms, they found periodicity in the
torus [S II] intensity at 10.14±0.03 hours—a period intermediate of System III and
System IV—and at 9.95 hours, consistent with the System III period.
In an effort to address the apparent inconsistencies between the previous spectro-
81
scopic measurements, Brown (1994a) observed the [S II] doublet at 6717Å and 6731Å
over a six month period in 1992 using a long-slit echelle spectrograph. To date, this
remains the longest time baseline of torus observations, and it thus provides the most
accurate measurement of the periodicities in the torus. Using the now ubiquitous LombScargle periodogram analysis, Brown (1995) found significant periodicity in the torus
at both the System III period and a period of 10.214±0.006 hours—2.91% longer than
the System III period. The latter period was found to remain constant between the
radial distances of 5.875 and 6.750 RJ and provides the basis for a minor revision to the
System IV (1979) coordinate system known as System IV (1992). Subsequent references
to “System IV” will refer to the System IV (1992) period defined by Brown (1995).
During the observing period, the variation of [S II] line brightness with System IV
longitude underwent a sudden phase shift of ∼100◦ . The sudden shift in phase resulted
in a spurious weak peak in the dawn ansa periodogram at a period of 10.16 hours—
quite similar to the value reported by Woodward et al. (1994). By subdividing the data
into two groups (before and after the sudden phase shift) the peak in the dawn ansa
periodogram becomes 10.217±0.010 hours, consistent with the value of 10.214±0.006
hours obtained from the dusk ansa. In light of the discovery that the phase of System IV
variations can shift rapidly, Woodward et al. (1997) reanalyzed their 1988 data and found
a similar phase shift was responsible for the reported periodicity of 10.14±0.03 hours.
By subdividing their data into two groups they found that the primary periodicity in
the data was, in fact, at 10.2 hours, consistent with the System IV period.
Direct measurements of the radial velocity of the torus plasma as a function of
radial distance were obtained by measuring the Doppler shift in the sum of all 222
spectra obtained in 1992 (Brown, 1994b). The torus plasma was found to lag rigid
corotation with System III, with the amount of corotational lag being a strong function
of radial distance. The corotational lag reached a maximum deviation of ∼4 km/s in
the range of 6–6.5 RJ . Between 6–7 RJ , the torus lags corotation by an average of 2%.
82
This measurement, coupled with the observation that the System IV period remained
constant between 5.875 and 6.75 RJ , led Brown (1995) to conclude that the System IV
periodicity cannot be caused by plasma lagging corotation.
The radial velocity profile of the Io torus was measured again in October 1999
using the 3.5 m European Southern Observatory’s New technology Telescope (NTT)
(Thomas et al., 2001). The radial velocities derived from S II and S III emission lines
were in good agreement with the range in velocities measured by Brown (1983) and
Brown (1994b), however the larger collecting area of the NTT telescope enabled Thomas
et al. (2001) to place much smaller relative error bars on their radial velocity profiles.
The radial velocity measurements of Thomas et al. (2001) represent a snapshot of the
Io torus radial velocity profile (they were derived from a single integration) whereas the
radial velocity profile of Brown (1994b) represents the average profile over a six-month
period.
Finally, a multi-year campaign to determine the long-term variability of torus
[S II] 6731Å and 6716Å emissions has been carried out by Nozawa et al. (2004). Using
small telescopes (diameters of 28 cm and 35 cm), Nozawa et al. (2004) obtained data
in four observing seasons between 1997 and 2000. Using Lomb-Scargle periodogram
analysis, they found periodicities of 10.18±0.06 hours in 1998, 10.29±0.14 hours in
1999, and 10.14±0.11 hours in 2000, all within measurement uncertainty of the 10.214
hour System IV period. Data from the 2000 observing season were acquired between
15 December 2000 and 5 January 2001, concurrent with the Cassini spacecraft’s closest
approach with Jupiter, but more than 30 days after the data presented in this paper
were acquired.
4.2
Observations and Data Analysis
The data used in this paper were obtained by the Cassini spacecraft’s Ultraviolet
Imaging Spectrograph (UVIS) (Esposito et al., 2004) between 1 October 2000 and 15
83
November 2000 (DOY 275–320) during the inbound leg of Cassini’s Jupiter flyby. During
this period, while the spacecraft was between 1100 RJ and 600 RJ from the planet
(1 RJ =71,492 km), 1904 spectrally-dispersed images of the Io torus, in its entirety, were
acquired. All of these spectral images have an integration time of 1000 seconds. The
duty cycle for UVIS consisted of six 20-hour blocks. During blocks 1, 2, 5, and 6 UVIS
observed the Io torus for 9 consecutive hours followed by 11 hours of downlink and
observations of other targets. Blocks 3 and 4 consisted of 28 hours of torus observation
followed by 12 hours of downlink and other observations. This cycle was repeated nine
times. Additional information about this dataset, including examples of the observing
geometry, images of the raw and processed data, and descriptions of the data reduction
and calibration procedures used, can be found in Steffl et al. (2004a).
Since the encounter distances were so large, the spatial resolution of this dataset
is relatively coarse (0.6–1.1 RJ per detector row). We therefore limited our analysis
to spectra from the ansa region on both sides (dawn and dusk) of the torus. The
ansa region was defined as the part of the torus subtended by the brightest row on the
detector, plus the two neighboring rows. Spectra contained in these three rows were
averaged together to obtain the ansa spectrum. The decreasing distance of the Cassini
spacecraft to Jupiter during the observation period meant that the range of projected
radial distances in the Io torus from which the ansa spectra were extracted went from
4.5–8.0 RJ on 1 October 2000 to 5.2–7.0 RJ on 15 November 2000.
The Io torus spectral model described in Steffl et al. (2004b) was used to derive
the ion composition, electron temperature, and electron column density from the ansa
spectra. Since the long axis of the UVIS entrance slit was oriented parallel to the Jovian
equator, information about the latitudinal distribution of the Io torus is convolved with
spectral information along the dispersion direction of the detector. To separate theses
effects, we assume a Gaussian scale height for the torus plasma, the value of which is
a parameter fit by the model. Additionally, we assume that the scale heights for all
84
ion species present in the torus are equal. Although this last assumption is somewhat
unphysical, given the relatively coarse spatial resolution of the UVIS dataset, it has no
significant effect on our results.
4.3
Results
4.3.1
Temporal Variation in Torus Composition
Figure 4.1 shows how the mixing ratios (ion density divided by electron density)
of four ion species in the torus: S II, S III, S IV, and O II, and electron temperature vary
with time during the observation period. The most obvious long-term change is that
the mixing ratio of S II falls from 0.10 to 0.05 over a 45-day timescale, while the mixing
ratio of S IV increases from 0.02 to 0.05 over the same period. The mixing ratios of O II
and S III, the two dominant ion species in the torus, remain relatively constant. The
temporal changes in the composition of the torus plasma coupled with observations by
the Galileo Dust Detector System of a four-orders-of-magnitude increase in the amount
of dust emitted from Io (Krüger et al., 2003) led Delamere et al. (2004) to propose a
factor of 3–4 increase in the amount of neutral material available to the torus on, or
around, 4 September 2000. Torus chemistry models including such an increase in the
neutral source rate (along with a corresponding increase in the amount of hot electrons
in the torus) can closely match the observed changes in plasma composition with time.
4.3.2
Azimuthal Variations in Torus Composition
Over the 45-day inbound staring period, the long-term variations of torus parameters with System III longitude are relatively small. As discussed in Section 2.3.6,
the relative variation of the EUV luminosity of the torus ansae with System III longitude is only about 5%, with a maximum near λIII =120◦ and a secondary peak near
λIII =270◦ (see Fig. 2.13). The relative variations of electron density and electron tem-
85
Mixing Ratio (Nion/Ne)
1.00
0.10
O II =
S II =
S III =
S IV =
Te=
0.01
275
280
285
290 295 300 305
Day of year 2000
310
315
320
Figure 4.1: Ion mixing ratios (ion column density divided by electron column density)
and electron temperature versus time, as derived from the dusk ansa of the torus.
Owing to uncertainty in the absolute calibration of the UVIS Extreme Ultraviolet (EUV)
channel below 800 Å, the electron temperature is presented in relative units. Results
from the dawn ansa are similar.
perature with System III longitude are shown in Fig. 4.2. Like the EUV luminosity,
both electron density and electron temperature show long-tern variations of only ∼5%.
In contrast, however, the variations of both electron density and electron temperature
show a single, clearly defined peak with a single, clearly defined minimum. Although
there is a large amount of scatter in the individual data points, the average variation
in electron density is clearly anti-correlated with the average variation in electron temperature: the electron density has a maximum value near λIII =160◦ , while the electron
temperature has a minimum value near λIII =170◦ .
Although the torus exhibits relatively small variations with System III longitude
on long timescales, azimuthal variations of up to 25% are observed on timescales of a few
days. This can be seen in the high-frequency component of the curves in Fig. 4.1. All
four ion mixing ratios, as well as the relative electron temperature and column density,
86
Relative Electron Temperature
Relative Electron Density
3,808 measurements from the torus ansae Oct 1 − Nov 14, 2000
0
1.40
1.30
30
60
90
120
150
180
210
240
270
300
330
10°Sliding density average
360
1.40
1.30
1.20
1.20
1.10
1.10
1.00
1.00
0.90
0.90
0.80
0.80
0.70
0.60
1.40
1.30
0.70
0.60
1.40
1.30
1.20
1.20
1.10
1.10
1.00
1.00
0.90
0.90
0.80
0.80
0.70
0.60
0
10°Sliding Temperature Average
30
60
90
120
150 180 210 240
System III Longitude
270
300
330
0.70
0.60
360
Figure 4.2: Relative torus electron density and electron temperature versus System III
longitude from both dawn and dusk ansae. The solid lines represent the average of
the data in 10◦ longitude bins. Both electron density and electron temperature show a
long-term correlation with System III longitude of ∼5%. Although the scatter of the
individual data points is considerable, on average, the electron density is anti-correlated
with the electron temperature.
exhibit near-sinusoidal variations with a period close to that of the 9.925-hour System
III (1965) rotation period of Jupiter. This can be more readily seen in Fig. 4.3, which
shows the mixing ratios of S II, S III, S IV, and O II; the electron temperature, and the
electron column density as derived from the dawn ansa of the torus over a typical three
day period (DOY 276.5–279.5). Results from the dusk ansa are virtually identical to
the dawn ansa, but the phase is shifted by 180◦ . For ease of comparison, we present
these quantities relative to their average value over the same three day period. The
overplotted solid curves are best-fit sinusoids to the data. These sinusoids have a period
equal to the System III rotation period of Jupiter.
The mixing ratios of S II and S IV, and the electron temperature and column
density show variations of roughly 25% over this three day period, while the mixing
Relative Variation
87
1.4
1.2
1.0
0.8
0.6
1.4
1.2
1.0
0.8
0.6
1.4
1.2
1.0
0.8
0.6
1.4
1.2
1.0
0.8
0.6
1.4
1.2
1.0
0.8
0.6
1.4
1.2
1.0
0.8
0.6
276.5
S II
S III
S IV
O II
Te
Ne
277.0
277.5
278.0
Day of Year 2000
278.5
279.0
279.5
Figure 4.3: Relative ion mixing ratios, electron temperature, and electron column density for a typical 3-day period. Derived values of the ion mixing ratios, electron temperature and electron column density are divided by the average value over the 3-day period.
The best-fit sinusoids for this period are overplotted. Note the strong anti-correlation
of S II with S IV and electron temperature with electron column density.
ratios of S III and O II show variations near the 5% level. In addition, the variations
of S II, S III, and electron column density are close to being in phase with each other,
while at the same time, they are nearly 180◦ out of phase with the variations in S IV,
O II, and electron temperature. Given that the only significant production mechanism
for S IV is the electron impact ionization of S III (which becomes more efficient at higher
temperatures for values typical of the Io torus):
S 2+ + e− → S 3+ + 2e−
(4.1)
it is not surprising that the S IV mixing ratio is positively correlated with electron
temperature. For S II, electron impact ionization is both a source and a loss process:
88
S + e− → S + + 2e−
(4.2)
S + + e− → S 2+ + 2e−
(4.3)
As the electron temperature increases the loss rate of S II via Eq. 4.3 more rapidly
than the production rate via Eq. 4.2, S II should show an anti-correlation with electron
temperature, which is what is observed. A similar anti-correlation between parallel ion
temperature and equatorial electron density has been reported by Schneider and Trauger
(1995). This anti-correlation results from the increased radiative cooling efficiency of
the torus with higher electron densities.
One of the historical difficulties in understanding the Io plasma torus has been to
separate phenomena that are legitimately time variable from those that are the result
of spatial variations in the torus that rotate in and out of the observation’s field of
view. Since the observed variations have a period very close to the rotation period
of Jupiter, and since the timescales for chemical processes, such as charge exchange,
ionization, recombination, etc., which produce significant changes in the Io torus are
generally much longer than this (Shemansky, 1988; Barbosa, 1994; Schreier et al., 1998;
Delamere and Bagenal , 2003; Delamere et al., 2004), the only plausible explanation is
azimuthal variability.
In order to quantify the azimuthal variations in composition, we fit generalized
cosine functions to the ion mixing ratios obtained within a 50-hour window centered on
each data point (e.g. the sinusoidal curves in Fig. 4.3):
Mi (λIII ) = Ai cos(λIII − φi ) + ci
(4.4)
where Mi is the ion mixing ratio at the torus ansa; Ai is the amplitude of the compositional variation; φi is the phase of the variation, i.e. the longitude of the compositional
maximum; and ci is a constant offset, i.e. the azimuthally-averaged value. The am-
89
plitude, phase, and constant offset were allowed to vary, while λIII , the System III
longitude of the ansa (dawn or dusk), is determined from the time of the observation.
Since we are using the System III longitude of the ansa to determine the phase of the
compositional variation, we are implicitly assuming that the period of the variations
is the 9.925 hour System III Jovian rotation period. The 50-hour window was chosen
as a compromise between the need for enough data points to produce a robust fit to
the data and the need to minimize the effects of the actual temporal changes in torus
composition evident from Fig. 4.1. The results of the sinusoidal fits are insensitive to
the size of the sliding window used for windows smaller than ∼100 hours. Although
there is some scatter in the data, the simple sinusoidal fits provide a good match to the
conditions in the Io torus.
4.3.3
4.3.3.1
Torus Periodicities
Drift of Phase With Time
The locations of the peak mixing ratio, i.e. the phase (φi ) of the azimuthal
variation, for each of the four ion species are plotted versus time in Fig. 4.4. As in
Fig. 4.3, the phase of the azimuthal variation for S II tracks with that of S III, while
the phase of S IV tracks roughly with the phase of O II, both of which are shifted
approximately 180◦ from the phase of S III and S II. All four of the main ion species
in the torus exhibit phase increases that are roughly linearly with time. Since the
System III coordinate system is a left-handed coordinate system (System III longitude
increases clockwise when viewed from the north, such that the sub-observer longitude
increases with time for an observer fixed in inertial space. See Dessler (1983) for more
information.) an increase in phase with time implies that the pattern of compositional
variation is rotating more slowly than Jupiter’s magnetic field. The linear nature of the
phase increase implies that the rate of the subcorotation of the compositional variation
System III longitude
360
330
300
270
240
210
180
150
120
90
60
30
360
330
300
270
240
210
180
150
120
90
60
30
0
275
90
S II
S III
S IV
O II
280
285
290
295
300
Day of Year 2000
305
310
315
320
Figure 4.4: Phase of azimuthal variations in the composition of the Io torus as a function
of time. For visual clarity, the top half of the figure is a copy of the bottom half. All
four ion species show a roughly linear trend of increasing phase with time. Data from
the dusk ansa are shown, results from the dawn ansa are similar.
is approximately uniform during the observation period.
The difference in angular frequency, ∆Ω, between the subcorotating compositional
variation and the magnetic field of Jupiter (System III) can be derived from the slope
of the phase increase with time. We used a single linear function to fit the slope of
the phase increases for each of the three sulfur ion species (both dawn and dusk ansae)
simultaneously. The resulting fits are presented in Fig. 4.5. The dotted lines show the
slope that would be observed if the compositional variations in the torus plasma were
rotating at the System IV period defined by Brown (1995). The value of ∆Ω derived
from the three sulfur ion species is 12.5◦ /day, corresponding to a period of 10.07 hours—
1.5% longer than the System III period of 9.925 hours. At a radial distance of 6 RJ ,
this corresponds to a drift of 1.1 km/s relative to the magnetic field. The value of ∆Ω
derived from the UVIS data is slightly less than half the previously reported values of
System III Longitude of Peak
91
0
270
180
90
0
270
180
90
0
270
180
90
0
270
180
90
0
S II
S III
S IV
O II
280
290
300
310
Day of Year 2000
280
290
300
310
Day of Year 2000
320
Figure 4.5: Linear fit to phase increase with time. The solid curve represents the phase
of azimuthal variations in composition. The solid line is the line best fit to this data.
The dotted line represents the slope (the intercept of this line is arbitrary) the data
would have if the plasma in the Io torus were subcorotating at the System IV period
defined by Brown (1995).
∆Ω ∼24.3◦ /day, which are the basis for the System IV period (Sandel and Dessler ,
1988; Woodward et al., 1994; Brown, 1995).
Although the phase increase is roughly linear, especially for S III, there are several
deviations from linearity. For example, O II appears to have a greater slope in the period
before DOY 295 than after, S II and S IV show an increase in slope during the period
of DOY 291-309, and all four ion species show a decrease in slope after day 310.
4.3.3.2
Periodograms
In order to examine our data for periodicities, we have constructed Lomb-Scargle
periodograms (Lomb, 1976; Scargle, 1982; Horne and Baliunas, 1986) using the fast
algorithm of Press and Rybicki (1989). The periodogram created from the UVIS dusk
ansa S II data is shown in Fig. 4.6. Periodograms created using from the S III, S IV,
92
Periodogram power
Periodogram power
Dusk Ansa S II
400
300
200
ωIo
100
0
0.00
0.05
0.10
0.15
Frequency (hours−1)
0.20
0.25
400
System III
System IV
300
200
100
0
0.090
0.095
0.100
Frequency (hours−1)
0.105
0.110
Figure 4.6: Lomb-Scargle periodogram of UVIS dusk ansa S II data. The primary peak
of the periodogram is found below the System III rotation frequency, but above the
System IV rotation frequency of Brown (1995).
or O II data are quite similar; likewise, periodograms made from the dusk ansa data
are virtually indistinguishable from periodograms made from the dawn ansa data. The
periodogram has a very large peak near a frequency of 0.10 h−1 , with smaller peaks
occurring near 0.05 h−1 and its harmonics. A secondary peak, located at Io’s orbital
frequency of 0.024 h−1 , is seen only in the S II data, in contrast to Sandel and Broadfoot
(1982b) who report a strong correlation of the brightness of the S III 685Å feature with
Io’s phase. No other significant peaks are present in the UVIS periodograms.
The lower panel of Fig 4.6 shows the region around the primary peak in more
detail. The locations of the System III and System IV frequencies are also shown. The
sharp peak seen in the upper panel actually consists of two closely spaced but separate
peaks: the primary located at a frequency of 0.099277 h−1 (period of 10.073 h) and
the secondary at 0.10061 h−1 , slightly below the System III frequency of 0.10076 h−1 .
93
Table 4.1: Peak periodogram values and uncertainties
Ion Species
S II
S III
S IV
O II
a
Dusk Ansa
Period ± Uncertaintya
10.073 ± 0.0036 h
10.057 ± 0.0125 h
10.067 ± 0.0039 h
10.049 ± 0.0188 h
Dawn Ansa
Period ± Uncertaintya
10.073 ± 0.0039 h
10.061 ± 0.0140 h
10.073 ± 0.0039 h
10.051 ± 0.0203 h
3σ uncertainty derived from the 99.7% value of synthetic datasets
The periods obtained from the frequency of the peak in the periodograms are given in
Table 4.1.
The probability that the tallest peak in a Lomb-Scargle periodogram is the result
purely of Gaussian-distributed noise in the data (also known as the false alarm probability) can be derived from the height of the tallest peak according to the equation:
h
iNi
F = 1 − 1 − exp−h
(4.5)
where h is the height of the tallest peak and Ni is the number of independent frequencies
in the periodogram. It is worth noting that Eq. 4.5 is only valid for the tallest peak, and
cannot be used to assess the significance of any other peaks present in the periodogram,
such as the peak near the System III frequency.
While it is relatively straightforward to use Eq. 4.5 to obtain the significance
of the primary peak in a Lomb-Scargle periodogram, it is much trickier to obtain an
estimate of the uncertainty in the frequencies of the peaks present, ∆f. Kovács (1981)
derives several expressions for calculating the ∆f from standard periodogram methods,
the derivation assumes the data contain only a single periodic signal with Gaussian
noise, even data spacing, and no gaps in the data. Although Baliunas et al. (1985)
found that that these expressions were still valid in the case of unevenly sampled data,
the UVIS data contain numerous gaps in the data and may also contain signals at
multiple frequencies, rendering this approach invalid.
94
An order-of-magnitude estimate of ∆f can be made by assuming that ∆f is equal
to the difference in frequency between a periodic signal that completes n cycles during
the observing period and one that completes n +
1
2
cycles. The UVIS inbound staring
mode observing period lasted slightly less than 1066 hours, which leads to a ∆f of
4.69 × 10−4 h−1 . For a signal with a period of ∼10 hours, this corresponds to an
uncertainty of 0.05 hours.
This method of estimating ∆f is clearly an oversimplification as it fails to account
for the actual sampling rate or the level of noise present in the data. We therefore adopt
the approach of Brown (1995) and use synthetic data sets to estimate the uncertainty
in our determination of frequency. We constructed 1000 synthetic data sets containing
a single periodic signal with a period of 10.073 hours. This signal had an amplitude
similar to that observed by UVIS and was sampled at the same times as the UVIS
dataset. Gaussian noise, at the level found in the UVIS data, was also added to the
synthetic data. A typical synthetic data set and the actual UVIS S II data from the
dusk ansa are plotted in Fig. 4.7.
We created a Lomb-Scargle periodogram from each synthetic dataset. An example
of a periodogram created from one of the synthetic datasets is presented in Fig. 4.8. Like
the periodogram created from the real data, c.f. Fig. 4.6, the synthetic periodogram
contains a large peak near 0.10 h−1 with secondary peaks near 0.05 h−1 and 0.15 h−1 .
The presence of the secondary peaks in the synthetic periodogram implies that they
are the result of what Horne and Baliunas (1986) call “spectral leakage”—side lobes
caused by the data sampling and the finite observation period. Since there is a 20-hour
periodicity in the actual data sampling, it should not be surprising that spectral power
from the primary peak is aliased to these frequencies.
For each synthetic periodogram, we recorded the difference between the frequency
of the peak and the frequency of the periodic signal actually present in the synthetic
data. We assigned the 68.3%, 95.5%, and 99.7% values a significance of 1σ, 2σ and 3σ,
95
1.6
1.4
UVIS S II DATA
1.2
Relative Mixing Ratio
1.0
0.8
0.6
0.4
1.6
1.4
SYNTHETIC S II DATA
1.2
1.0
0.8
0.6
0.4
280
290
300
Day of Year 2000
310
320
Figure 4.7: Comparison of real UVIS S II data from the dusk ansa with synthetic
data. The synthetic data consist of a sinusoidal variation with a period of 10.069 hours
with added Gaussian noise sampled at the same times as the UVIS observations. The
amplitude of the sinusoidal variation in the synthetic data changes with time in order
to match the real UVIS data.
respectively. This method yielded a 3σ estimate of ∆f for the dusk ansa S II periodogram
of 3.56×10−3 h−1 or 0.0354%. The corresponding 3σ estimate of the uncertainty in the
periods derived from the peak frequency of the periodograms are given in Table 4.1. Like
Brown (1995), we find that our estimates of ∆f derived from the synthetic data sets are
much smaller than the order-of-magnitude estimate of ∆f derived from the length of the
observation period. However, given that the slope of the phase increase with time shown
in Fig. 4.5 varies over the observing period, it is doubtful whether this result has any
real physical significance. To illustrate this point, we divided the observing period into
three equal parts and made periodograms from the data in each. The resulting periods
derived from the periodogram peaks are given in Table 4.2. The ion S II provides an
extreme example, with a period that varies from 9.996–10.137 hours. This effect can
be readily seen in the varying slope of the S II curve in Fig. 4.5. Since the value of the
96
Synthetic S II data
Periodogram power
500
SYNTHETIC DATA
400
300
200
100
0
0.00
0.05
0.10
0.15
Frequency (hours−1)
0.20
0.25
Periodogram power
500
System III
System IV
Actual Period
400
300
200
100
0
0.090
0.095
0.100
Frequency (hours−1)
0.105
0.110
Figure 4.8: Periodogram from synthetic S II data. The primary peak is displaced slightly
from the actual period in the synthetic data. The secondary peaks near 0.05 h−1 and
0.15 h−1 found in Fig. 4.6 also appear in this periodogram, suggesting that they are
spurious peaks due to the sampling of the UVIS data.
period derived from the location of the periodogram peak depends on both the time
and the duration of the observation window, it should be used with some caution.
4.3.4
Amplitude Variations and System III Modulation
Figure 4.9 shows the relative amplitude of the azimuthal variation in composition
(Ai /ci ) derived from the sinusoidal fit to the mixing ratios of the 4 main torus ion
species (cf. Section 4.3.2). All four ion species have non-zero amplitude for the entire
observation period, suggesting that azimuthal variation in plasma composition is an
omnipresent feature of the Io torus. The amplitudes for the relatively minor species of
S II and S IV, show dramatic changes with time. From the start of the UVIS observations
on day 275, the amplitude of the azimuthal variation in torus composition for both S II
97
Table 4.2: Peak periodogram values of subdivided data
Ion
S II
S III
S IV
O II
Epoch
All
Beginning
Middle
End
All
Beginning
Middle
End
All
Beginning
Middle
End
All
Beginning
Middle
End
Dusk Ansa
10.073
10.019
10.137
9.996
10.057
10.041
10.032
10.023
10.067
10.041
10.087
10.014
10.049
10.028
10.014
9.983
Dawn Ansa
10.073
10.014
10.137
9.992
10.061
10.059
10.041
10.028
10.073
10.032
10.091
10.014
10.051
10.050
10.010
9.974
98
0.25
S II
S III
S IV
O II
Amplitude (% of base level)
0.20
0.15
0.10
0.05
0.00
280
290
300
Day of Year 2000
310
Figure 4.9: Relative amplitude (Ai /ci ) of the azimuthal variations in composition as a
function of time. The relative amplitudes of the major ion species O II and S III remain
around the few percent level, while the relatively minor ion species S II and S IV vary
between 4–25%.
and S IV increases rapidly with time. When the amplitudes reach their peak value
around day 279, they are nearly a factor of two greater than when first observed. After
reaching their peak value, both amplitudes fall rapidly to a minimum value around day
293, at which time they are roughly 1/4–1/3 of their peak value. The amplitudes of the
two ion species again increase quickly until day 300 when the S II amplitude levels out
and the amplitude of S IV decreases somewhat. By day 306, the amplitudes of both ion
species are increasing again, reaching a peak around day 308.
The ion species O II and S III also show variations in amplitude with time, but less
dramatically than for S II and S IV. The amplitudes for these ion species remain in the
range of 1–6% during the observing period. Given that O II and S III are the primary
ion species for oxygen and sulfur in the Io torus and that S III serves as an intermediate
99
product of the chemical processes that convert S II into S IV (or vice versa), this is not
surprising. Neither O II nor S III show a well-defined amplitude peak around day 279,
although both have amplitude peaks coincident with the amplitude peaks of S II and
S IV on day 308.
The period of time between the peaks of S II amplitude is ∼29 days—the same
period as the beat between the 9.925-hour System III rotation period and the observed
10.07-hour periodicity. This suggests that the amplitude of the azimuthal variation in
torus composition might be modulated by System III. To illustrate this, the amplitude
of the compositional modulation as a function of time is plotted separately for each
species in Fig. 4.10. The color of the plotting symbols represents the System III phase
of the azimuthal variation, i.e. the location of the mixing ratio peak, for each ion species.
The steady increase of phase with time is readily apparent in all four ion species. The
peaks in amplitude of S II occur at a phase of λIII ≈ 210◦ . The S II amplitude minimum
occurs at a phase of λIII ≈ 30◦ . Conversely, the amplitude peaks for S IV occur at a
phase of λIII ≈ 30◦ , while the amplitude minimum occurs at a phase of λIII ≈ 210◦
Figure 4.11 shows the modulation of the amplitude of the compositional variation
by System III longitude in a graphical manner for the three times marked in Fig. 4.10.
In contrast to Fig. 4.10, which shows the values of amplitude and phase derived from
the sinusoidal fits, Fig. 4.11 shows the actual mixing ratio observed in each 10◦ System
III longitude bin, relative to the azimuthal average. During periods 1 and 3, the mixing
ratio of S II shows a strong enhancement in the longitude sector λIII =180–270◦ and a
strong depletion in the longitude sector λIII =340–70◦ . During the same periods, the
mixing ratio of S IV shows a strong enhancement between λIII =330–60◦ and a strong
depletion between λIII =180–270◦ . During period 2, S II shows a very weak enhancement
between λIII =320–50◦ and a weak depletion between λIII =160–250◦ , while S IV shows
an enhancement between λIII =160–250◦ and a slight depletion between λIII =330–60◦
100
System III Longitude of peak mixing ratio
Amplitude of Azimuthal Compositional Variation
0.30
0.25
0
30
60
90
120
150
S II
180
210
240
270
300
330
360
S III
0.20
0.15
0.10
0.05
0.25
S IV
O II
0.20
0.15
0.10
0.05
0.00
275 280 285 290 295 300 305 310 315
280 285 290 295 300 305 310 315 320
Day of Year 2000
Figure 4.10: Relative amplitude of the azimuthal compositional variations as a function
of time. The color of the plotting symbols represents the location (in System III longitude) of the peak mixing ratio. Numbers mark the locations of the three intervals used
in Fig. 4.11
4.4
Discussion
Initial analysis of the UVIS observations of the Io torus found long-term azimuthal
variations in EUV brightness (Steffl et al., 2004a), electron density, and electron temperature (Fig. 4.2) on the order of ∼5%. However, over shorter timescales (a few days)
the torus is found to exhibit azimuthal variations in ion composition of up to 25%.
Significant azimuthal compositional variations were present during the entire observing
period, suggesting that this is the natural state of the Io torus. Although the primary
ion species of S III and O II displayed azimuthal variations of only a few percent, S II
and S IV displayed azimuthal variations of up to 25%. Models of the torus that treat
the mixing ratios of these ion species as azimuthally uniform must therefore be used
with some caution. Similar caution must be exercised when attempting to apply in situ
101
% Deviation From Azimuthal Average
−30
−25
#1
DOY 278.7−279.9
S II
−20
−15
−10
−5
0
5
270°
180°
#2
DOY 293.6−294.8
20
0° 180°
180°
S IV
0°
90°
270°
0° 180°
90°
30
0°
0° 180°
180°
25
90°
270°
90°
270°
#3
15
270°
90°
270°
DOY 306.1−308.1
10
0°
90°
Figure 4.11: Graphical representation of the modulation of the amplitude of the azimuthal variation with System III longitude. For each time interval, the torus has been
divided into 36 10◦ longitude bins. Each bin is colored according to its deviation from
the average mixing ratio during that time interval. Intervals 1 and 3 correspond to
periods of maximum amplitude, while interval 2 corresponds to minimum amplitude.
The locations of these intervals are marked in Fig. 4.10.
102
measurements obtained in one azimuthal region to the torus as a whole. This may help
to explain some of the wide range in electron densities measured by the Galileo PLS
(Frank and Paterson, 2001).
The azimuthal variations in the composition of the Io torus are observed to have
a period of 10.07 hours—1.5% longer than the System III rotation period of Jupiter
and 1.3% shorter than the System IV period. In ultraviolet, optical, and near-infrared
observations of S II and S III obtained between 1979 and 1999, the 10.21 hour System
IV period remained remarkably constant (Roesler et al., 1984; Sandel and Dessler ,
1988; Brown, 1995; Woodward et al., 1997; Nozawa et al., 2004), which suggested that
this period might be somehow intrinsic to the Jovian magnetosphere. The presence
of a strong periodicity at 10.07 hours (and corresponding lack of any periodicity at
the System IV period), is therefore rather surprising. While both Brown (1995) and
Woodward et al. (1997) observed abrupt changes in the phase of the azimuthal variation
in brightness of [S II] 6731Å which caused their initial analysis to identify a spurious
periodicity of 10.16 hours, it is evident from Fig. 4.4 that no such change in phase
occurred during the UVIS observations.
Given the phenomenological similarity between the UVIS 10.07 hour periodicity
and the System IV periodicity, we propose that the same physical mechanism is responsible for both. It is plausible that the factor of 3–4 increase in the amount of neutrals
supplied to the torus in September 2000 (Delamere et al., 2004) altered the mechanism responsible for producing the System IV period in such a manner that a 10.07
hour period was produced. Based on measurements of Iogenic dust by the Galileo Dust
Detector System (Krüger et al., 2003), such events occur relatively infrequently (only
one event of this magnitude was detected during 6.5 years of observations). If future
observations of the Io torus detect periodicity at the 10.21 hour System IV period (and
not at 10.07 hours), it would suggest that the intermediate period observed by UVIS
was a result of the neutral source “event” that occurred in September 2000. Ground-
103
based observations in December 2000 (roughly one month after the end of the UVIS
staring-mode observations presented in this paper) found the brightness of torus [S II]
6712Å and 6731Å emissions varied with a period of 10.14±0.11 hours (Nozawa et al.,
2004), which suggests the torus periodicity might have been returning to the “typical”
System IV period. However, given the relatively large uncertainty in this value, it is
consistent with both the 10.07 hour period measured by UVIS and the canonical 10.21
hour System IV period, so no firm conclusions can be drawn.
It is important to reiterate that we do not (and can not) directly measure the
rotation speed of the torus plasma with UVIS. Rather, we derive the rotation period of
azimuthal variations in the composition of the Io torus. This value will be affected by
both the actual rotation speed of the plasma and any temporal changes in the plasma
composition resulting from torus chemistry.
In order to produce the 10.07 hour periodicity in the UVIS data by subcorotation
of torus plasma, the plasma would need to lag the local corotation velocity by 1.5%
(∼0.19 km/s/RJ ). In order to maximize signal-to-noise in the torus spectra, we averaged together spectra from three rows on the detector, as described in Section 4.2.
However, if we analyze spectra extracted from just a single row on the detector, the
same 10.07 hour periodicity is evident throughout the observing period. Given that the
spatial resolution of UVIS increased by a factor of two during the observing period (a
result of Cassini’s decreasing distance to Jupiter), this would require the deviation from
corotation to remain constant over a large range of radial distances—in direct conflict
with observations of the radial velocity of S II that showed a strong variation in the
amount of subcorotation with radial distance (Brown, 1994b). In order for subcorotation of the torus plasma to be directly responsible for the periodicity in the UVIS data,
the Io torus must have been in a radically different state during the Cassini encounter
than it was in 1992 (when the observations of Brown (1994b) were made). Since there
are also theoretical arguments against producing such periodicities in the torus directly
104
from plasma subcorotation (Dessler , 1985; Sandel and Dessler , 1988), we consider this
possibility unlikely.
Instead, the UVIS observations are consistent with the theory proposed by Brown
(1994a) that the System IV periodicity is the result of the pattern speed of a compositional wave propagating through the Io torus. While the individual particles of the torus
lag corotation by an amount appropriate for their radial distance, the group velocity of
the compositional wave lags rigid corotation by 1.5%.
The amplitude of the azimuthal variation in composition appears to be modulated
by its position relative to System III longitude. During times when the peak (minimum)
in S II (S IV) mixing ratio is aligned with a System III longitude of 210◦ ±15◦ the amplitude of the azimuthal variation in composition is enhanced. When the peak (minimum)
in S II (S IV) mixing ratio is aligned with a System III longitude of 30◦ ± 15◦ , the amplitude of the variation is diminished, i.e. the torus becomes more azimuthally uniform.
Since UVIS observed only 1 1/2 modulation cycles, it is difficult to say whether the
apparent modulation by System III longitude is real or just coincidental. However, similar modulations in the brightness of the S III 685Å feature observed by the Voyager 2
UVS, the probability of detecting nKOM emission with the Voyager PRA instruments,
and the brightness of torus [S II] 6731Å emissions were reported by Sandel and Dessler
(1988) and Schneider and Trauger (1995) and may also be present in the data of Pilcher
and Morgan (1980).
In light of the UVIS observations of a subcorotating azimuthal variation in composition whose amplitude is modulated by its position relative to System III longitude,
several apparently contradictory observations of the Io torus can be explained. First,
because the azimuthal variation subcorotates relative to System III, the phase of the
variation (i.e. the location of peak) should be observed over the full 360◦ range of longitude. However, because the amplitude of the azimuthal variation is greatest when
the peak in S II mixing ratio is located near λIII = 200◦ azimuthal variations in the
105
brightness of S II emissions will be preferentially detected in the “active sector” centered
around λIII = 200◦ .
The detection of azimuthal variability in the brightness of the [S II] 6716Å/6731Å
and 4069Å/4076Å doublets but not in the brightness of the [O II] 3726Å/3729Å doublet
(Morgan, 1985), arises from the fact that the amplitude of the azimuthal variation of
the S II mixing ratio ranges from 10–25% while the amplitude of the azimuthal variation
of the O II mixing ratio is ≤5%. The correlation of S II brightness with S III brightness
observed by Rauer et al. (1993) is also consistent with the correlation of the S II and
S III mixing ratios observed by UVIS.
The two week transition between azimuthally varying and azimuthally uniform
states observed by Pilcher and Morgan (1980) is just the manifestation of the modulation period, assuming that the modulation period was ∼14 days (which corresponds
to the beat between the 9.925 hour System III period and the 10.214 hour System IV
period). The ∼14 day modulation period of the amplitude of the azimuthal compositional variation also explains why Morgan (1985) observed a strong azimuthal variation
in the brightness of the torus [S II] 6731Å emission with a peak near λIII = 180◦ during
the period of 14–17 February 1981, while Brown and Shemansky (1982) detected no
significant azimuthal variation in the same emission line on 23–24 February 1981. Furthermore, the subcorotation and amplitude modulation of the azimuthal variation in
composition explains why the Voyager 2 UVS observed only a weak azimuthal variation
in the brightness of the S III 685Å feature with a peak between 330◦ < λIII < 40◦
on day 122 of 1979 (the amplitude of the azimuthal variation was at a minimum), a
stronger azimuthal variation (the azimuthal variation had reached it’s minimum amplitude with the S III peak near 20◦ and was increasing in amplitude) with a peak between
40◦ < λIII < 100◦ on day 124 of 1979 (assuming the azimuthal pattern had the 10.2
hour System IV period, the phase should increase by ∼24◦ /day), and no significant
System III variation when the spectra were averaged over the 44 day pre-encounter
106
period (the System III longitude of the peak varies with time). Whereas the failure of
Gladstone and Hall (1998) to detect any significant variation in the brightness of torus
emissions with System III longitude results from the averaging of EUVE data obtained
during the interval from 19–24 June 1996. During this time, the peak of the azimuthal
variation would have shifted by over 120◦ in System III longitude.
Finally, it is also interesting to note that the two largest torus EUV luminosity
events reported by Steffl et al. (2004a) occurred on days 280 and 307, near the modulation peaks. During these events, which last for roughly 20 hours, the power radiated by
the Io torus in the EUV increases rapidly by ∼ 20% before gradually returning to the
pre-event level. Since several other brightening events occurred throughout the 45-day
observing period, the timing of the two largest events may be coincidental.
The next step is to model the UVIS observations by extending the torus chemistry
model of Delamere et al. (2004). Preliminary results suggest that the interaction of a
subcorotating (at 10.07 hours), azimuthally varying source of hot (∼55 eV) electrons
with a corotating (i.e. fixed in System III), azimuthally varying source of hot electrons
can produce torus behavior that is both qualitatively and quantitatively similar to the
UVIS observations. The 28.8 day modulation period arises naturally from the beating
of the 10.07 hour period with the 9.925 hour System III period. While it is not too
difficult to imagine a source mechanism capable of producing hot electrons in amounts
that vary as a function of System III longitude, it is far from obvious what could cause
an additional, azimuthally-varying pattern of hot electrons to rotate with a period 1–
3% slower than the System III period. At present we know of no suitable physical
mechanism capable of producing such behavior.
4.5
Conclusions
We have presented an analysis of the temporal and azimuthal variability of the
Io plasma torus during the Cassini encounter with Jupiter. Our main conclusions are:
107
(1) The torus exhibited significant long-term compositional changes during the
UVIS inbound observing period. These compositional changes are consistent
with models predicting a factor of 3–4 increase in the amount of neutral material supplied to the torus in early September, 2000. These results are discussed
in more detail by Delamere et al. (2004).
(2) Persistent azimuthal variability in torus ion mixing ratios, electron temperature,
and equatorial electron column density was observed. The azimuthal variations
in S II, S III, and electron column density mixing ratios are all approximately
in phase with each other. The mixing ratios of S IV and O II and the torus
equatorial electron temperature are also approximately in phase with each other,
and as a group, are approximately 180◦ out of phase with the variations of S II,
S III, and equatorial electron column density.
(3) The phase of the observed azimuthal variation in torus composition drifts 12.2◦ /day,
relative to System III longitude. This implies a period of 10.07 hours, 1.5%
longer than the System III rotation period. This period is confirmed by LombScargle periodogram analysis of the UVIS data.
(4) The relative amplitude of the azimuthal variation in composition is greater for
S II and S IV. These species have relative amplitudes that vary between 5–25%
over the observing period. The major ion species, S III and O II, have relative
amplitudes that remain in the range of 2–5%.
(5) The amplitude of the azimuthal compositional variation appears to be modulated by its position relative to System III longitude such that when the peak
in S II mixing ratio is aligned with a System III longitude of 210±15◦ the amplitude is enhanced, and when the peak in S II mixing ratio is aligned with a
System III longitude of 300±15◦ the amplitude is diminished.
Chapter 5
Modeling
or
Theoretical Wiggles Match Observational Wiggles1
Analysis of remote sensing and in situ observations can provide a snapshot of the
composition, temperature and density of the Io plasma torus. However, in order to gain
an insight into the underlying physical processes that govern the properties of the Io
torus, it is necessary to model the flow of mass and energy through the torus. This
chapter presents the results of modeling the composition of the Io plasma torus and its
temporal and azimuthal variability during the UVIS observations.
5.1
Model Description
The first attempt to model the physical processes in the Io plasma torus ab initio
was by Barbosa et al. (1983). In their model, all the energy supplied to the torus came
from the “pickup” energy of newly created ions. The extended neutral clouds that
are the source of plasma for the Io torus orbit Jupiter on Keplerian orbits, which at a
distance of 6 RJ corresponds to an orbital velocity of 17.2 km/s. Plasma in the torus
corotates (to within a few percent) with the magnetic field of Jupiter. Since Jupiter’s
magnetic field rotates every 9.925 hours, torus plasma at 6 RJ has a rotational velocity
of 75.4 km/s. If a neutral atom becomes ionized, it is “picked-up” by Jupiter’s magnetic
field and rapidly accelerated to corotation speeds. The energy required to do this heats
the ion to the pickup temperature, which is given by:
1
N. M. Schneider’s summary of modeling work presented at my comps II defense on 10 April 2002
109
1
3
2
kTpu = mα vrel
2
2
(5.1)
where
µ
vrel = ΩJ r −
GMJ
r
¶1/2
(5.2)
where ΩJ is the angular frequency of Jupiter’s rotation and MJ is the mass of Jupiter.
The class of models that used the energy from pickup ions to power the torus became
known as “neutral cloud theory” (NCT).
Shemansky (1988) noted that NCT models that used realistic values for the average charge state of the Io torus and improved atomic data failed to supply the torus with
enough energy to match the observed ion composition and power output. This apparent
failure of NCT models became known as the “energy crisis” (Smith et al., 1988). The
solution to the energy crisis came by adding energy to the torus via a small suprathermal
population of electrons (Shemansky, 1988). There is observational evidence to support
the existence of a high-energy component of the torus electron distribution function
(Smith and Strobel , 1985; Meyer-Vernet et al., 1995; Frank and Paterson, 2000b).
In the past 15 years, several other models have used the modified NCT approach
to model the mass and energy flow of the Io plasma torus (Barbosa, 1994; Schreier
et al., 1998; Lichtenberg et al., 2001; Smyth and Marconi, 2003; Delamere and Bagenal ,
2003). The torus model of Delamere and Bagenal (2003) was used for the work in this
thesis. This model is presented in some detail by Delamere and Bagenal (2003) and to
a lesser extent by Delamere et al. (2004).
5.1.1
Governing Equations
Since the model of Delamere and Bagenal (2003), and extensions to it, is used
throughout this chapter, it is useful to recapitulate their description of the equations
110
governing the model. The model uses a second-order Runge-Kutta method to integrate
the following equations for the flux of particles:
∂nα
= Sm − Lm
∂t
(5.3)
∂( 32 nα Tα )
= SE − LE
∂t
(5.4)
and energy:
where nα is the number density of species α, Tα is the temperature (in eV) of species
α and S and L are the source and loss rates of either particles or energy. The particle
number source term for each ion species is given by:
Sm = Iα− (Te )nα− ne + Iαh− (Te,hot )nα− ne,hot + Rα+ (Te )nα+ ne +
X
kβ,γ nβ nγ
(5.5)
β,γ
where I(Te ) and I h (Te,hot ) are the electron impact ionization rate coefficients for the
thermal and hot electron populations, R is the total recombination rate coefficient, and
α− and α+ are the lower and higher ionization states of ion species α. The final term
of Eq. 5.5 represents the sum of all charge exchange reactions between species β and
γ that convert species β into species α. The charge exchange reactions included in the
model and their rate coefficients are listed in Table 5.1.
Similarly, the loss term for particles of species α is given by:
Lm = Iα (Te )nα ne + Iαh (Te,hot )nα ne,hot + Rα (Te )nα ne +
X
β
where τ is the timescale for radial transport of torus plasma.
The source term for the energy of species α is given by:
kα,β nα nβ +
nα
τ
(5.6)
111
SE
= Iα− (Te )ne nα− Tα− + Iαh− (Te , hot)ne,hot nα− Tα− + Rα+ (Te )nα+ ne Tα+ (5.7)
+
X
kγ,β nγ nβ Tβ +
γ,β
X
ν̄²α\β nβ nα (Tβ − Tα )
β=i,e
For reactions involving the ionization or charge exchange of neutral atoms, the temperature of the newly created ions is obtained from Eq 5.1. At 6 RJ , the pickup temperature
is 378 eV for sulfur ions and 189 eV for oxygen ions.
The last term in Eq. 5.7 is the thermal equilibration between species α and species
β, summed over all ion and electron species. Although this term is included in the
energy source term, SE , (Tβ − Tα ) can be either positive or negative. Assuming a
Maxwellian distribution of species α and β, the thermal equilibration rate coefficient,
α\β
ν̄²
is obtained from the NRL Plasma Formulary (Huba, 2002):
ν̄²α\β = 1.8 × 10−19
(mα mβ )1/2 Zα2 Zβ2 nβ λαβ
3/2
(mα Tβ + mβ Tα )
cm3 sec−1
(5.8)
where m is the mass of the particle, Z is the charge of the particle, and λαβ is the
Coulomb logarithm. The Coulomb logarithm is an approximation derived from scattering theory (Huba, 2002). This approximation is good to ∼10% and fails when λαβ ≈ 1.
Typical values of λαβ fall in the range of 20–30. For electron-hot electron collisions the
Coulomb logarithm is given by:
λee =

³
´



23 − ln n1/2 T −3/2 ,
Te & 10eV
³
´



24 − ln ne1/2 Te−1 ,
Te . 10eV
e
e
For electron-ion collisions the Coulomb logarithm is given by:
(5.9)
112

´
³


1/2
−3/2

23
−
ln
n
ZT
,

e
e




³
´
−1 ,
λei = λie = 24 − ln n1/2
T
e
e




³
´



2 T −3/2 µ−1 ,
30 − ln n1/2
Z
i
i
Ti me /mi < Te < 10Z 2 eV
Ti me /mi < 10Z 2 eV < Te
(5.10)
Te < Ti Zme /mi
where ne and Te are the density and temperature of the thermal electron population.
Finally, for ion-ion collisions the Coulomb logarithm is given by:
"
λii0 = λi0 i
(µ + µ0 )
= 23 − ln ZZ
µTi0 + µ0 Ti
0
µ
ni Z 2 n0i Z 02
+
Ti
Ti0
¶1/2 #
(5.11)
where µ is the ion mass in proton units (mi /mp ).
The energy loss for ion species α is given by:
LE
= Iα (Te )ne nα Tα + Iαh (Te , hot)ne,hot nα Tα + Rα (Te )nα ne Tα
+
X
kα,β nα nβ Tα +
α,β
(5.12)
nα Tα
τ
The temperature of the thermal electron population is determined by the balance
of energy gain via Coulomb interactions with ions and the hot electron population
and losses of energy via collisions with ions that excite radiative transitions and radial
transport:
∂(ne Te ) X e\β
2X
ne T e
=
ν² ne (Tβ − Te ) −
ρβ,λ (Te , ne )ne nβ −
∂t
3
τ
β
(5.13)
β,λ
where ρβ,λ (Te , ne ) is the radiative rate coefficient for ion species β for an electron temperature Te and electron density ne and the sum is over all wavelengths and ion species.
The factor of 2/3 results from the radiative rate coefficients being given in units of
energy.
113
5.1.2
Model Parameters
The basic model of Delamere and Bagenal (2003) has five parameters that can
be adjusted to match the conditions observed in the Io torus: Sn , O/S, fh , Te,hot , and
τ . Sn is quite simply the sum of the neutrals (O I plus S I) added at the centrifugal
equator of the torus in units of cm−3 s−1 .
O/S is the ratio of oxygen to sulfur in the neutral source such that:
SO =
SS =
(O/S)Sn
1 + (O/S)
Sn
1 + (O/S)
(5.14)
(5.15)
Since Io’s atmosphere is predominantly SO2 , with smaller amounts of S2 , SO, and S
(McGrath et al., 2004), the value of O/S should be .2.
As noted by Shemansky (1988) NCT models must include an additional source
of energy to produce an ion composition similar to those observed in the Io torus. For
the model of Delamere and Bagenal (2003), this is done by separating the electrons
into two independent Maxwellian populations: a thermal electron population which
contains the bulk of the electrons, and a much smaller hot electron population. The
relative abundance of the two populations is controlled by the parameter fh , with fh of
the total electrons in the hot population, and 1-fh in the thermal electron population.
For “equilibrium” conditions in the Io torus, fh ≈ 0.002.
While the temperature of the thermal electron population is determined by Eq. 5.13,
the temperature of the hot electron population held constant at Te,hot . Since the hot
electron population is a significant source of energy for the thermal electron population
and the colder ion species, holding Te,hot constant is equivalent to continuously supplying this population with energy. Of the five parameters of the basic model, Te,hot is the
least sensitive, owing largely to the relatively flat ionization curves over the range in
energy of 40–200 eV.
114
The details of convective radial transport are ignored by the basic model. Instead,
a single parameter, τ , is used to specify the lifetime of torus ions against radial transport.
Radial transport affects all ion species equally.
5.1.3
Reaction Rate Coefficients
Rate coefficients for electron impact ionization are calculated using the fit formulae given by Voronov (1997). These fits are based on the “Belfast group” recommended
data (Bell et al., 1983; Lennon et al., 1988).
While important for many astrophysical plasmas, photoionization has very little
effect on the Io plasma torus. At Jupiter, during solar maximum, the lifetime of atomic
oxygen against photoionization is approximately 530 days, while atomic sulfur has a
lifetime of 130 days (Hübner et al., 1992). The lifetimes against photoionization for
ionic species of oxygen and sulfur will be even longer. Since these lifetimes are several
orders of magnitude greater than the timescales for other processes (e.g. electron impact
ionization, charge exchange, recombination, etc.), the effects of photoionization can be
ignored.
For ions with multiple electrons, recombination rate coefficients are usually divided into two separate processes: radiative recombination and dielectronic recombination (Osterbrock , 1989). Radiative recombination is the inverse process of direct
photoionization:
X ++ + e− → X + + ν
(5.16)
while dielectronic recombination is a two-step process whereby an incident electron
combines with the target ion, leaving the target ion in a doubly excited, potentially
autoionizing, state. The doubly excited ion will either autoionize (One electron moves
to a less energetic state. The released potential energy is absorbed by the second, excited
electron. The energy of the second electron now exceeds the ionization potential.) or
115
settle into a bound state after radiating away the excess potential energy:
X ++ + e− → (X + )∗∗ →




X ++ + e−



X + + ν
(5.17)
The total recombination rate coefficient, αr (Te ) cm3 s−1 , is just the sum of the
rate coefficients for radiative and dielectronic recombination. The recombination rate
coefficients used in this work differ from those used in previous versions of the torus
chemistry model (Delamere and Bagenal , 2003; Delamere et al., 2004). However, since
recombination reactions are generally much slower than other processes that occur in
the torus (cf. Tables 5.3–5.19, these changes do not significantly affect the model results.
Total recombination rate coefficients for oxygen ion species are obtained from
Nahar (1999), and total recombination rates for the sulfur species S II and S III are
obtained from Nahar (1995) and the associated erratum Nahar (1996). (By convention, recombination rate coefficients are listed by the final ionization state, so αrS I is
the rate coefficient for S II recombining to form S I). In general, the rate coefficients
published by S. Nahar agree well with previously published results at low temperatures.
At temperatures typical of the Io torus, however, the Nahar rates can be up to an order
of magnitude lower than previously published values. Since the work by Nahar is the
most recent treatment of the recombination rate problem for sulfur and oxygen ions
and employs a more sophisticated technique than previous studies, these rates are used
in the model. For the recombination of S II to S I (αrS I ) S I, the radiative recombination rate coefficient of Shull and van Steenberg (1982) is used, while the dielectronic
recombination rate coefficient is obtained from Mazzotta et al. (1998).
In addition to ionization and recombination, charge exchange reactions play an
important role in the torus chemistry. Sixteen charge exchange reactions between atomic
and ionic species of sulfur and oxygen are included in the model. Charge exchange reaction rates are taken from McGrath and Johnson (1989) and Smith and Strobel (1985).
116
Table 5.1: Charge exchange reactions
Reaction
S+ + S++ → S++ + S+
S + S+ → S+ + S∗
S + S++ → S+ + S+
S + S++ → S++ + S∗
S + S+++ → S+ + S++
O + O+ → O+ + O∗
O + O++ → O+ + O+
O + O++ → O++ + O∗
O + S+ → O+ + S∗
S + O+ → S+ + O∗
S + O++ → S+ + O+
S + O++ → S++ + O+ + e−
O + S++ → O+ + S+
O++ + S+ → O+ + S++
O + S+++ → O+ + S++
O++ + S++ → O+ + S+++
S+++ + S+ → S++ + S++
useda
Rate Coefficientb (cm3 s−1 )
k0 = 8.1 × 10−9
k1 = 2.4 × 10−8
k2 = 3 × 10−10
k3 = 7.8 × 10−9
k4 = 1.32 × 10−8
k5 = 1.32 × 10−8
k6 = 5.2 × 10−10
k7 = 5.4 × 10−9
k8 = 6 × 10−11
k9 = 3.1 × 10−9
k10 = 2.34 × 10−8
k11 = 1.62 × 10−8
k12 = 2.3 × 10−9
k13 = 1.4 × 10−9
k14 = 1.92 × 10−8
k15 = 9 × 10−10
k16 = 3.6 × 10−10
a
Table from Delamere and Bagenal (2003).
Rate coefficients from McGrath and Johnson (1989) except k0 from Smith and Strobel (1985),
assuming relative velocities at L=6.0.
∗
Denotes a fast neutral atom that is lost from the system
b
Table 5.1 of lists the charge exchange reactions used in the model and their rate coefficients.
The radiative rate coefficients of the model are obtained from the CHIANTI
atomic physics database (described in section 3.3.1). To reduce computation time, the
model uses a lookup table of total power radiated from each ion species as a function
of electron temperature and density rather than computing the spectrum emitted from
each ion species at every time step.
5.1.4
Latitudinal Averaging
The work of (Delamere and Bagenal , 2003; Delamere et al., 2004) assumed a
homogeneous torus: the chemistry and energetics of the torus were modeled at a single
point on the centrifugal equator with a radial distance of 6.0 RJ and λIII = 110◦ or
117
λIII = 290◦ . The next step in model complexity is to take into account the latitudinal
(vertical) distribution of torus plasma.
The rapid rotation of Jupiter means that corotating plasma will experience a
significant centrifugal force. Torus plasma will be distributed along magnetic field lines
so that the force from the ambipolar electric field balances the centrifugal and pressure
gradient forces. Since the effects of the magnetic mirror force on ions in the Io torus can
be ignored (Bagenal and Sullivan, 1981), the plasma will find an equilibrium position at
the point on a given magnetic field line that is maximally distant from Jupiter’s rotation
axis. The locus of these points define the centrifugal equator plane, which lies 1/3 of
the way to the rotational equator from the magnetic equator plane (Hill et al., 1974;
Cummings et al., 1980). Since the axis of Jupiter’s dipole magnetic field is offset by 9.6◦
from the spin axis, the centrifugal equator is inclined by 6.4◦ relative to the rotational
equator.
Close to the centrifugal equator (i.e. θ . 10◦ ) the distribution of plasma along a
magnetic field line is very nearly Gaussian, i.e. the temperature of ions and electrons
is constant with latitude (θ). For a Gaussian-distributed plasma consisting of a single
ion species the density along a magnetic field line is described by a simple exponential
scale height distribution:
2
n(z) = n(0)e−(z/Hi )
(5.18)
where Hi is the scale height given by the equation:
s
2kTi (1 + Zi Te /Ti )
3mi Ω2J
s
Ti (1 + Zi Te /Ti )
RJ
= 0.64
Ai
Hi =
(5.19)
where Zi is the ion charge state of the ion, mi is the ion mass, and Ai is the ion mass
118
number (Hill and Michel , 1976; Bagenal and Sullivan, 1981; Bagenal , 1994). Eq. 5.19
is only strictly valid for a single-species plasma. For a multi-species plasma, the ambipolar electric field (and thus the scale heights of the various ion species) must be
calculated numerically from the force balance equations. However, near the centrifugal
equator, differences between scale heights calculated using Eq. 5.19 and those derived
from the force balance equations are relatively minor (P. Delamere, private communication). Since the volumetric rates of ionization, recombination and those charge exchange
reactions involving two ion species are proportional to the density squared (knα nβ ) most
of these reactions will occur near the centrifugal equator. As a result, there is no significant difference in the flux tube integrated quantities between models that use the
approximation of Eq. 5.19 and those that rigorously calculate ion scale heights.
Using this approximation greatly simplifies the expressions for the total flux tube
content of species γ:
Z
Nγ
+∞
≡
−∞
= nγ (0)
=
nγ (z) dz
Z
+∞
e−z
(5.20)
2 /H 2
γ
dz
−∞
√
πnγ (0)Hγ
where nγ (z) is the density at a distance of z from the centrifugal equator plane. The
flux tube integrated mixing ratio, Nγ /Ne , will be used for all comparisons to the UVIS
data.
For reactions between two charged species (i.e. ion-ion or ion-electron reactions),
α and β that produce species γ the change in flux tube content of species γ with time
is given by:
119
∂Nγ
∂t
Z
+∞
=
knα nβ dz
Z +∞
2
2
2
2
= knα (0)nβ (0)
e−z /Hα e−z /Hβ dz
−∞
Z +∞
2
02
= knα (0)nβ (0)
e−z /H dz
(5.21)
−∞
−∞
√
= knα (0)nβ (0) πH 0
r
where k is the reaction rate coefficient and
H0
=
2 H2
Hα
β
2
Hα +Hβ2
(P. Delamere, private com-
munication).
Because the centrifugal equator plane is tilted by 6.4◦ relative to the rotational
equator plane, the distance of the centrifugal equator from the rotational equator will
be a function of radial distance and System III longitude. Since the dipole field points
toward a System III longitude of 200◦ , the two planes will intersect at λIII =110◦ and
λIII =290◦ .
The extended neutral clouds that are the source for the plasma in the Io torus
are tightly confined to the rotational equator plane. The distance of the neutral clouds
to the centrifugal equator is a sinusoidally-varying function of System III longitude.
Mathematically, this is equivalent to introducing an offset in the scale height of one of
the distributions. Thus, for reactions involving ions (or electrons) and neutrals, Eq. 5.21
becomes:
∂Nγ
∂t
Z
+∞
=
−∞
kni nn dz
= kni (0)nn (0)
Z
+∞
−∞
Z +∞
(5.22)
e−z
2 /H 2
i
2
e−(z−z0 (λIII ))
2
/Hn
dz
2
= kni (0)nn (0)
e−(az +bz+c) dz
−∞
r
π (b2 −4ac)/4a
e
= kni (0)nn (0)
a
where z0 (λIII ) is the offset distance between the rotational equator plane and the cen-
120
trifugal equator plane at a System III longitude of λIII and
a=
Hi2 + Hn2
Hi2 Hn2
b=
−2z0 (λIII )
Hn2
c=
z02 (λIII )
Hn2
The scale height of the extended neutral clouds, Hn , is not well determined. However,
because the neutrals are cold, Hn should be small, relative to the ion scale heights. Over
the range of reasonable values for the neutral scale height, the model output is relatively
insensitive to the exact value chosen for Hn . For this work, the angular extent of the
neutral clouds was chosen to be ±1◦ from the equatorial plane, as seen from Jupiter,
which leads to a neutral scale height of 0.1 RJ at 6 RJ . For comparison, the ion scale
heights at this distance are in the range of 0.9–1.3 RJ .
The scale height for the hot electron population is assumed to be large, so that the
density of hot electrons remains approximately constant as a function of z. Therefore,
for all reactions involving hot electrons Eq. 5.21 becomes:
∂Nγ
∂t
Z
+∞
=
knα ne,hot dz
Z +∞
2
2
= knα (0)fh ne (0)
e−z /Hα dz
(5.23)
−∞
−∞
√
= knα (0)fh ne (0) πHα
where fh is the ratio of the hot electron density to the total electron density at the
centrifugal equator.
For ionization, recombination and charge exchange reactions, equations for the
change in flux tube integrated energy are obtained by replacing Nγ with Nγ Tγ and nβ
with nβ Tβ in Eqs. 5.21–5.23. The reaction rate coefficients for thermal equilibration
and radiation, however, are density dependent. For these reactions, the rate coefficient,
averaged over the flux tube, is used:
121
D
*
X
β,λ
ν̄²α\β
R +∞
E
=
+
ρβ,λ (Te , ne )
=
α\β
nβ (z)nα (z) dz
−∞ ν̄²
R +∞
−∞ nβ (z)nα (z) dz
R +∞ P
β,λ ρβ,λ (Te , ne )ne (z)nβ (z) dz
−∞
R +∞
−∞ ne (z)nβ (z) dz
(5.24)
(5.25)
Technically, the presence of a hot electron population will alter the level populations of
the ions, and thus affect the collisional excitation rates of the thermal electron populaP
tion, β,λ ρβ,λ (Te , ne ). However, this effect is minor and can be ignored.
Assuming that ions and electrons will redistribute themselves along the field line
rapidly, i.e. within one time step of the model, the density of species γ in the centrifugal
equator plane is:
Nγ
nγ (0) = √
πHγ
(5.26)
Taking the time derivative of both sides of Eq. 5.26 yields:
∂nγ (0)
1 ∂Nγ
=√
∂t
πHγ ∂t
∂Nγ
∂t
where
5.1.5
(5.27)
is given by Eq. 5.21, Eq. 5.22, or Eq. 5.23, depending on the type of reaction.
Addition of the Azimuthal Dimension
The use of latitudinal averaging introduces an azimuthally varying quantity, z0 ,
to the model. At 6 RJ , z0 will vary from 0–0.68 RJ . Since ions in the Io torus have
typical scale heights of approximately 1 RJ , the density of ions at the rotational equator
(where the neutral clouds are located) will vary by 40%. Although the actual effect on
ion-neutral reaction rates will be somewhat smaller than this (since the torus will not
be azimuthally uniform as the previous calculation assumes), the offset of the neutral
clouds can significantly affect the rate of reactions involving neutrals.
122
To investigate the effect of the varying offset distance of the extended neutral
clouds on the torus plasma, an azimuthal dimension was added to the model. In total,
24 azimuthal bins, corresponding to 15◦ segments in longitude at a radial distance of
6 RJ were included. The chemistry in each azimuthal bin is handled independently.
Approximately 80% of the ions supplied to the torus are picked-up far from the local
interaction at Io (Bagenal , 1997). Since the length of the model timestep is large
compared to the timescale for a neutral moving at 57 km/s to cross one azimuthal bin,
each azimuthal bin will see the same effective neutral density.
If the rotation speed of the torus plasma differs from rigid corotation with the
System III coordinate system, the plasma will drift from one azimuthal bin to another.
Therefore, a new model parameter, ∆v, corresponding to the difference in velocity
between the torus plasma and corotation, is required. If desired, ∆v can be a function
of System III longitude. The azimuthal transport of mass and energy is handled via
a two-step Lax-Wendroff scheme (Press et al., 1992). This method is second-order
accurate in both space and time, and is implemented after the densities and energies
for all the species have been updated.
After each time step, a sinusoidal curve is fit to the azimuthal bins of the model.
The resulting phase, amplitude, and constant offset of the best-fit sinusoidal curve are
recorded for each ion species. This is entirely equivalent to the procedure applied to the
UVIS data in Section 4.3.2.
The inclusion of an azimuthal dimension to the original IDL code resulted in a
factor of ∼30 increase in the runtime of the model. In order to keep the runtime of
the model within reasonable limits, the code was substantially rewritten. Much of the
code changes focused on vectorizing the code (taking advantage of IDL’s native array
operations to reduce or eliminate the use of FOR loops). These revisions resulted in
more than an order of magnitude decrease in the runtime of the model.
123
Table 5.2: Comparison of UVIS data and steady state model results for 14 January
2001
UVIS mixing ratios
Basic Modela
Latitude Avg.
Azimuthal Model
6.0
21.2
3.4
24.2
3.0
6.6
22.4
3.3
26.2
1.8
6.1
21.8
3.8
24.5
2.1
2.0x1028
1.9
0.25
46
46
2.0x1028
1.5
0.23
49
70
Mixing ratios
NS II /Ne , %
NS III /Ne , %
NS IV /Ne , %
NO II /Ne , %
NO III /Ne , %
Model Parameters
Snb , s−1
O/S
fh , %
Te,hot , eV
τ , days
a
Results from Delamere and Bagenal (2003)
b
Assumes an equivalent torus volume of 3.1x1031 cm3
i.e. a torus with inner radius 5.9 R
5.2
J
and outer radius 7.0 RJ
Model Results
5.2.1
Comparison to Steady-State Model Results
To assess how the addition of latitudinal averaging and the azimuthal dimension
affected the model parameters, the new model results are compared to those reported by
Delamere and Bagenal (2003) for the 14 January 2001 UVIS observations. Both models
were allowed to run until they had reached a steady-state condition, and the five model
parameters were varied so that the output mixing ratios matched the observed mixing
ratios as closely as possible. For ease of comparison, the output mixing ratios from
the latitude-averaged azimuthal model are the total flux tube-integrated mixing ratios
(see Eq. 5.20) averaged over the azimuthal dimension. The mixing ratios of the UVIS
observations and models, along with the model parameters that produced them, are
presented in Table 5.2.
The most obvious difference between the basic, one-box model and the latitudinally-
124
averaged azimuthal model (hereafter the lat-az model) is that the timescales for reactions
are significantly longer. As a result, the lat-az model settles into a steady-state condition very slowly. In this case it took approximately two years for the torus to settle
into an equilibrium state, compared to approximately one half of a year for the one-box
model. Since the actual conditions in the torus will not be constant over such long
periods, it is highly unlikely that the Io plasma torus ever reaches a true steady-state
condition. These increased reaction timescales of the lat-az model are reflected in the
increased radial transport time, τ . If the radial transport time of the lat-az model were
increased, the ionization and charge exchange reactions responsible for producing the
proper ion composition would not have enough time to act upon the torus plasma.
The second major difference between the one-box model and the lat-az model is
the O/S ratio. Both the one-box model and the lat-az model require and O/S ratio less
than 2 to match the observed composition. This is particularly so for the lat-az model,
which required an O/S ratio as low as 1.5 to bring the model oxygen mixing ratios in
line with the UVIS observations. One side-effect of the low O/S ratio is a slight excess of
S III and S IV compared to the UVIS-derived composition. However, these excesses are
within the 8–10% uncertainty in the UVIS mixing ratios. The last significant difference
between the two models is that the lat-az model requires ≈10% fewer hot electrons than
the one-box model.
5.2.1.1
Neutrals
For conditions on 14 January 2001, a total neutral source of 0.00462 atoms s−1 cm−3
was used. The the ratio of (O I)/(S I) was 1.7. Values for the various source and loss
processes of the neutrals are given in Tables 5.3 and 5.4.
Neutrals are lost through either ionization or charge exchange reactions with ions.
For S I, ionization is the dominant loss process, accounting for 60.8% of the total losses.
Owing to the relatively low ionization potential of S I (10.35 eV), most of the ionization
125
Table 5.3: Source and Loss Mechanisms for S I; 14 January 2001 equilibrium conditions
Particles
s−1 cm−3
%
Source Mechanisms
Torus neutral source
Total Sources
0.00171
0.00171
100.0
100.0
Loss Mechanisms
Ionization of S I by e−
Ionization of S I by hot e−
S + S+ → S+ + S∗
S + S++ → S+ + S+
S + S++ → S++ + S∗
S + S+++ → S+ + S++
S + O+ → S+ + O∗
S + O++ → S+ + O+
S + O++ → S++ + O+ + e−
Total Losses
0.000994
4.75x10−5
0.000173
8.88x10−6
0.000231
6.51x10−5
8.62x10−5
6.35x10−5
4.39x10−5
0.00171
58.0
2.8
10.1
0.5
13.5
3.8
5.0
3.7
2.6
100.0
Table 5.4: Source and Loss Mechanisms for O I; 14 January 2001 equilibrium conditions
Particles
s−1 cm−3
%
Source Mechanisms
Torus neutral source
Total Sources
0.00291
0.00291
100.0
100.0
Loss Mechanisms
Ionization of O I by e−
Ionization of O I by hot e−
O + O+ → O+ + O∗
O + O++ → O+ + O+
O + O++ → O++ + O∗
O + S+ → O+ + S∗
O + S++ → O+ + S+
O + S+++ → O+ + S++
Total Losses
0.000521
7.01x10−5
0.00157
5.86x10−6
6.09x10−5
1.80x10−6
0.000283
0.000394
0.00291
17.9
2.4
54.1
0.2
2.1
0.1
9.7
13.5
100.0
of S I is caused by the thermal electron population. The two most important charge
exchange reactions for S I are reaction 3 (S + S++ → S++ + S∗ ) and reaction 1 (S
+ S+ → S+ + S∗ ). In sharp contrast to S I, 79.7% of O I is lost via charge exchange
reactions. By far, the dominant charge exchange reaction in the loss of neutral oxygen
126
is O + O+ → O+ + O∗ .
5.2.1.2
Ions
Values for the particle and energy source and loss processes for torus S II ions
can be found in Table 5.5. The primary source process for S II is the charge exchange
reaction: S+ + S++ → S++ + S+ . Although this reaction results in no net flux of S II,
since the temperature of S III (58.4 eV) is nearly a factor of two less than the temperature
of S II (110.9 eV), it is a significant energy loss process. When this reaction is excluded,
the dominant source of S II is the ionization of S I by the thermal electron population.
The pickup energy from freshly ionized S I is the primary source of energy to the S II
population. The principal loss mechanism of both S II particles and energy is ionization
by the thermal electron population.
Table 5.6 provides the source and loss processes for S III. Similar to S II, the
charge exchange reaction S+ + S++ → S++ + S+ is the major source and loss of S III.
As noted by Smith and Strobel (1985), this reaction produces no net change in the
amount of S III, but it is a significant source of energy. Excluding this reaction, the
primary source of both particles and energy is the ionization of S II by the thermal
electron population. The primary loss mechanism for S III is radial transport, while the
primary loss mechanism of energy from S III are Coulomb interactions with the colder
thermal electron population. It is worth reiterating that this is not the process that
produces radiation from S III. Rather these Coulomb interactions are responsible for
heating the thermal electron population. Collisions that produce radiative transitions
are the energy loss processes for the thermal electron population, not the radiating ions.
The source and loss processes for S IV are given in Table 5.7. Ionization of S III is
the primary source of both particles and energy to the S IV population. Since the ionization potential of S III is relatively large (34.8 eV), the small (ne,hot /ne, total=0.23%)
hot electron population (Te , hot=55 eV) is responsible for the majority of the ionization
127
Table 5.5: Source and Loss Mechanisms for S II; 14 January 2001 equilibrium conditions
s−1
Particles
cm−3
%
eV
s−1
Energy
cm−3
%
Source Mechanisms
Ionization of S I by e−
Ionization of S I by hot e−
Recombination of S III
S+ + S++ → S++ + S+
S + S+ → S+ + S∗
S + S++ → S+ + S+
S + S+++ → S+ + S++
S + O+ → S+ + O∗
S + O++ → S+ + O+
O + S++ → O+ + S+
Total Sources
8.62x10−5
4.12x10−6
1.83x10−5
0.000385
1.50x10−5
1.54x10−6
5.64x10−6
7.47x10−6
5.50x10−6
2.46x10−5
0.000553
15.6
0.7
3.3
69.6
2.7
0.3
1.0
1.4
1.0
4.4
100.0
0.0325
0.00156
0.00107
0.0225
0.00566
0.000336
0.00213
0.00282
0.00208
0.00144
0.0721
45.1
2.2
1.5
31.2
7.8
0.5
3.0
3.9
2.9
2.0
100.0
Loss Mechanisms
Ionization of S II by e−
Ionization of S II by hot e−
Recombination of S II
S+ + S++ → S++ + S+
S + S+ → S+ + S∗
O + S+ → O+ + S∗
O++ + S+ → O+ + S++
S+++ + S+ → S++ + S++
Thermal equilibration with
Thermal equilibration with
Thermal equilibration with
Thermal equilibration with
Thermal equilibration with
Thermal equilibration with
Radial transport
Total Losses
8.63x10−5
3.50x10−5
1.14x10−6
0.000385
1.50x10−5
1.56x10−7
6.33x10−6
2.84x10−6
0.000
0.000
0.000
0.000
0.000
0.000
2.15x10−5
0.000553
15.6
6.3
0.2
69.6
2.7
0.0
1.1
0.5
0.0
0.0
0.0
0.0
0.0
0.0
3.9
100.0
0.00957
0.00389
0.000126
0.0426
0.00166
1.73x10−5
0.000701
0.000315
0.00334
0.00162
0.000733
0.000506
0.00460
1.84x10−7
0.00238
0.0721
13.3
5.4
0.2
59.1
2.3
0.0
1.0
0.4
4.6
2.2
1.0
0.7
6.4
0.0
3.3
100.0
S III
S IV
O II
O III
e−
e−
hot
128
Table 5.6: Source and Loss Mechanisms for S III; 14 January 2001 equilibrium conditions
Particles
s−1 cm−3
%
Energy
eV s−1 cm−3
%
Source Mechanisms
Ionization of S II by e−
Ionization of S II by hot e−
Recombination of S IV
S+ + S++ → S++ + S+
S + S++ → S++ + S∗
S + S+++ → S+ + S++
S + O++ → S++ + O+ + e−
O++ + S+ → O+ + S++
O + S+++ → O+ + S++
S+++ + S+ → S++ + S++
Thermal equilibration with S II
Thermal equilibration with O II
Total Sources
0.000113
4.57x10−5
1.06x10−5
0.000501
2.61x10−5
7.35x10−6
4.96x10−6
8.24x10−6
4.45x10−5
7.40x10−6
0.000
0.000
0.000768
14.6
5.9
1.4
65.2
3.4
1.0
0.6
1.1
5.8
1.0
0.0
0.0
100.0
0.0125
0.00506
0.000522
0.0556
0.00985
0.000363
0.00187
0.000914
0.00220
0.000593
0.00334
0.00316
0.0959
13.0
5.3
0.5
57.9
10.3
0.4
2.0
1.0
2.3
0.6
3.5
3.3
100.0
Loss Mechanisms
Ionization of S III by e−
Ionization of S III by hot e−
Recombination of S III
S+ + S++ → S++ + S+
S + S++ → S+ + S+
S + S++ → S++ + S∗
O + S++ → O+ + S+
O++ + S++ → O+ + S+++
Thermal equilibration with S IV
Thermal equilibration with O III
Thermal equilibration with e−
Thermal equilibration with e−
hot
Radial transport
Total Losses
1.30x10−5
5.16x10−5
2.39x10−5
0.000501
1.00x10−6
2.61x10−5
3.20x10−5
2.10x10−5
0.000
0.000
0.000
0.000
9.86x10−5
0.000768
1.7
6.7
3.1
65.2
0.1
3.4
4.2
2.7
0.0
0.0
0.0
0.0
12.8
100.0
0.000761
0.00302
0.00140
0.0293
5.86x10−5
0.00152
0.00187
0.00123
0.00740
0.00227
0.0413
2.08x10−7
0.00576
0.0959
0.8
3.1
1.5
30.5
0.1
1.6
2.0
1.3
7.7
2.4
43.1
0.0
6.0
100.0
of S III. The only other source of S IV is the charge exchange reaction: O++ + S++ →
O+ + S+++ . Ion-ion collisions are often overlooked, but for S IV they are the dominant
source of energy. Coulomb interactions with S III, for example, provide nearly twice
as much energy to the S IV population as the ionization of S III. The dominant loss
process of S IV is the charge exchange reaction O + S+++ → O+ + S++ , however, radial
transport and recombination are also significant loss processes. Fully 3/4 of the total
129
Table 5.7: Source and Loss Mechanisms for S IV; 14 January 2001 equilibrium conditions
Particles
s−1 cm−3
%
Energy
eV s−1 cm−3
%
Source Mechanisms
Ionization of S III by e−
Ionization of S III by hot e−
O++ + S++ → O+ + S+++
Thermal equilibration with S II
Thermal equilibration with S III
Thermal equilibration with O II
Thermal equilibration with e−
hot
Total Sources
1.35x10−5
5.33x10−5
2.17x10−5
0.000
0.000
0.000
0.000
8.84x10−5
15.2
60.3
24.5
0.0
0.0
0.0
0.0
100.0
0.000786
0.00312
0.00127
0.00162
0.00740
0.00280
1.30x10−7
0.0170
4.6
18.3
7.5
9.5
43.6
16.5
0.0
100.0
Loss Mechanisms
Ionization of S IV by e−
Ionization of S IV by hot e−
Recombination of S IV
O + S+++ → O+ + S++
S+++ + S+ → S++ + S++
Thermal equilibration with O III
Thermal equilibration with e−
Radial transport
Total Losses
8.93x10−8
3.26x10−6
1.09x10−5
4.60x10−5
3.82x10−6
0.000
0.000
1.67x10−5
8.08x10−5
0.1
4.0
13.5
56.9
4.7
0.0
0.0
20.7
100.0
4.41x10−6
0.000161
0.000539
0.00227
0.000188
0.000147
0.0128
0.000825
0.0170
0.0
0.9
3.2
13.4
1.1
0.9
75.7
4.9
100.0
energy lost from S IV is via thermal equilibration with the cold electron population.
Table 5.8 lists the source and loss mechanisms for O II. There are 13 independent
reactions that produce O II. However, of these, the charge exchange reaction O + O+
→ O+ + O∗ is dominant. Although this reaction produces no net flux of O II, it
is a significant source of energy, similar to the S+ + S++ → S++ + S+ reaction for
S III. However, unlike the sulfur reaction, O II ions lost through this reaction become
fast neutrals. This is the dominant mechanism for oxygen fast neutrals. Primarily
due to this reaction’s large cross section, the torus produces 4.2 times as many fast
oxygen neutrals as fast sulfur neutrals. Excluding this reaction, ionization of O I by
the thermal electron population is the dominant source of particles and energy. The
primary loss mechanism of O II is radial transport, although losses through ionization
are also significant. The main losses of O II energy are from collisions with the thermal
130
Table 5.8: Source and Loss Mechanisms for O II; 14 January 2001 equilibrium conditions
Particles
s−1 cm−3
%
Energy
eV s−1 cm−3
%
Source Mechanisms
Ionization of O I by e−
Ionization of O I by hot e−
Recombination of O III
O + O+ → O+ + O∗
O + O++ → O+ + O+
O + S+ → O+ + S∗
S + O++ → S+ + O+
S + O++ → S++ + O+ + e−
O + S++ → O+ + S+
O++ + S+ → O+ + S++
O + S+++ → O+ + S++
O++ + S++ → O+ + S+++
Thermal equilibration with S II
Total Sources
4.07x10−5
5.48x10−6
4.44x10−7
0.000123
9.17x10−7
1.40x10−7
4.96x10−6
3.44x10−6
2.22x10−5
5.71x10−6
3.08x10−5
1.45x10−5
0.000
0.000253
16.1
2.2
0.2
48.8
0.4
0.1
2.0
1.4
8.8
2.3
12.2
5.8
0.0
100.0
0.00769
0.00104
2.12x10−5
0.0233
0.000108
2.65x10−5
0.000237
0.000164
0.00418
0.000272
0.00582
0.000692
0.000733
0.0442
17.4
2.3
0.0
52.6
0.2
0.1
0.5
0.4
9.5
0.6
13.2
1.6
1.7
100.0
Loss Mechanisms
Ionization of O II by e−
Ionization of O II by hot e−
Recombination of O II
O + O+ → O+ + O∗
S + O+ → S+ + O∗
Thermal equilibration with S III
Thermal equilibration with S IV
Thermal equilibration with O III
Thermal equilibration with e−
Thermal equilibration with e−
hot
Radial transport
Total Losses
5.38x10−6
3.25x10−5
1.59x10−6
0.000123
6.74x10−6
0.000
0.000
0.000
0.000
0.000
8.30x10−5
0.000252
2.1
12.9
0.6
48.8
2.7
0.0
0.0
0.0
0.0
0.0
32.9
100.0
0.000356
0.00215
0.000106
0.00815
0.000446
0.00316
0.00280
0.000967
0.0206
2.85x10−7
0.00549
0.0442
0.8
4.9
0.2
18.4
1.0
7.1
6.3
2.2
46.6
0.0
12.4
100.0
electron population and radial transport.
Values for the source and loss mechanisms of O III are given in Table 5.9. The
relative importance of source and loss processes for O III are similar to those for S IV.
Again, due to the large ionization potential of O II (35.1 eV) the ionization of O II by
the hot electron population provides the main source of both particles and energy. O III
also gains significant amounts of energy from Coulomb interactions with S III and O II
and the charge exchange reaction: O + O++ → O++ + O∗ . The two most important
131
Table 5.9: Source and Loss Mechanisms for O III; 14 January 2001 equilibrium conditions
Particles
s−1 cm−3
%
Energy
eV s−1 cm−3
%
Source Mechanisms
Ionization of O II by e−
Ionization of O II by hot e−
O + O++ → O++ + O∗
Thermal equilibration with S II
Thermal equilibration with S III
Thermal equilibration with S IV
Thermal equilibration with O II
Thermal equilibration with e−
hot
Total Sources
5.99x10−6
3.62x10−5
5.30x10−6
0.000
0.000
0.000
0.000
0.000
4.75x10−5
12.6
76.2
11.2
0.0
0.0
0.0
0.0
0.0
100.0
0.000397
0.00239
0.00100
0.000506
0.00227
0.000147
0.000967
7.29x10−8
0.00768
5.2
31.2
13.0
6.6
29.6
1.9
12.6
0.0
100.0
Loss Mechanisms
Ionization of O III by e−
Ionization of O III by hot e−
Recombination of O III
O + O++ → O+ + O+
O + O++ → O++ + O∗
S + O++ → S+ + O+
S + O++ → S++ + O+ + e−
O++ + S+ → O+ + S++
O++ + S++ → O+ + S+++
Thermal equilibration with e−
Radial transport
Total Losses
6.06x10−9
1.17x10−6
4.94x10−7
5.10x10−7
5.30x10−6
5.52x10−6
3.82x10−6
6.35x10−6
1.62x10−5
0.000
8.09x10−6
4.74x10−5
0.0
2.5
1.0
1.1
11.2
11.6
8.1
13.4
34.1
0.0
17.1
100.0
2.89x10−7
5.58x10−5
2.36x10−5
2.43x10−5
0.000253
0.000263
0.000182
0.000303
0.000770
0.00542
0.000386
0.00768
0.0
0.7
0.3
0.3
3.3
3.4
2.4
3.9
10.0
70.6
5.0
100.0
loss processes for O III are the charge exchange reaction O++ + S++ → O+ + S+++ and
radial transport, although several other charge exchange reactions are also significant
loss mechanisms. From the perspective of O III energy losses, thermal equilibration
with the cold electron population is completely dominant.
5.2.1.3
Thermal Electrons
As a result of the charge neutrality condition imposed on the torus, the flux of
electrons is not calculated directly. Rather, at each time step, the electron density
is adjusted so that the torus, as a whole, remains charge neutral. Additionally, it is
132
Table 5.10: Source and Loss Mechanisms for
e− ;
14 January 2001 equilibrium conditions
Energy
eV s−1 cm−3
Source Mechanisms
Thermal equilibration
Thermal equilibration
Thermal equilibration
Thermal equilibration
Thermal equilibration
Thermal equilibration
Total Sources
Loss Mechanisms
Collisional excitation
Collisional excitation
Collisional excitation
Collisional excitation
Collisional excitation
Radial transport
Total Losses
with
with
with
with
with
with
of
of
of
of
of
S II
S III
S IV
O II
O III
e−
hot
S II
S III
S IV
O II
O III
%
0.00460
0.0413
0.0128
0.0206
0.00542
0.116
0.201
2.3
20.6
6.4
10.3
2.7
57.8
100.0
0.0335
0.122
0.0224
0.0220
0.00287
0.00179
0.205
16.4
59.7
11.0
10.7
1.4
0.9
100.0
assumed that electrons produced via ionization or the charge exchange reaction S +
O++ → S++ + O+ + e− provide no energy to the thermal electron population (i.e.
they have a temperature of 0 eV), and electrons lost via recombination remove no
energy from the thermal electron population. This last assumption is responsible for
the slight difference between the total energy source and loss terms in Table 5.10.
With these assumptions, the only sources of energy to the thermal electron population are Coulomb interactions with the other species, and the only loss mechanisms
are collisions with ions that produce radiation. The dominant electron energy source is
the hot electron population, followed by collisions with S III and O II. This is hardly
surprising since these are the most abundant ion species in the torus. Collisional excitation of radiative transitions accounts for 99% of the electron energy losses. S III
radiates is responsible for a disproportionate share of the electron losses, which is not
surprising given that the S III 680Å feature alone contains approximately 25% of the
total power radiated by the torus.
133
5.2.2
Comparison to Time-Variable Model Results
The next step up in model complexity, and it is a significant one, is to reproduce
the time variability of the UVIS mixing ratios. (Recall from Fig. 4.1 that the mixing
ratio of S II decreases by a factor of two between 1 October 2000 and 14 November 2000,
while the mixing ratio of S IV increases by a similar amount.) For the one-box model,
this work was presented by Delamere et al. (2004). Again, for ease of comparison the
values presented for the lat-az model are the flux tube-integrated mixing ratios, averaged
over the azimuthally dimension.
The primary result of Delamere et al. (2004) was that a factor of 3–4 increase
in the amount of neutral material supplied to the torus occurred around 5 September
2000. Based on the profile of a 3 order-of-magnitude increase in the amount of Iogenic
dust detected by the Galileo dust detector (Krüger et al., 2003), Delamere et al. (2004)
modeled this increase as a simple Gaussian profile:
³
´
2
2
Sn (t) = Sn,0 1 + αn e−(t−t0,n ) /σn
(5.28)
where Sn,0 is the nominal neutral source rate, αn is the amplitude of the neutral source
increase, t0 is the time of the peak neutral source rate, and σn is the width of the
neutral source profile. Delamere et al. (2004) found the parameters that best fit the
UVIS mixing ratios over the observing period were: αn =2.5, t0 =250 (5 September 2000),
and σn =25 days. Since the one-box model that used this neutral source rate profile was
fairly successful in reproducing the observed changes in ion mixing ratios with time,
the same functional form of the neutral source rate was used in the time-variable lat-az
model.
In order to obtain the mixing ratios and total EUV power observed by UVIS
in October 2000, the neutral source increase in September 2000 must be accompanied
by a corresponding decrease in the radial transport timescale. Without this decrease,
134
the densities in the torus increase rapidly and the torus radiates vastly more energy
in the EUV than was observed. Additionally, with densities of the higher ionization
states like S IV go to near zero as these ions are efficiently destroyed by charge exchange
reactions with neutrals and lower charge state ions. Since this is not observed, the
transport time must decrease. Although the details of radial convective transport are
not well understood, an inverse relationship between the neutral source rate (or amount
of plasma in the torus) and transport timescale is expected (Southwood and Kivelson,
1989; Brown and Bouchez , 1997; Pontius et al., 1998). The functional form of this
inverse relationship, however, is not clear. Delamere et al. (2004), use a radial transport
timescale that is inversely proportional to the neutral source rate (τ ∝ 1/Sn ). One might
expect that the radial transport timescale would not be directly related to the neutral
source rate, but rather to the total ion density in the torus. However, models that set
the transport timescale inversely proportional to the total ion density failed to match
the observed mixing ratios as a function of time. Indeed, the entire family of models
where the transport timescale is inversely proportional to the total ion density to some
power (τ ∝ 1/nγi ) yields an unsatisfactory match to the observed mixing ratio profiles.
Therefore we use the same relationship as Delamere et al. (2004):
τ (t) = τ0
Sn,0
Sn (t)
(5.29)
After several runs of the time-variable lat-az model, it became apparent that
the increased reaction timescales caused by the latitudinal averaging prohibited the
rapid decline of the S II mixing ratio (and corresponding rise in the S IV mixing ratio)
required by the UVIS observations. Since hot electrons are the only means by which
the composition of the lat-az model can change so swiftly, a Gaussian increase in the
hot electron fraction of the form:
135
2 /σ 2
h
fh (t) = fh,0 + αh e−(t−t0,h )
(5.30)
was added to the model. This addition can be loosely justified by the following thought
argument. The increase in mass supplied to the torus caused by the neutral source
increase will require additional currents to accelerate the pickup ions to corotation
velocity. If the torus system is current limited, the torus will lag from rigid corotation,
which will drive currents that could generate hot electrons. This thought experiment
is not intended to suggest that this is actually what is occurring in the Io torus, rather
it merely intended to suggest the plausibility of an increase in hot electrons that would
accompany an increase in neutral source rate.
The time-variable lat-az model thus has 11 parameters: the five parameters from
the basic model (Sn,0 , O/S, fh , Te,hot , and τ0 ) which are held constant, as well as
three parameters each to describe the Gaussian increase in neutral source rate and
hot electron fraction. With such a large number of free parameters, an extensive and
systematic exploration of parameter space was not possible. However, a manual search
of the parameter space yielded the “best-fit” values contained in Table 5.11.
The azimuthally-averaged, flux tube-integrated ion mixing ratios from the timevariable latitude-averaged azimuthal model are presented in Fig. 5.1. Due to the observational setup of the inbound staring observations (day 275–320), data from the FUV
channel were not used in the spectral fitting procedure (See Section 3.3). Without the
inclusion of the FUV O III lines at 1661Å and 1666Å in the spectral analysis, it is not
possible to derive an accurate O II/O III ratio from the UVIS data (see Section 3.4.2).
This ratio is required by the spectral fitting procedure to calculate the total electron
density. The lat-az model predicts that the O II/O III ratio should vary between 8–24
as a result of the temporal changes in the neutral source rate and hot electron fraction.
A value of 16—in the center of the range of predicted values—was used for the analysis
136
Table 5.11: Best-fit time-variable lat-az model parameters
Parameter
Basic Parameters
Sn,0
O/S
fh
Te,hot
τ0
Value
2.0x1028 s−1
1.4
0.23 %
49 eV
70 days
Neutral source parameters
αn (amplitude)
t0,n (time of peak)
σn (width)
2.3
249 (5 September 2000)
30 days
Hot electron parameters
αh (amplitude)
t0,h (time of peak)
σh (width)
0.08%
279 (5 October 2000)
60 days
of the inbound UVIS spectra. Although the ratio of O II to O III cannot be determined
from the UVIS EUV spectra, for the range in values predicted by the lat-az model,
the total oxygen ion mixing ratio (NO II +NO III )/Ne derived from the spectra will be
approximately constant. Therefore, the total oxygen ion mixing ratio is shown instead
of the individual O II and O III mixing ratios.
The sulfur ion mixing ratios obtained from the time-variable lat-az model show a
remarkably good fit to the mixing ratios derived from UVIS spectra during the inbound
staring period (days 275–320). The model sulfur ion mixing ratios are also well within
the statistical uncertainty (≈8%) in the mixing ratios derived from the radial scan
observation on 14 January 2001 (day 380). Although the total oxygen ion mixing ratio
predicted by the lat-az model matches the January UVIS observations, it is 9% too high
on day 275 and 2% too high on day 320. Additionally, the model fails to predict the
general shape of the oxygen ion mixing ratio curve (increasing with time, as opposed to
the model curve that decreases with time).
The discrepancy in total oxygen ion mixing ratio between the model and the
Avg. FT−Integrated Mixing Ratio
137
0.30
0.25
0.20
Model Otot
UVIS Otot
Model S III
UVIS S III
Model S II
UVIS S II
Model S IV
UVIS S IV
0.15
0.10
0.05
0.00
180
210
240 270 300 330
Day of Year 2000
360
390
Figure 5.1: Azimuthally-averaged, flux tube-integrated mixing ratios of the sulfur
species S II, S III and S IV and total oxygen ion mixing ratio (O II+O III) from the
latitude-averaged azimuthal chemistry model as a function of time. The plot symbols
and connecting lines show the mixing ratios derived from UVIS spectra. The neutral
source peaks on day 249, while the hot electron fraction peaks on day 279.
data may in part be due to the calibration of the UVIS EUV channel. Although the
effective area of the EUV channel increases by a factor of two between 740Å and 903Å
no measurements of the effective area were made in this wavelength range (see Fig. 2.3).
The standard UVIS EUV effective area curve assumes a linear increase between these
points. If the actual effective area of the EUV instrument at 833Å were less than the
assumed value, the true brightness of the O II/O III 833Å feature, and hence the total
oxygen ion mixing ratio, would be underestimated (See Fig. 2.5).
An error in the EUV channel effective area calibration, as described above, would
shift the entire UVIS-derived oxygen ion mixing ratio curve upwards. This would bring
the data closer in line with the model values. However, changing the calibration of the
EUV channel would not affect the slope of the oxygen curve. The simplest explanation
of the difference in slope between data and model curves is a time-varying O/S ratio in
138
the torus neutral source. The torus neutral source rate Sn was a factor of 3.3 higher in
September 2000 than in January 2001 (Delamere et al., 2004). Presumably this increase
was in response to some volcanic event on Io, possibly the eruption of Tvashtar Catena
that deposited a Pele-like ring of red material 1200 km in diameter and produced a plume
400 km high (Geissler et al., 2004; Porco et al., 2003). If the volcanic event produced
significantly more S2 , SO, S, or some other sulfur-bearing species, the O/S ratio of the
torus neutral source could decrease. As the O/S ratio returned to more “typical” values
(presumably close to 2) the total oxygen ion mixing ratio would increase, as is seen in
the UVIS data.
The azimuthally-averaged ion parameters (temperature, scale height, density,
and total flux tube content) are shown versus time in Fig. 5.2. Figure 5.3 shows the
same information for the thermal electrons. The top panel of these figures shows the
azimuthally-averaged ion (or electron) temperature. The primary feature is a factor of
≈2.5 increase in the temperature centered around day 265. The temperature increase
is a result of the large flux of pickup ions entering the torus. Although the neutral
source peaks on day 249, and the density of the neutral clouds peaks on day 251, the
temperatures in the torus continue to rise for another two weeks. This is primarily due
to the radial transport of torus plasma: colder plasma in the torus is convected radially
outwards and is replaced with hotter fresh pickup ions (TS,pu =380 eV and TO,pu =190
eV, assuming Eq. 5.1 holds). Ion scale heights, as calculated from Eq. 5.19, are purely
√
a function of temperature and scale as Ti . The third panel of Figs. 5.2 and 5.3 shows
density on the centrifugal equator, (nγ (0) in Eq. 5.20). All species except S II show a
decrease in equatorial density with a minimum occurring on, or around, day 260. This
counter-intuitive result is caused by the sharp increase in ion temperatures. With the
resulting increase in ion scale heights, the plasma is distributed over a large latitudinal
extent and densities on the centrifugal equator actually drop. The latitude-integrated
column density (Nγ in Eq. 5.20) is plotted in the final panel of Figs. 5.2 and 5.3. This
139
Ion Temperature (eV)
300
S II
S III
S IV
O II
O III
250
200
150
100
50
Lat. Int Column Density (cm−2)
Ion Density (cm−3)
Scale Height (RJ)
0
2.5
2.0
1.5
1.0
0.5
700
600
500
400
300
200
100
0
1.2•108
1.0•108
8.0•107
6.0•107
4.0•107
2.0•107
0
200
250
300
Day of Year 2000
350
Figure 5.2: Azimuthally-averaged ion temperature, scale height, density, and total flux
tube content as a function of time. The neutral source rate reaches a maximum on day
249, while the hot electron fraction reaches a maximum on day 279.
140
Temperature (eV)
7.0
6.5
6.0
5.5
5.0
4.5
Scale Height (RJ)
4.0
2.0
1.8
1.6
1.4
1.2
Lat. Int. Column Density(cm−2)
Density (cm−3)
1.0
2400
2200
2000
1800
1600
1400
4.0•108
3.8•108
3.6•108
3.4•108
3.2•108
3.0•108
200
250
300
Day of Year 2000
350
Figure 5.3: Azimuthally-averaged electron temperature, scale height, density, and total
flux tube content as a function of time. The neutral source rate reaches a maximum on
day 249, while the hot electron fraction reaches a maximum on day 279.
141
panel shows that while the equatorial densities drop, the total amount of plasma in the
torus increases as a result of the increase in neutral source rate. The integrated column
densities of S IV and O III do show a decrease with time due to losses from charge
exchange reactions with neutrals:
O + S +++ → O+ + S ++
S + O++ → S + + O+
S III and the electrons show a distinct double-peak structure; the second peak is related
to the increase in hot electron fraction, which reaches a maximum on day 279.
5.2.2.1
Neutrals
The source and loss rates for neutrals on 1 October 2000 (day 275) are presented
in Table 5.12 and 5.13. (Although the torus has not reached equilibrium by 14 January
2001, the source and loss processes of the non-equilibrium time-variable are quite similar
to the equilibrium case presented in Tables 5.3–5.10.) The neutral source rate on day
275 is 2.5 times higher than on day 380 (14 January 2001). Source and loss rates for both
S I and O I are roughly a factor of 2 higher than the 14 January 2001 equilibrium values.
The neutral source rate peaked at 3.3 times its equilibrium value on day 249. Therefore,
the net flux of both S I and O I is negative. As a result of the increased thermal
electron temperature, ionization has become more important as a loss mechanism for
both neutral sulfur and neutral oxygen.
5.2.2.2
Ions
Source and loss processes for the ion species in the torus on 1 October 2000 are
given in Tables 5.14–5.18. All of the ion species, except S II show a net flux in the
number of particles, a sign that the torus is returning to equilibrium levels. As with the
142
Table 5.12: Source and Loss Mechanisms for S I; 1 October 2000 non-equilibrium conditions
Particles
s−1 cm−3
%
Source Mechanisms
Torus neutral source
Total Sources
0.00438
0.00438
100.0
100.0
Loss Mechanisms
Ionization of S I by e−
Ionization of S I by hot e−
S + S+ → S+ + S∗
S + S++ → S+ + S+
S + S++ → S++ + S∗
S + S+++ → S+ + S++
S + O+ → S+ + O∗
S + O++ → S+ + O+
S + O++ → S++ + O+ + e−
Total Losses
0.00304
9.48x10−5
0.000508
1.55x10−5
0.000404
5.41x10−5
0.000174
9.33x10−5
6.46x10−5
0.00444
68.3
2.1
11.4
0.3
9.1
1.2
3.9
2.1
1.5
100.0
Net Flux
-6.17x10−5
143
Table 5.13: Source and Loss Mechanisms for O I; 1 October 2000 non-equilibrium
conditions
Particles
s−1 cm−3
%
Source Mechanisms
Torus neutral source
Total Sources
0.00745
0.00745
100.0
100.0
Loss Mechanisms
Ionization of O I by e−
Ionization of O I by hot e−
O + O+ → O+ + O∗
O + O++ → O+ + O+
O + O++ → O++ + O∗
O + S+ → O+ + S∗
O + S++ → O+ + S+
O + S+++ → O+ + S++
Total Losses
0.00244
0.000178
0.00403
1.09x10−5
0.000113
6.66x10−6
0.000625
0.000414
0.00781
31.2
2.3
51.5
0.1
1.4
0.1
8.0
5.3
100.0
Net Flux
-0.000364
neutrals, the role of ionization in the mass and energy balance in the torus is much more
important on 1 October 2000 than on 14 January 2001. This is due almost entirely to
the higher temperature of the core electron population. Since the neutral source rate is
a factor of 2.5 higher on day 275 (1 October 2000) than on day 380 (14 January 2001),
charge exchange reactions involving neutrals are also enhanced. The radial transport
rate is proportional to the neutral source rate, and consequently, radial transport plays
a larger role in the removal of mass and energy from the torus.
5.2.2.3
Thermal Electrons
The relative importance of the source and loss mechanisms for the thermal electron population are fairly similar between 1 October 2000 and 14 January 2001. The
notable differences in the sources of electron energy in October, as compared to January,
are that Coulomb interactions with S III are relatively more important, while collisions
with the hot electrons population are somewhat less important. On the loss process
144
Table 5.14: Source and Loss Mechanisms for S II; 1 October 2000 non-equilibrium
conditions
s−1
Particles
cm−3
%
eV
s−1
Energy
cm−3
%
Source Mechanisms
Ionization of S I by e−
Ionization of S I by hot e−
Recombination of S III
S+ + S++ → S++ + S+
S + S+ → S+ + S∗
S + S++ → S+ + S+
S + S+++ → S+ + S++
S + O+ → S+ + O∗
S + O++ → S+ + O+
O + S++ → O+ + S+
Total Sources
0.000171
5.34x10−6
1.06x10−5
0.000265
2.87x10−5
1.75x10−6
3.05x10−6
9.83x10−6
5.25x10−6
3.52x10−5
0.000536
31.9
1.0
2.0
49.5
5.4
0.3
0.6
1.8
1.0
6.6
100.0
0.0646
0.00202
0.00217
0.0541
0.0108
0.000509
0.00115
0.00371
0.00198
0.00719
0.148
43.6
1.4
1.5
36.5
7.3
0.3
0.8
2.5
1.3
4.9
100.0
Loss Mechanisms
Ionization of S I by e−
Ionization of S I by hot e−
Recombination of S III
S+ + S++ → S++ + S+
S + S+ → S+ + S∗
O + S+ → O+ + S∗
O++ + S+ → O+ + S++
S+++ + S+ → S++ + S++
Thermal equilibration with
Thermal equilibration with
Thermal equilibration with
Thermal equilibration with
Thermal equilibration with
Thermal equilibration with
Radial transport
Total Losses
0.000181
3.09x10−5
1.06x10−6
0.000265
2.87x10−5
3.76x10−7
3.67x10−6
8.90x10−7
0.00
0.00
0.00
0.00
0.00
0.00
5.91x10−5
0.000571
31.7
5.4
0.2
46.4
5.0
0.1
0.6
0.2
0.0
0.0
0.0
0.0
0.0
0.0
10.4
100.0
0.0485
0.00827
0.000283
0.0709
0.00766
0.000100
0.000983
0.000239
0.000587
0.000223
0.000425
0.000181
0.00536
4.65x10−7
0.0158
0.160
30.4
5.2
0.2
44.4
4.8
0.1
0.6
0.1
0.4
0.1
0.3
0.1
3.4
0.0
9.9
100.0
Net Flux
S III
S IV
O II
O III
e−
e−
hot
-3.50x10−5
-0.0113
145
Table 5.15: Source and Loss Mechanisms for S III; 1 October 2000 non-equilibrium
conditions
s−1
Particles
cm−3
%
eV
s−1
Energy
cm−3
%
Source Mechanisms
Ionization of S II by e−
Ionization of S II by hot e−
Recombination of S IV
S+ + S++ → S++ + S+
S + S++ → S++ + S∗
S + S+++ → S+ + S++
S + O++ → S++ + O+ + e−
O++ + S+ → O+ + S++
O + S+++ → O+ + S++
S+++ + S+ → S++ + S++
Thermal equilibration with S II
Total Sources
0.000204
3.47x10−5
2.36x10−6
0.000298
2.56x10−5
3.43x10−6
4.09x10−6
4.13x10−6
2.62x10−5
2.00x10−6
0.00
0.000604
33.7
5.7
0.4
49.3
4.2
0.6
0.7
0.7
4.3
0.3
0.0
100.0
0.0545
0.00929
0.000368
0.0797
0.00966
0.000533
0.00154
0.00111
0.00408
0.000424
0.000587
0.162
33.7
5.7
0.2
49.3
6.0
0.3
1.0
0.7
2.5
0.3
0.4
100.0
Loss Mechanisms
Ionization of S II by e−
Ionization of S II by hot e−
Recombination of S IV
S+ + S++ → S++ + S+
S + S++ → S+ + S+
S + S++ → S++ + S∗
O + S++ → O+ + S+
O++ + S++ → O+ + S+++
Thermal equilibration with S IV
Thermal equilibration with O II
Thermal equilibration with O III
Thermal equilibration with e−
Thermal equilibration with e−
hot
Radial transport
Total Losses
2.39x10−5
2.52x10−5
1.19x10−5
0.000298
9.84x10−7
2.56x10−5
3.96x10−5
6.38x10−6
0.00
0.00
0.00
0.00
0.00
0.000148
0.000580
4.1
4.4
2.1
51.4
0.2
4.4
6.8
1.1
0.0
0.0
0.0
0.0
0.0
25.6
100.0
0.00491
0.00517
0.00243
0.0608
0.000201
0.00522
0.00809
0.00131
0.00119
0.00208
0.00119
0.0395
3.29x10−6
0.0303
0.162
3.0
3.2
1.5
37.4
0.1
3.2
5.0
0.8
0.7
1.3
0.7
24.3
0.0
18.7
100.0
Net Flux
2.40x10−5
-0.000629
146
Table 5.16: Source and Loss Mechanisms for S IV; 1 October 2000 non-equilibrium
conditions
Particles
s−1 cm−3
%
Energy
eV s−1 cm−3
%
Source Mechanisms
Ionization of S III by e−
Ionization of S III by hot e−
O++ + S++ → O+ + S+++
Thermal equilibration with S II
Thermal equilibration with S III
Thermal equilibration with O II
Total Sources
2.67x10−5
2.81x10−5
7.12x10−6
0.00
0.00
0.00
6.19x10−5
43.1
45.4
11.5
0.0
0.0
0.0
100.0
0.00546
0.00576
0.00146
0.000223
0.00119
9.56x10−6
0.0141
38.7
40.8
10.3
1.6
8.5
0.1
100.0
Loss Mechanisms
Ionization of S III by e−
Ionization of S III by hot e−
Recombination of S V
O + S+++ → O+ + S++
S+++ + S+ → S++ + S++
Thermal equilibration with O III
Thermal equilibration with e−
Thermal equilibration with e−
hot
Radial transport
Total Losses
1.52x10−7
7.83x10−7
2.63x10−6
2.92x10−5
1.12x10−6
0.00
0.00
0.00
1.21x10−5
4.61x10−5
0.3
1.7
5.7
63.5
2.4
0.0
0.0
0.0
26.4
100.0
2.39x10−5
0.000123
0.000410
0.00455
0.000174
0.000106
0.00537
4.11x10−7
0.00189
0.0127
0.2
1.0
3.2
35.9
1.4
0.8
42.5
0.0
15.0
100.0
Net Flux
1.58x10−5
0.00145
side, the role of S II in removing energy from the electron population is enhanced, while
the role of S IV is diminished. This difference is almost entirely due to the change in
densities of these two ions.
5.2.3
Azimuthal Model Results
Up to this point, all of the model parameters have been azimuthally independent.
For example, the model bin at λIII =20◦ had the same fraction of hot electrons as the
bin at λIII =200◦ . The azimuthal variations that developed were solely the result of the
varying distance of the centrifugal equator (about which the torus plasma is symmetric)
to the rotational equator plane. These differences are small (only a few percent), remain
147
Table 5.17: Source and Loss Mechanisms for O II; 1 October 2000 non-equilibrium
conditions
Particles
s−1 cm−3
%
Energy
eV s−1 cm−3
%
Source Mechanisms
Ionization of O I by e−
Ionization of O I by hot e−
Recombination of O III
O + O+ → O+ + O∗
O + O++ → O+ + O+
O + S+ → O+ + S∗
S + O++ → S+ + O+
S + O++ → S++ + O+ + e−
O + S++ → O+ + S+
O++ + S+ → O+ + S++
O + S+++ → O+ + S++
O++ + S++ → O+ + S+++
Thermal equilibration with S II
Thermal equilibration with S III
Total Sources
0.000126
9.20x10−6
2.25x10−7
0.000208
1.12x10−6
3.44x10−7
4.82x10−6
3.34x10−6
3.23x10−5
3.36x10−6
2.14x10−5
5.21x10−6
0.00
0.00
0.000415
30.4
2.2
0.1
50.1
0.3
0.1
1.2
0.8
7.8
0.8
5.1
1.3
0.0
0.0
100.0
0.0238
0.00174
2.78x10−5
0.0393
0.000175
6.50x10−5
0.000593
0.000410
0.00610
0.000414
0.00404
0.000642
0.000425
0.00208
0.0798
29.8
2.2
0.0
49.2
0.2
0.1
0.7
0.5
7.6
0.5
5.1
0.8
0.5
2.6
100.0
Loss Mechanisms
Ionization of O I by e−
Ionization of O I by hot e−
Recombination of O III
O + O+ → O+ + O∗
S + O+ → S+ + O∗
Thermal equilibration with
Thermal equilibration with
Thermal equilibration with
Thermal equilibration with
Radial transport
Total Losses
1.43x10−5
2.05x10−5
1.07x10−6
0.000208
9.01x10−6
0.00
0.00
0.00
0.00
0.000162
0.000414
3.4
4.9
0.3
50.2
2.2
0.0
0.0
0.0
0.0
39.0
100.0
0.00224
0.00321
0.000168
0.0326
0.00141
9.56x10−6
0.000200
0.0169
1.22x10−6
0.0253
0.0820
2.7
3.9
0.2
39.7
1.7
0.0
0.2
20.6
0.0
30.9
100.0
Net Flux
S IV
O III
e−
e−
hot
1.03x10−6
-0.00222
148
Table 5.18: Source and Loss Mechanisms for O III; 1 October 2000 non-equilibrium
conditions
Particles
s−1 cm−3
%
Energy
eV s−1 cm−3
%
Source Mechanisms
Ionization of O II by e−
Ionization of O II by hot e−
O + O++ → O++ + O∗
Thermal equilibration with S II
Thermal equilibration with S III
Thermal equilibration with S IV
Thermal equilibration with O II
Total Sources
1.56x10−5
2.24x10−5
6.41x10−6
0.00
0.00
0.00
0.00
4.44x10−5
35.1
50.4
14.4
0.0
0.0
0.0
0.0
100.0
0.00245
0.00351
0.00121
0.000181
0.00119
0.000106
0.000200
0.00884
27.7
39.7
13.7
2.1
13.4
1.2
2.3
100.0
Loss Mechanisms
Ionization of O II by e−
Ionization of O II by hot e−
Recombination of O IV
O + O++ → O+ + O+
O + O++ → O++ + O∗
S + O++ → S+ + O+
S + O++ → S++ + O+ + e−
O++ + S+ → O+ + S++
O++ + S++ → O+ + S+++
Thermal equilibration with e−
Thermal equilibration with e−
hot
Radial transport
Total Losses
2.87x10−8
5.38x10−7
2.47x10−7
6.17x10−7
6.41x10−6
5.29x10−6
3.66x10−6
3.69x10−6
5.70x10−6
0.00
0.00
1.13x10−5
3.75x10−5
0.1
1.4
0.7
1.6
17.1
14.1
9.8
9.8
15.2
0.0
0.0
30.2
100.0
3.57x10−6
6.66x10−5
3.05x10−5
7.59x10−5
0.000788
0.000650
0.000450
0.000454
0.000703
0.00355
2.31x10−7
0.00140
0.00816
0.0
0.8
0.4
0.9
9.7
8.0
5.5
5.6
8.6
43.4
0.0
17.1
100.0
Net Flux
6.92x10−6
0.000681
fixed in System III longitude, and show a two-peak structure. This is in contrast to the
azimuthal variations in the Io torus observed by UVIS (Ch. 4), which have amplitudes
that vary between 5–25% (for S II and S IV); drift in phase, relative to System III
longitude; and show only one peak as a function of azimuth.
5.2.3.1
Longitudinally-Varying Hot Electron Fraction
In order to try and generate the observed azimuthal variations in composition,
the hot electron fraction was varied sinusoidally with System III longitude:
149
Table 5.19: Source and Loss Mechanisms for
ditions
e− ;
1 October 2000 non-equilibrium con-
Energy
eV s−1 cm−3
Source Mechanisms
Thermal equilibration
Thermal equilibration
Thermal equilibration
Thermal equilibration
Thermal equilibration
Thermal equilibration
Total Sources
Loss Mechanisms
Collisional excitation
Collisional excitation
Collisional excitation
Collisional excitation
Collisional excitation
Radial transport
Total Losses
Net Flux
with
with
with
with
with
with
of
of
of
of
of
S II
S III
S IV
O II
O III
e−
hot
S II
S III
S IV
O II
O III
%
0.00537
0.0395
0.00536
0.0169
0.00354
0.0571
0.128
4.2
30.9
4.2
13.2
2.8
44.7
100.0
0.0301
0.0706
0.00672
0.0149
0.00148
0.00357
0.127
23.6
55.4
5.3
11.7
1.2
2.8
100.0
0.000354
³
´
2
2
fh (t, λIII ) = fh,0 + αh e−(t−t0,h ) /σh × (1 + αh,λIII cos (λIII − φh,λIII ))
(5.31)
where αh,λIII is the amplitude of the System III variation in hot electron fraction, λIII
is the System III longitude of the model bin, and φh,λIII is the phase of the variation i.e.
the longitude of the maximum hot electron fraction. φh,λIII was set to 20◦ to match the
phase of the 5% variation in electron temperature with System III longitude observed
by UVIS.
Although the addition of the second (azimuthal) term in Eq. 5.31 did introduce
an azimuthally varying composition, it did not change the azimuthally-averaged composition of the torus. This is probably due to the symmetric nature of the azimuthal
perturbation. The independence of the azimuthal-variation model parameters from the
temporal-variation model parameters greatly simplifies the model fitting procedure.
150
Varying the hot electron fraction with System III longitude as in Eq. 5.31 does
indeed produce an azimuthally-varying composition. A value of αh,λ =0.2 yields a sinusoidal azimuthal variation in composition with an amplitude of ≈ 10% for both S II and
S IV. However, the phase of such an azimuthal variation in composition remains fixed
in System III; the amplitude of the variation also remains constant–in contrast with the
UVIS observations.
Modulation of amplitude, as observed by UVIS (Section 4.3.4), requires the interference of phenomena with periods of 9.925 hours (System III) and 10.07 hours. The
longitudinally-varying hot electron fraction introduced a System III periodicity to the
data. To add the second period, the model plasma was allowed to uniformly lag corotation with the magnetic field (i.e. System III) by 1.2 km/s, which corresponds to a
rotation period of 10.07 hours. This model reproduced many of the general characteristics of the variations seen in the UVIS data: the phase of the azimuthal variation in
composition increased roughly linearly with time and amplitudes that varied between
10-25% on a 28.8-day modulation cycle.
Producing an azimuthal variation with the appropriate amplitude required a relatively large azimuthal variation in hot electron fraction (≈20-30%). With this large
variation in the hot electron fraction, the phase of the the azimuthal variation in composition eventually (after 100-300 days) becomes fixed in System III longitude.
The real failing of this model to match the data is in the temporal behavior of
the amplitude of the azimuthal variation. As seen in Fig. 4.9, the maximum amplitude
of the S II azimuthal variation seen by UVIS was 21% for the first modulation cycle,
and 24% for the second, while for S IV the maximum amplitude was 25% for the first
cycle and 17% for the second. The model’s maximum amplitude for both S II and S IV
decreased rapidly from one modulation cycle to the next. It was simply not possible to
match the observed amplitude behavior with this model.
Furthermore, if the model was allowed to run for two years (so that it had reached
151
either a steady-state condition or an oscillatory state with constant amplitude and
period) prior to increasing the neutral source rate and the hot electron fraction, it could
not produce azimuthal variations with the proper amplitude and modulation at the 28.8day period during the UVIS observing period. The only way this model could produce
azimuthal variations in composition with an amplitude of 20–30% was as a transient
response to the model’s initial conditions. Even then, the model failed to produce the
observed temporal variation in S II and S IV amplitude.
5.2.3.2
Non-Uniform Corotational Lag
Hill and Dessler (2004) and P. Delamere (private communication) have suggested
that azimuthally non-uniform corotational lag might be a mechanism capable of reproducing the UVIS results. The idea behind this mechanism is that certain System III
longitudes might be better able to enforce corotation than others, perhaps to due longitudinal variations in the conductivity of Jupiter’s ionosphere. At System III longitudes
where Jupiter had a higher value of ionospheric conductivity, the plasma would be
moving closer to the corotation velocity, while at System III longitudes where Jupiter
had lower conductivity, the plasma velocity would deviate more from corotation. The
variation in plasma velocity, relative to the System III coordinate system, would cause
plasma to pile up in azimuthal regions that had high conductivity, Since, on average,
the plasma still lagged rigid corotation by 1.2 km/s (in order to produce the 10.07-hour
periodicity in the UVIS data), eventually a “blob” of plasma that had built up in this
manner would drift out of the region of high conductivity. The drift of this blob would
cause the phase of the azimuthal variation to increase with time.
However, this mechanism (alone and in conjunction with a System III varying
hot electron fraction) suffers from many of the same deficiencies as the System III
varying hot electron model. Namely, failure to generate azimuthal variations with amplitudes of ≈20% and modulation with a 28.8-day period from an equilibrium state.
152
The non-uniform corotational lag model also failed to match the temporal evolution of
the azimuthal variation amplitude.
Since models incorporating corotational lag (either uniform or non-uniform) had
failed to reproduce the observed torus behavior, this line of modeling was dropped. This
result supports the finding of Brown (1995) that corotational lag is not the cause of the
System IV periodicity.
5.2.3.3
System III and System IV-Varying Hot Electron Fraction
A different approach is to assume two independent sources of hot electrons, one
that remains fixed in System III longitude, and another that drifts relative to System
III. The hot electron fraction as a function of time and System III longitude is then
given by the following equation:
fh (t, λIII ) =
³
´
2
2
fh,0 + αh e−(t−t0,h ) /σh × (1 + αh,λIII cos (λIII − φh,λIII )) (5.32)
× (1 + αh,λIV cos (λIII − φh,λIV − ∆Ωt))
where αh,λIV is the amplitude of the drifting hot electron source, φh,λIV is the phase of
the drifting hot electron source, and ∆Ω is the difference in angular velocity between
the System III coordinate system and the drifting hot electron source. To match the
phase increase in the UVIS data, ∆Ω was set to 12.2◦ /day.
The phase of the azimuthal variation produced by the dual hot electron source
model increases in a nearly linear fashion: when the amplitude of the azimuthal variation
nears its minimum value, the phase increases somewhat more rapidly than when the
amplitude is near its maximum. This trend was also seen, although weakly, in the UVIS
S II and S IV data. Unlike the models of Section 5.2.3.2 and 5.2.3.1 that could only
produce a transient linear increase in the phase of the azimuthal variation, the dual hot
electron source model produces a linear increase in the phase of the azimuthal variation
153
in its equilibrium state. Additionally, the amplitude of the variation continues to be
modulated at the 28.8-day period, even in the equilibrium state, which is reached in as
little as 60 days. For equilibrium conditions, the amplitude of S II varies between 5–16%
over the 28.8-day modulation cycle, while the amplitude of S IV varies between 1–13%.
As the neutral source rate increases, the peak amplitude of S II increases only to 18%,
but the peak amplitude of S IV increases by a factor of two, reaching a maximum value
of 29% on day 250.
The dual hot electron source model produces a good fit to the UVIS data. The
behavior of both the phase of the azimuthal variation in composition and its amplitude
are reproduced by the dual hot electron model. Figure 5.4 shows the phase of the
azimuthal variation in composition from the dual hot electron model and the UVIS
data for the ion species S II and S IV. The UVIS data is the same as presented in
Fig. 4.4. The phase of the model azimuthal variation closely matches that of the UVIS
data for both ion species for most of the observing period, although after day 305, the
phase of the model S IV variation is offset by ∼30◦ from the data.
The amplitude of the azimuthal variation for S II and S IV as a function of time is
shown in Fig. 5.5. The dual hot electron source model successfully reproduces both the
strength of the amplitude variation and its general behavior with time. In particular, the
dual electron model correctly predicts that the amplitude of the S II azimuthal variation
on day 308 should be approximately the same as on day 280, while the amplitude of
the S IV azimuthal variation on day 308 should be ≈40% less than the value on day
280—something which none of the previous models could do.
The model parameters used to produce Figs. 5.1–5.5 are given in Table 5.20. It is
important to note that these parameters were were obtained by assuming that the torus
plasma was rigidly corotating with Jupiter’s magnetic field (i.e. with System III). In this
case, the ratio of the amplitudes of the two sources (αh,λIV /αh,λIII ) is 10:1, in favor of the
subcorotating hot electron source. However, measurements of the radial velocity of torus
Longitude of Peak Mixing ratio
154
360
300 S II
240
180
120
UVIS Data
Model
60
0
360
300 S IV
240
180
120
60
0
275 280 285 290 295 300 305 310 315 320
Day of Year 2000
Amplitude of Azimuthal Variation
Figure 5.4: Comparison of model azimuthal variation phase with UVIS data. Modelderived phases for the azimuthal variation of S II and S IV are plotted for the UVIS
observing period.
0.30
UVIS Data
S II
0.25
Model
0.20
0.15
0.10
0.05
0.00
0.30
S IV
0.25
0.20
0.15
0.10
0.05
0.00
275 280 285 290 295 300 305 310 315 320
Day of Year 2000
Figure 5.5: Comparison of azimuthal variation amplitude from the torus chemistry
model with UVIS data. Model-derived amplitudes for the azimuthal variation of S II
and S IV are plotted for the UVIS observing period.
plasma have shown that between 6–7 RJ the plasma typically lags rigid corotation by
∼2–3 km/s (Brown, 1994b; Thomas et al., 2001). If the plasma in the model is allowed to
155
Table 5.20: Best fit parameters for the time-variable, azimuthally-varying model
Parameter
Basic Parameters
Sn,0
O/S
fh
Te,hot
τ0
Value
2.0x1028 s−1
1.4
0.23 %
49 eV
70. days
Temporal Variation Model Parameters
αn
t0,n
σn
αh
t0,h
σh
2.3
249 (5 September 2000)
30 days
0.08%
279 (5 October 2000)
60 days
Azimuthal Variation Model Parameters
αh,λIII
φh,λIII
αh,λIV
φh,λIV
∆Ω
0.025
20◦
0.25
300◦
12.2◦ /day
lag rigid corotation by this amount, the hot electron source amplitude ratio approaches
2:1 with αh,λIV ≈ 0.30, αh,λIII ≈ 0.15, and φh,λIV ≈ 250◦ . The resulting plots of
model composition vs. time, phase vs. time, and amplitude vs. time are qualitatively
similar to those in Figs. 5.1, 5.4, and 5.5. Since qualitatively similar model results can
be obtained with a relatively wide range of azimuthal variation parameters, depending
on the speed by which the model plasma lags rigid corotation, the azimuthal model
parameters listed in Table 5.20 should not be considered unique. In general, however,
in order to generate a subcorotating azimuthal variation in composition, as seen in the
UVIS data, αh,λIV & 2αh,λIII . If this inequality is not satisfied, the azimuthal variation
in composition rapidly becomes fixed in System III longitude.
156
5.3
Discussion
While it is relatively easy to come up with mechanisms that produce hot elec-
trons as a function of System III longitude, it is not at all obvious how to produce an
additional, subcorotating pattern of hot electrons. One idea that has been proposed is
that Jupiter, like the sun, might rotate differentially, with high latitude regions having
a longer rotation period than equatorial regions (Dessler , 1985; Sandel and Dessler ,
1988). A component of Jupiter’s magnetic field that originates at high latitudes might
then rotate more slowly than the System III rotation period. If the hot electrons that
drive the observed azimuthal variation in composition were fixed to this high latitude
component, this could explain the 10.07-hour period. Presumably, a subcorotating high
latitude magnetic field component, if it exists, would affect the Jovian aurora as well
as the Io plasma torus. However, the morphology of the Jovian aurora is strongly fixed
in System III longitude, and although the temporal coverage of the Jovian aurora is
relatively poor, there have been no auroral phenomena reported at the System IV or
10.07-hour periods (Clarke et al., 2004).
Another possible mechanism of creating subcorotating hot electrons is the azimuthal drift of electrons due to the gradients in and curvature of the magnetic field of
Jupiter. The azimuthal drift period for electrons is given by:
τd =
=
πeRJ2 B0 T (α)
3ELc A(α)
5.8 × 105 T (α)
hours
LE(keV ) A(α)
(5.33)
where e is the electron charge, E is the kinetic energy of the particle, L is the L-shell
of the particle, c is the speed of light, and
T (α)
A(α)
is the ratio of the bounce time integral
to the azimuthal drift integral for particles with an equatorial pitch angle, α (Cowley,
1972). There are two cases for which
T (α)
A(α)
can be solved analytically:
157




3,
T (α)
=
A(α) 


2,
α = 0◦
(5.34)
α = 90◦
Using Eq. 5.33 to solve for the kinetic energy of an electron with pitch angle α = 0◦
at L = 6 with an azimuthal drift period of 28.8 days yields E = 420 eV. In order for
the azimuthal drift of electrons to be responsible for creating the observed amplitude
modulation, there must be a mechanism that preferentially heats electrons at L = 6 to
420 eV. Furthermore, since the System IV period remains constant over a wide range
of radial distances in the Io torus, the preferred energy must decrease linearly with
increasing L. However, the Plasma Science instrument on the Galileo spacecraft found
a wide range of electron energies in the Io plasma torus, and no preferential enhancement
at 420 eV (Frank and Paterson, 2000a).
In the dual hot electron source model, the subcorotating source of hot electrons
produces the observed azimuthal variation, while the weaker System III-fixed hot electron source produces the modulation of the azimuthal variation. None of the previous
observations of System IV periodicity in the Io plasma torus reported modulation of
amplitude at the beat frequency between System III and System IV, although Pilcher
and Morgan (1980) did report that the torus transitioned between a state where the
[S II] 6731Å brightness was peaked between 160◦ ¡λIII ¡340◦ and a more azimuthally uniform state in approximately two weeks. The detection of 28.8-day modulation in the
UVIS data could be due to the improved capabilities of the Cassini UVIS instrument
over the Voyager UVS (10x higher spectral resolution and an imaging detector) and
advantages of observing in the EUV region of the spectrum, as opposed to the optical
(numerous bright emission lines of all the major ion species in the torus, no atmospheric
effects, etc.). Alternatively, it is possible that the amplitude modulation was simply not
present during previous observations of the Io torus. By reducing the amplitude of the
System III-fixed hot electron source relative to the subcorotating hot electron source,
158
the degree of amplitude modulation would be diminished. In the limiting case of no
System III-fixed hot electron source, the model produces output that is quite similar to
the previously observed System IV periodicity.
5.4
Conclusions
The 0-d torus chemistry model of Delamere and Bagenal (2003) has been extended
to include the latitudinal and azimuthal distribution of plasma in the Io torus. This
model can accurately reproduce the observed composition of the torus on 14 January
2001 for steady-state conditions. By introducing a factor of 3 increase in the rate of
oxygen and sulfur atoms supplied to the extended neutral clouds that are the source of
the torus plasma coupled with a ∼35% increase in the amount of hot electrons in the Io
torus, the model produces temporal changes in the composition of the Io plasma torus
that match the UVIS observations. By adding two independent, azimuthally-varying
sources of hot electrons—a primary source that slips 12.2◦ /day relative to the System
III coordinate system and a secondary source that remains fixed in System III—to the
time-variable model, the temporal behavior of the phase and amplitude of the azimuthal
variation in composition seen in the UVIS data can also be reproduced. Although the
dual hot electron source model can not reproduce all of the fine structure seen in the
UVIS data, given the numerous simplifying assumptions that went into the model, the
fit between the model and the data illustrated in Figs. 5.1, 5.4, and 5.5 is remarkable.
This result suggests that the System IV periodicity observed in the Io torus may be
caused by a subcorotating source of hot electrons. However, at the present time, there
is no known physical mechanism capable of producing such a source of subcorotating
hot electrons.
Chapter 6
Conclusions
6.1
Temporal Variations
The total power emitted by the torus in the EUV region of the spectrum (561 Å–
1182 Å) is highly variable, with “typical” values during the Cassini epoch in the range
of 1.3–1.8x1012 W. These values are 2–4 times fainter than the total luminosity derived
from the Voyager 1 and Voyager 2 UVS (Shemansky, 1980, 1987). Stochastic luminosity variations of 5% were observed on timescales of ∼15 minutes. Intermediate-length
events, lasting roughly 20 hours from start to finish, change the total torus EUV luminosity by ∼20%. Long-term variations of 25% were observed on timescales of ∼40
days.
The torus exhibited significant long-term compositional changes during the UVIS
inbound observing period from 1 October 2000 to 14 November 2000. During this
period, the mixing ratio of S II fell from 0.10 to 0.05, while the mixing ratio of S IV
increased from 0.02 to 0.05. The mixing ratios of O II and S III, the two dominant ion
species in the torus, remained relatively constant. This change in composition is well
matched by neutral cloud models that introduce a factor of 3 increase in the rate of
oxygen and sulfur atoms supplied to the extended neutral clouds that are the source of
the torus plasma on 5 September 2000, coupled with a ∼35% increase in the amount of
hot electrons in the Io torus on 5 October 2000.
160
6.2
Radial Variations
The profile of the brightness of the S III 680 Å feature versus distance from
Jupiter has a half-width at half-maximum, as measured radially outward from the peak,
of 1.3RJ . This width is comparable to that measured by Voyager UVS and EUVE. We
find no evidence for an extremely narrow ribbon feature in the EUV spectra, such as
that described by Dessler and Sandel (1993). In addition, a radial scan of the midnight
sector of the Io plasma torus, obtained on 14 January 2001, has been analyzed using a
spectral fitting model that incorporates the latest atomic physics from the CHIANTI
database. These observations record the radial structure of the Io torus at a local time of
01:50, which has not been previously observed. Fortuitously, this observation occurred
during a period of minimum azimuthal variability. The torus electron temperature is
found to be somewhat less than that predicted by the Voyager-era model of Bagenal
(1994). The radial profile of the electron column density is well matched by assuming
that the local electron number density is proportional to r−5.4 in the range of 6.0 RJ –
7.8 RJ and r−12 outside of 7.8 RJ . If we use this profile for electron density and the
ion temperatures derived by Bagenal (1994), we find that the flux tube content of the
Io torus is proportional to r−2 , which is consistent with flux tube interchange acting to
transport plasma radially outward.
The plasma composition derived from the UVIS spectra of 14 January 2001 is
significantly different than the torus composition during the Voyager era. However,
Steffl et al. (2004a) (Chapter 2) has shown significant temporal variations over the sixmonth flyby of Jupiter. Both O II and S II are depleted compared to the Voyager values,
while S III and S IV show enhancements. The O/S ion ratio of 0.9, obtained from the
UVIS spectra, is much lower than the Voyager value of 1.6. Ground-based observations
of the torus have also found less oxygen than predicted by the Voyager models. In
addition to the lower O/S ratio, we find that the charge per ion has increased to 1.7
161
from 1.4. The spectral resolution of UVIS allows us to report the 3-σ detection of S V.
S V, which has not previously been detected in the Io torus, is present in the torus at
a mixing ratio of ∼0.5%.
The spectral emissions model developed for this thesis has the ability to approximate the effects of an arbitrary, non-thermal electron distribution as the linear
combination of Maxwellian components. We explored the effects of using a non-thermal
κ-distribution, which is quasi-Maxwellian at low energies and a power law at high energies, to analyze the torus spectra. Models using a κ-distribution of electrons had a
marginally lower value of the χ2 statistic, although the actual spectral fits were qualitatively very similar to those produced by the Maxwellian model. The ion composition
derived using the κ-distribution function model was identical to the ion composition
derived using a Maxwellian distribution function. However, due to the the shape of the
distribution function in the 5–60 eV range of energy, the κ models required a higher
electron column density to match the brightness of the UVIS torus spectra. The value
of the κ-parameter, which determines the index of the power law, high-energy tail of the
distribution, was found to generally decrease with radial distance. The derived radial
profile value of the κ-parameter is consistent with the measurement of κ = 2.4 at 8 RJ
made by the Ulysses URAP instrument (Meyer-Vernet et al., 1995).
The 0-d torus chemistry model of Delamere and Bagenal (2003) has been extended
to include the latitudinal and azimuthal distribution of plasma in the Io torus. This
model can accurately reproduce the observed composition of the torus at 6.5 RJ on 14
January 2001 for steady-state conditions.
6.3
Azimuthal Variations
Persistent azimuthal variability in torus ion mixing ratios, electron temperature,
and equatorial electron column density was observed. The azimuthal variations in S II,
S III, and electron column density mixing ratios are all approximately in phase with each
162
other. The mixing ratios of S IV and O II and the torus equatorial electron temperature
are also approximately in phase with each other, and as a group, are approximately 180◦
out of phase with the variations of S II, S III, and equatorial electron column density.
The phase of the observed azimuthal variation in torus composition drifts 12.2◦ /day,
relative to System III longitude. This implies a period of 10.07 hours, 1.5% longer than
the System III rotation period. This period is confirmed by Lomb-Scargle periodogram
analysis of the UVIS data.
The relative amplitude of the azimuthal variation in composition is greater for
S II and S IV. These species have relative amplitudes that vary between 5–25% over the
observing period. The major ion species, S III and O II, have relative amplitudes that
remain in the range of 2–5%. The amplitude of the azimuthal compositional variation
appears to be modulated by its position relative to System III longitude such that:
when the peak in S II mixing ratio is aligned with a System III longitude of 210±15◦ ,
the amplitude is enhanced; and when the peak in S II mixing ratio is aligned with a
System III longitude of 300±15◦ , the amplitude is diminished.
By adding two independent, azimuthally-varying sources of hot electrons—a primary source that slips 12.2◦ /day relative to the System III coordinate system and a
secondary source that remains fixed in System III—to the time-variable neutral cloud
theory model, the temporal behavior of the phase and amplitude of the azimuthal variation in composition seen in the UVIS data can also be reproduced. Although the dual
hot electron source model can not reproduce all of the fine structure seen in the UVIS
data, given the numerous simplifying assumptions that went into the model, the fit
between the model and the data illustrated in Figs. 5.1, 5.4, and 5.5 is remarkable. This
result suggests that the System IV periodicity observed in the Io torus may be caused
by a subcorotating source of hot electrons.
163
6.4
Outstanding Questions
Scientific research often has a quality similar to that of the mythical hydra: for
every one question answered, two new questions arise. This thesis has proven no exception. The following is a listing of some of the outstanding questions and issues from
each chapter.
6.4.1
Chapter 2
During the 45-day staring mode observation period, 6 torus brightening events
were observed. These events have yet to be examined in detail. The spatial morphology
of these events is completely unknown. Does the entire torus brighten by 20%, or is the
brightening restricted to certain longitudes, local times, or radial distances? What is
the cause of these events?
There is tentative evidence that suggests that the torus brightening events were
generally preceded by a brightening of the Jovian aurora. However, given the sampling
of the UVIS observations, it is not possible to make a definitive statement about the
possible correlation of torus and aurora. Are the torus brightening events correlated
with auroral emissions, and if so, what is the mechanism that connects the two?
The largest two of these events occur within one day of the amplitude of the
azimuthal variation in composition reaching its peak value. Is this coincidental, or are
the brightening events more likely to occur when the System III and System IV (or the
10.07-hour period) coordinate systems align?
6.4.2
Chapter 3
Observations by the Voyager UVS suggested that ∼80% of the torus EUV emissions originated from an extremely narrow region with a FWHM of only 0.22 RJ (Dessler
and Sandel , 1993; Volwerk et al., 1997). While the UVIS observations rule out the exis-
164
tence of such a strong, tightly-confined peak, they do not have enough spatial resolution
to determine the radial profile of the torus composition, density, and temperature near
the orbit of Io.
The orientation of the UVIS entrance slits during the 14 January 2001 radial scans
(parallel to Jupiter’s rotation axis) makes them well-suited for examining the latitudinal
distribution of torus plasma. With proper treatment of the observing geometry and lineof-sight effects, these observations could be used to derive the scale heights of the ion
species in the torus.
6.4.3
Chapter 4
Periodicity in the torus at period of 10.21 hours, i.e. the System IV period, has
been detected by a variety of observers at a variety of wavelengths over a (sporadicallysampled) 21-year period. However, during the Cassini era, no such periodicity was
detected. Instead, a periodicity of 10.07 hours was present in the torus. Is the UVISobserved 10.07-hour periodicity produced by the same mechanism responsible for the
System IV periodicity in previous observations? If so, what caused the change in period?
Does the torus currently have a 10.07-hour periodicity, a System IV periodicity, or some
other periodicity?
If the 10.07 hour period and System IV are indeed manifestations of the same
underlying physical mechanism, why was the period at 10.07 hours during the UVIS
observations and not at the traditionally observed 10.21 hours?
UVIS was also the first to observe modulation of the amplitude of azimuthal
variations in composition at the beat frequency between the System III rotation period
and a subcorotating period. For UVIS and the observed 10.07-hour periodicity, this
modulation has a period of 28.8 days, although it would be 14 days for the 10.21-hour
System IV periodicity. Is the 28.8 day-modulation (or 14-day modulation in the case of
a System IV periodicity) a long-lived characteristic of the Io torus, or was it a transient
165
response to the factor of three increase in the neutral source rate in September 2000?
6.4.4
Chapter 5
Neutral cloud models of the Io torus (that include additional energy from a hot
electron population) can match the observed temporal changes in torus composition by
assuming a factor of three increase in the amount of neutral material supplied to the
extended neutral clouds. Presumably, this was in response to some volcanic event on
Io. However, the process whereby neutrals go from Io to the extended neutral clouds is
not fully understood. Specifically, how does an increase in the neutral source rate relate
to dust production or volcanic activity on Io?
The observed azimuthal variability of the torus is can be reproduced by a neutral
cloud theory model that incorporates two independent sources of hot electrons. What
is the mechanism that produces such a source of subcorotating hot electrons?
In the dual hot electron source model, the torus plasma was assumed to corotate
with Jupiter’s magnetic field. However, there is observational evidence that the plasma
between 6.0–6.5 RJ radial distance lags rigid corotation by 2–4 km/s (Brown, 1994b).
Models incorporating a uniform corotational lag of this magnitude can still produce
a phase that increases at a rate of ∼ 12◦ /day. However, since the underlying plasma
drifts relative to both the System III and the 10.07-hour periods, the amplitude of both
the overall azimuthal variation in composition and the 28.8 modulation are significantly
reduced. While it is possible that a set of model parameters can be found that produces
results that match the UVIS data, to date, they have not been found.
This issue raises some additional questions about the nature of the corotational
lag in the Io plasma torus. The profile of corotational lag presented by Brown (1994b)
was created from the sum of roughly six months of observations of the Io torus. It
is possible, and perhaps even likely, that the actual rotation velocities in the Io torus
vary with time both on intermediate timescales (weeks) and long timescales (years).
166
It is certainly possible that during the UVIS encounters, when there was an increased
amount of fresh pickup ions, the corotational lag profile could have been significantly
different.
6.5
Future Observations
The Jupiter Magnetospheric Explorer (JMEX) is perhaps the ideal mission to
address the unanswered questions about the Io plasma torus. As a dedicated Jupiterobserving satellite it will be able to obtain the long baseline of observations necessary for
understanding the temporal behavior of the torus. However, given the recent decision
by NASA not to select the mission, its status is uncertain.
The New Horizons spacecraft, on the other hand, is scheduled to launch in January
or February of 2006. If all goes well, it will fly past Jupiter in February 2007 on its way to
Pluto. Its trajectory past Jupiter is fairly similar to that taken by Cassini nearly seven
years earlier. The ALICE ultraviolet spectrometer aboard the New Horizons spacecraft
covers roughly the same wavelength range as UVIS, though at somewhat lower spectral
resolution (Stern et al., 1998). During the Jupiter flyby, ALICE will make an extended
series of observations of the Io plasma torus and Jovian aurora. This dataset could yield
a new understanding of the nature of the Io torus.
There is also the potential for future ground-based observations of the Io plasma
torus. However, to the author’s knowledge, only one group currently has an active
ground-based Io torus observing campaign (Nozawa et al., 2004).
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Appendix A
Flatfielding
All instruments have their own imperfections and idiosyncracies that need to be
dealt with properly in order for data to be successfully interpreted. The Cassini UVIS
is no exception; for any rigorous analysis of the UVIS data, careful attention must be
paid to the detector flatfield correction. The following is a somewhat technical description of the techniques used to derive the flatfield corrections for the UVIS EUV
and FUV detectors. These flatfields are ultimately derived from observations of the
star Spica and were used in the analysis of all data in this thesis. Reflecting their origin, these flatfields will be referred to as the Spica flatfields. An independent flatfield
correction for the FUV channel has been derived from observations of the local interstellar medium/interplanetary medium (Don Shemansky, private communication). This
second flatfield correction will be referred to as the LISM flatfield.
This appendix will describe (in some detail) the methodology used in creating the
Spica flatfield and present qualitative and quantitative comparisons of the Spica and
LISM flatfields. While this may be of limited use to the casual reader, it is included in
the hope (perhaps naı̈ve) that those wishing to understand the gory details of UVIS or
to reproduce the results in this thesis will find this information useful.
179
A.1
Definitions and Instrumental Details
The UVIS CODACON (Lawrence and McClintock , 1996) detectors are subdi-
vided into 21 6 pixels (1024 columns in the spectral dimension by 64 rows in the spatial
dimension). Individual UVIS pixels are not square. Rather, they are 100x25 µm (spatial
by spectral) in physical size and subtend a field of view of 1 x 0.25 mrad (1 mrad =
0.001 radians).
Both the EUV and FUV channels of UVIS are equipped with a 3-position slit
changer mechanism. The three positions are referred to as the occultation slit (8 mrad
wide), lo-resolution slit (2.0 mrad wide for the EUV channel and 1.5 mrad wide for
the FUV channel) and the hi-resolution slit (1.0 mrad wide for the EUV channel and
0.75 mrad wide for the FUV channel). The FUV occultation slit is equipped with a
cylindrical MgF2 lens designed to spread light from a point source perpendicular to
the dispersion direction, thereby preventing the FUV detector from saturating during
observations of particularly bright stars. The presence of this lens and its support
structure reduce the effective field of view to an 8x8 mrad area in the center of the slit
(where the lens is transmitting) and two 11x8 mrad windows at the ends of the slit. As
such, the FUV occultation slit is poorly suited for observations designed to determine
the detector flatfield correction, and therefore, the FUV lo-resolution slit was used.
A Cartesian coordinate system has been defined for the Cassini spacecraft. The
boresights of the UVIS EUV and FUV channels are defined as the geometric center of
the CODACON detectors (spectral pixel 511.5, spatial pixel 31.5). The UVIS boresight
(and the boresights of the other remote sensing instruments) is nominally aligned to the
spacecraft -Y axis, while the UVIS entrance slits are approximately parallel with the
spacecraft Z axis. The instrument azimuth angle (φ) is defined as the angle a vector
makes with respect to the spacecraft Y-Z axis, measured from the Z axis. The spacecraft
coordinate system is shown relative the the orientation of UVIS in Fig. A.1.
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Figure A.1: The orientation of the Cassini UVIS relative to the spacecraft Cartesian
coordinate system. Figure from the Cassini UVIS Calibration Report (Bill McClintock,
private communication).
A review of the UVIS instrument is given by Esposito et al. (2004). In addition,
the Cassini UVIS Calibration Report (Bill McClintock, private communication) is an
invaluable resource for those wishing a more detailed description of the instrument.
The UVIS flatfield correction is a two-dimensional, multiplicative array applied to
data during the reduction process in order to correct for spatial variations in the detector
sensitivity. This is separate from—though closely related to—the instrument calibration
which is a one-dimensional multiplicative vector used to correct for variations in the
detector sensitivity as a function of wavelength. In principle, pixel-to-pixel variations
in detector sensitivity could be corrected by using a two-dimensional calibration array.
However, for largely historical reasons, these two corrections are applied separately to
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UVIS data.
The source of the dual correction procedures dates back to laboratory calibration of the UVIS instrument. The radiometric sensitivity of the UVIS instruments was
measured by illuminating a large area of the detector and comparing the flux measured
by the UVIS detector to that measured by a NIST calibrated diode, or to theoretical
models of the spectrum (e.g. H2 ) used to illuminate the detector. During the laboratory
calibration, the severity of the flatfield artifacts of the UVIS detectors (especially for the
FUV channel) was not fully appreciated, and so the counts over the whole detector were
summed up to increase the signal to noise ratio. This process yielded measurements
of the detector radiometric sensitivity at a few tens of wavelengths. The sensitivity at
wavelengths other than those directly measured was derived through linear interpolation. In this manner, a 1024-element multiplicative calibration correction was created.
A.2
Methods for Obtaining Flatfield Corrections
The easiest way to derive a flatfield correction is to illuminate the detector with a
spatially-uniform monochromatic source. In this case, any differences in the number of
counts in the individual detector pixels are the result of spatial (pixel-to-pixel) variations
in the detector sensitivity (assuming that the signal to noise ratio is large). However,
the presence of a grating in the UVIS optical path means that while the entrance slit
may be evenly illuminated, only a small fraction of the detector (the projected width
of the slit on the detector divided by the length of the detector, or 3% for the UVIS
occultation slits) will be illuminated by a monochromatic source. This problem can be
solved by using a spatially uniform white-light (equal intensity at all wavelengths) source
to illuminate the entrance slits. After dividing the resulting image by the instrument
sensitivity as a function of wavelength (also referred to as the detector calibration curve)
any pixel variations are due to variations in detector sensitivity. Sadly though, no such
source exists. The next best thing is to use a spatially uniform source with a known
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spectrum. Then, after dividing the raw image by the detector calibration curve and the
known spectrum, one can use the pixel to pixel variations to derive a flatfield correction.
Ideally UVIS would have been taken to a synchrotron radiation facility and the beam
source used to illuminate the entrance slits. However, for various practical reasons (like
time and money) this was not possible, and UVIS was launched before the flatfield
correction was properly determined. Therefore, UVIS is limited to using astrophysical
sources to derive the flatfield correction. Unfortunately, astrophysical sources are rarely
spatially uniform (the local interstellar medium/interplanetary medium being a possible
exception), and the EUV/FUV spectra of such objects (in physical units) are not as
well determined as one might like them to be.
A.2.1
Spica Flatfields
Assuming that the background count rate of an instrument (from RTGs, dark
counts, etc.) is low compared to the signal count rate, a star bright in the UV can serve
as a good approximation to a spatially uniform source. The star, Spica, is relatively
bright in the EUV/FUV. Three sets of Spica observations were obtained by UVIS on 3
April 2001, 17 July 2002, and 19 May 2003.
A.2.1.1
Row-to-Row Variations in Detector Sensitivity
Since the absolute radiometric sensitivity of the instrument has already been
measured in the lab (albeit in a one-dimensional form), it is only necessary to derive the
relative row-to-row, column-to-column or pixel-to-pixel variations in detector sensitivity,
and then normalize this relative correction so that the absolute radiometric calibration
of the instrument remains unchanged. This greatly simplifies the process of deriving a
flatfield correction from an astrophysical source, since it is no longer critical to know
the spectrum of the source object.
The flatfield correction is given by:
183
Fλ =
Ci,m
Aλ fi t
photons
cm2 s
(A.1)
where Fλ is the flux from the star at a wavelength of λ, Ci,m is the counts observed
in a pixel in column i on scan m, (i.e. a spectrum shifted 0.2× m milliradians); Aλ is
the effective area of a pixel illuminated with light of wavelength λ,as determined by the
laboratory calibration; and fi is the flatfield correction for the pixel in column i.
By rotating the Cassini spacecraft about the X axis, the elevation angle of Spica
changes, i.e. it appears to move along the spatial dimension of the detector. If the
rotation of the spacecraft is held at a constant angular velocity, than the star will spend
an equal amount of time in each row of the detector. By starting the observation with the
star outside of the UVIS field of view, scanning it uniformly across the slit, and ending
the observation with the star outside the instrument’s field of view on the opposite side,
each row will have received equal illumination by both the star the scattered light profile
associated with the star (assuming that the instrument scattering function is reasonably
constant over the length of the entrance slits).
Spica is relatively bright in the EUV/FUV, so photon counting statistics are by
far the largest source of noise. With the integration times used in the Spica observations,
the total signal to noise ratio is ∼30 for pixels in the EUV detector below 900Å and
more than an order of magnitude higher than that for all other pixels. The “signal”
from Spica below 900Å—a significant portion of it is internally-scattered light from
longer wavelengths—is ∼10 times greater than the count rate produced by the mesa
background feature. Since each row of the detector has received equal illumination
from the source and noise in the data is small, any difference in the counts measured
in the pixels of a given column must be the result of row-to-row variations in detector
sensitivity.
Dividing the average value of pixels in a particular column by the value of an
184
individual pixel in that column yields a relative correction factor for that pixel. This
procedure is described by the following equation:
60
P
fi,j =
j=3
Ci,j
58Ci,j
(A.2)
where fi,j is the flatfield correction for a pixel in column i, row j and Ci,j is the number of
counts in the pixel located in column i, row j. The limits of the sum are chosen such that
the first few rows on either end of the detector (which are either completely or partially
masked out) are excluded. When applied to all pixels of the detector, Eq. A.2 yields a
two-dimensional flatfield correction. However, this flatfield only corrects for row-to-row
variations in detector sensitivity. This means that if the detector were illuminated with
a spatially-uniform, monochromatic source, all the pixels in a given column would have
the same value (within photon counting statistics) after multiplying the raw data by
the flatfield correction described above. However, pixels in a neighboring column (or
any other column on the detector, for that matter) might have a different value, even
though they received the same illumination.
A.2.1.2
Column-to-Column Variations in Detector Sensitivity
In order to obtain a correction for the column-to-column variations, it is reasonable to imagine that the spacecraft might be rotated about the Z axis, moving Spica in
the dispersion direction on the detector. However, since Spica is a point source, only a
single detector row will be illuminated. The trick is to start by scanning the star uniformly through the field of view by rotating about the spacecraft X axis, as described
above. After each scan, the spacecraft is rotated slightly about the Z axis and a new
scan across length of the slit—in the opposite direction to the previous scan—is begun.
Since the spacecraft was rotated by a small angle between each scan, the stellar
spectra from successive scans will be shifted slightly (in the spectral dimension) relative
185
to the previous spectra. If the rotation between scans is an integer multiple of the
angular width of the detector pixels, pixel x in observation α will have received
Fi,0 = Fi+δ,1 = Fi+2δ,2 = · · · = Fi+mδ,m
(A.3)
where Fi,m is the flux of photons incident on column i on scan m. For the UVIS observations of Spica, the azimuth angle of the spacecraft was incremented 0.2 milliradians
after each scan across the slit, resulting in a shift to the spectrum of 0.8 pixels (in the
dispersion direction) relative to the previous scan. The subpixel shift in the spectrum
between successive scans means that Eq. A.3 is only strictly valid for shifts that are an
integer multiple of 5. For the May 2003 observation of Spica, there were 13 scans across
the slit, with a 0.2 milliradian shift between each scan. Therefore, the following set of
equations applies:
Fi,0 = Fi+4,5 = Fi+8,10
(A.4)
Fi,1 = Fi+4,6 = Fi+8,11
(A.5)
Fi,2 = Fi+4,7 = Fi+8,12
(A.6)
Fi,3 = Fi+4,8 = Fi+8,13
(A.7)
Fi,4 = Fi+4,9
(A.8)
So for any column on the detector, the column 4 columns away received the
same illumination 5 scans later, and the column 8 columns away received the same
illumination 10 scans later. These three values could be averaged together and the
result divided by the individual pixel values to obtain corrections for the sensitivity
of column i relative to the sensitivity of columns i+4 and i+8. There are four sets
of these identically illuminated triplets with one additional pair. Using all five sets
results in five correction factors for the sensitivity of a given column relative to its
186
neighbors. To decrease the statistical error in the correction factor for a given pixel, the
five values could be averaged together. This procedure, applied to all columns on the
detector produces a flatfield correction that compensates for the variations in detector
sensitivity from column to column.
Although this procedure works reasonably well for the EUV channel, where the 8milliradian-wide occultation slit could be used, it fails for the FUV channel, where, owing
to the presence MgF2 lens and its support structure in the center of the occultation slit,
the lo-resolution slit was used. Since the FUV lo-resolution slit is only 1.5 milliradians
wide, Spica will be in the field of view on, at most, 7 scans. A slight twist in the slit
further reduces the number of usable scans to 5. Therefore, only the first two columns
of Eq. A.7 are applicable. Since each pixel is compared with only one other pixel on the
detector, this method is quite susceptible to errors.
By making the assumption that the flux of photons varies slowly over the range in
wavelength covered by one pixel, it is possible to use all scans where the target (Spica) is
within the UVIS field of view. The UVIS EUV channel has a spectral resolution of 2.25Å
(2.75Å FUV) FWHM (full width at half-maximum) and a dispersion of 0.6049Å/pixel
(0.7794Å/pixel FUV); more than 3 pixels fit into the width of a spectral resolution
element. Since the UVIS instruments are oversampled in the spectral dimension, the
above assumption is valid. With this assumption, the following set of equations now
holds:
187
Fi,m Aλ t =
Fi,m Aλ t ≈
Fi,m Aλ t ≈
Fi,m Aλ t ≈
Fi,m Aλ t ≈
1.0Ci,m
fi
0.2Ci,1 0.8Ci+1,m+1
+
fi
fi+1
0.4Ci+1,2 0.6Ci+2,m+2
+
fi+1
fi+2
0.6Ci+2,3 0.4Ci+3,m+3
+
fi+2
fi+3
0.8Ci+3,4 0.2Ci+4,m+4
+
fi+3
fi+4
(A.9)
(A.10)
(A.11)
(A.12)
(A.13)
To see how equations A.9–A.13 are derived, we refer to Table A.1 and Eq. A.1.
The top half of Table A.1 shows a schematic representation of 5 pixels lying in the same
row on the detector. For each pixel, there is a flatfield correction, fi , that will be derived.
The number of counts observed in the pixel in column i on scan m is given by Ci,m .
Each pixel is divided into 5 equal subpixel regions. The lower half of Table A.1 shows
schematically the illumination each pixel is receiving on each of 5 scans. The spectrum
of Spica is given as Fλ , and it is assumed that the spectrum is constant over the width
of one pixel (∆λ). On scan 0, each pixel is fully illuminated by a single spectral element
e.g. column i is completely illuminated by Fλ . Eq. A.9 is derived from this information
and Eq. A.1. On scan 1, the position of Spica on the detector has been displaced by 0.2
milliradians in the dispersion direction relative to its position on scan 0. As a result,
only 1/5 of Fλ now falls on the pixel in column i, with the remaining 4/5 falling on
the pixel in column i+1. information about the location of the spectral element Fλ can
again be used in conjunction with Eq.A.1 to derive Eq. A.10, and so on, until all five
equations have been derived.
Equations A.9–A.13 form a system of 6 unknowns (Fλ , fi , fi+1 , fi+2 , fi+3 , fi+4 )
in 5 equations. In order to solve this system, it is necessary to supply an additional
equation. This equation is obtained by assuming that the average row-to-row flatfield
correction has a value of 1. As the number of points included in the row-to-row calcu-
Irradiance:
m=0
m=1
m=2
m=3
m=4
Column
Flatfield
Counts
Subdivision
Fλ−2∆λ
Fλ−∆λ
Fλ−2∆λ
Fλ−3∆λ
Fλ
Fλ−∆λ
i
fi
Ci,m
Fλ
Fλ−∆λ
Fλ−2∆λ
Fλ+∆λ
i+1
fi+1
Ci+1,m
Fλ
Fλ−∆λ
Fλ+2∆λ
Fλ+∆λ
i+2
fi+2
Ci+2,m
Fλ
i+3
fi+3
Ci+3,m
Fλ
Fλ+3∆λ
Fλ+2∆λ
Fλ+∆λ
Table A.1: Description of Flatfield Method
Fλ+2∆λ
Fλ+∆λ
Fλ+∆λ
Fλ+2∆λ
Fλ+4∆λ
Fλ+3∆λ
i+4
fi+4
Ci+4,m
188
189
lation increases, the validity of this assumption increases. The reason for this is that
the average flatfield correction, when the entire detector is considered, must be equal
to 1. If the average flatfield correction over the whole detector were not equal to 1, this
would have the effect of modifying the laboratory calibration. This assumption yields
a final equation:
fi + fi+1 + fi+2 + fi+3 + fi+4
=1
5
(A.14)
which can be used to close the system and solve for the various flatfield corrections. This
technique can be readily extended to an include an arbitrary number of vertical scans.
For each point on the detector, m flatfield correction factors are produced, where m is
the number of scans. These are then averaged together to produce a better estimate of
the “true” column-to-column flatfield correction.
A.2.1.3
Total Flatfield Correction and Normalization
The row-to-row flatfield correction array (Section A.2.1.1) is multiplicatively combined with the column-to-column flatfield correction array (Section A.2.1.2). The resulting flatfield array will correct for both row-to-row and column-to-column variations in
the detector sensitivity. In order to maintain the laboratory radiometric calibration, the
resulting flatfield array is normalized to unity over the range of pixels [15:997,3:60]—a
range of pixels that are free from vignetting and masking. With this normalization, if
the UVIS entrance slit was uniformly illuminated with a spectrally white (equal intensity at all wavelengths) source, the number of counts in the normalized region would be
the same after flatfielding as it was before the flatfield correction was applied.
It is important to note that the flatfield will conserve the total number of counts
in an image only in the case of a uniformly (spectrally as well as spatially) illuminated
detector. If the illumination of the slit is not uniform or if there is any kind of structure
in the spectrum of the source, then the number of counts will be different after the
190
flatfield is applied. The veracity of this point is illustrated by the following thought
experiment. A point object, e.g. a star, is observed, illuminating a single row of the
detector that has an average sensitivity. A second observation of the same star is made,
but this time the spectrum illuminates a detector row that has half the sensitivity of the
first row. Before flatfielding, the total number of counts on the detector will be twice
as much in the first observation as in the second. After flatfielding, both observations
will have the same number of counts.
Raster scan observations of Spica were obtained on 17 July 2002 and 19 May 2003.
An independent flatfield correction array was derived from each observation. These two
flatfields are averaged together to produce the final Spica flatfield.
A.2.2
LISM Flatfields
Shortly after the flyby of the Cassini spacecraft past the Earth in 1999, a series
of observations of the local interstellar medium (LISM)/ interplanetary medium were
made. Observations were obtained with all three slit positions, and unlike subsequent
LISM observations the full detector was read out with no binning. Since emission from
the LISM is uniform over the length of the UVIS entrance slits, these observations can be
used to construct a flatfield correction. However, stellar spectra are occasionally present
in the UVIS LISM. Careful attention must be paid to the individual LISM images to
ensure that images contaminated by stellar spectra are excluded from further analysis.
The LISM spectrum consists of a single line in the FUV, H I 1216Å (Lyman-α),
and two lines in the EUV: H I 1026Å (Lyman-β) and He I 584Å. The Lyman-γ transition
and subsequent of the Lyman series are not detected since they are both intrinsically
faint and swamped by noise from the EUV mesa background feature. Indeed the EUV
LISM observations are, in general, completely dominated by the mesa background feature. As such, they are poorly suited for obtaining a flatfield correction. Fortunately,
the FUV channel is free of the mesa feature. Although Lyman-α is the only detectable
191
spectral feature in the FUV LISM observations, it is so bright that photons scattered
from this feature are detected over the entire detector. At the long wavelength end of
the FUV detector the count rate from scattered Lyman-α photons is a factor of ∼2
higher than the background count rate (which is primarily caused by γ-rays emitted
by the spacecraft RTGs). Equation A.2 can be used to obtain a row-to-row flatfield
correction, however in order to obtain a column-to-column correction, a detailed model
of the Lyman-α line shape and instrument scattering function is required. A flatfield
correction for the FUV channel has been produced in this manner, which is known as
the LISM flatfield (Don Shemansky, private communication).
Since the LISM observations have much lower counts, especially at the longest
wavelengths of the detector, than the Spica observations, it was necessary to smooth
the data by a 1-4-6-4-1 kernel before creating the flatfield correction. The smoothing
operation was performed only in the dispersion direction, and not in the spatial direction. Therefore, all UVIS data must be similarly smoothed before the LISM flatfield
correction can be applied.
A.2.3
Solar Flatfields
The EUV channel is equipped with a small pickoff mirror that allows sunlight to
enter the EUV optical path without striking the primary mirror. Light admitted via the
solar occultation port is not in focus when it hits the EUV detector, and consequently it
is spread over the central 2/3 (in the spatial direction) of the detector. Perhaps because
of the different optical path taken by light entering UVIS via the solar occultation port,
the EUV detector displays a different row-to-row sensitivity profile when illuminated
with sunlight via the solar port than when illuminated with other astrophysical sources
via the standard telescope aperture. In particular, rows 13–20 are anomalously high in
counts in the solar images, and row 18 is visibly brighter than the neighboring rows.
This could be caused by a glint off of a surface either internal or external to UVIS or
192
by some other, as yet undetermined, mechanism. Since the row-to-row profile obtained
using the solar occultation port is not fully understood, no attempt was made to derive
a flatfield correction from this data.
A.3
Temporal Changes in the Flatfield
On and around 6 June 2002 the Cassini ISS (Imaging Science Subsystem) engaged
in a series of observations of the star Spica, designed to characterize the scattered light
function of the instrument. In order to build up enough counts over the entire ISS field of
view, the pointing was held constant for a long period of time. During this observation,
UVIS was operating normally, although no data were recorded or sent back to earth.
Due to the exceptional stability in the pointing of the Cassini spacecraft, the position
of Spica on the detector was held constant to within a single row for the duration of
these observations. As a result a very large number of photons were incident on a small
region of the detector microchannel plate, which had the effect of removing some of
the photocathode material from the microchannel plates, resulting in a decrease in the
sensitivity of the affected rows. The loss in sensitivity in the affected rows is directly
correlated to the number of photons incident on the detector, and therefore is strongly
correlated with Spica’s spectrum (i.e. where Spica is bright, the loss in sensitivity
is large, and where Spica is fainter, the decrease in sensitivity is less). The loss of
sensitivity, which affects rows 31–33 of the EUV channel and rows 30–33 of the FUV
channel, is referred to as starburn.
Since the two Spica raster observations used to derive the UVIS flatfield correction
were made after June 2000, they too are affected by the starburn. However, the data
analyzed in this thesis were all obtained prior to the starburn. If not properly removed,
the presence of the starburn in the flatfield correction, but not the data, will result in
an artificially increased level of flux in the affected rows. Fortunately, a single scan of
Spica across the UVIS occultation slits was obtained on 3 April 2001, before the starburn
193
occurred. Using Eq. A.2, a pre-burn, row-to-row flatfield correction was derived for the
EUV channel. Since there was no raster scan for this observation, column to column
corrections could not be obtained. After normalizing the pre-burn flatfield correction
to unity, the affected rows of the starburned flatfield were replaced with values from
the pre-burn flatfield correction. The spectrum of Spica is quite faint below 900Å, so
only pixels in starburned rows corresponding to wavelengths above 900Å were replaced.
Due to the MgF2 lens in the FUV occultation slit, the 3 April 2001 observation of Spica
could not be used to derive a pre-burn flatfield for the FUV channel. Instead, a similar
flatfield was derived from observations of the LISM.
A.4
Bad Pixels
Bad pixels are pixels that have anomalously low sensitivity. These pixels are
found exclusively in the FUV channel. Bad pixels tend to be grouped in columns, with
roughly every 7th column of the FUV detector affected. Generally, only 1/3–1/2 of an
affected column will contain bad pixels. There is still some debate within the UVIS team
whether these pixels merely have low sensitivity or are also non-linear in their response
(the so-called “evil” pixels). In any event, it is safest to exclude these pixels from
data analysis, as their large flatfield correction factors will amplify noise. Figure A.2
shows the effect of bad pixels on two columns of the FUV detector. These row profiles
were extracted from one of the Spica raster scans, so all rows have received identical
illumination. Rows 0–33 of Column 782 have virtually no counts, while rows 33–62 seem
to be behaving normally. Conversely, rows 3–32 of column 783 appear unaffected, while
rows 34–62 show very little counts.
The distribution of bad pixels per row of the FUV detector is shown in Fig. A.3.
The average number of bad pixels per row is 157, which corresponds to 15% of the total
number of pixels in the FUV detector.
194
4000
Column 783
Column 782
Counts
3000
2000
1000
0
0
10
20
30
40
Row Number
50
60
Figure A.2: Comparison of the counts in FUV columns 782 and 783. All of the rows
have been uniformly illuminated by the spectrum of Spica.
Number of bad pixels
180
160
140
120
0
10
20
30
Row Number
40
50
60
Figure A.3: Number of bad pixels per FUV detector row.
A.5
Comparison of Spica and LISM Flatfields
In order to quantitatively compare the effect of the Spica and LISM flatfields on
reducing the scatter in UVIS data, the following statistical measure was used:
195
v
u
60 1000
u1 X
X (xij − x¯j )2
p
³
´
σ̄ = χ2ν = u
t
N
2 + σ2
σ
i=3 j=32
x¯j
xij
(A.15)
where N is the total number of pixels, i is the row index, j is the column index, xij is
the number of counts in the ith row and jth column, x¯j is the average value of pixels in
the jth column, and σxij is the statistical uncertainty in xij . Since the first and last few
rows of the detector are masked, they are not included in the calculation. Likewise, the
columns at the short and long wavelength ends of the detector are excluded from the
calculation in order to remove the effects of vignetting and masking, respectively. In
the case of 14641-smoothed data:
xij =
σij =
1x(i−2)j + 4x(i−1)j + 6xij + 4x(i+1)j + 1x(i+2)j
16
q¡
¢2 ¡
¢2
¡
¢2 ¡
¢2
1σ(i−2)j + 4σ(i−1)j + (6σij )2 + 4σ(i+1)j + 1σ(i+2)j
16
(A.16)
(A.17)
Six independent datasets were used to compare the effectiveness of the two flatfield corrections: H2 lamp spectra from the laboratory calibration, an image from the
Spica observations of May 2003, the summed post-earth low-resolution slit LISM observations, the difference between the summed post-earth low- and high-resolution LISM
observations, and spectra of Jupiter’s aurora and reflected sunlight from 29 December
2000. However, since the spectra of both the Jovian aurora and the reflected sunlight
will exhibit spatial variations, the quantitative measure σ̄ could not be applied to the
Jupiter data.
Table A.2 shows the values of σ̄ before and after the flatfield corrections have
been applied. Also included are values of σ̄ for raw data that has been smoothed using
a 1-4-6-4-1 kernel like that required for the LISM flatfield and for raw data excluding
the “bad” pixels.
196
For the H2 lamp data, much of the improvement over the raw data comes from
simply removing the bad pixels. There is very little further improvement achieved
by applying the Spica flatfield correction, while the LISM flatfield correction actually
increases σ̄ over the simple bad pixel removal case.
For the Spica spectrum, however, the Spica flatfield is clearly the preferable
method. It produces a σ̄ close to the theoretically perfect value of 1. However, since this
image was one of several that was used to create Spica flatfield, it should do a good job.
The LISM flatfield reduces the value of σ̄ below that of the bad pixel removal alone.
For the LISM low-resolution slit image, both the Spica flatfield and the LISM
flatfield improve the quality of the image over simple bad pixel removal. However, the
LISM flatfield produces a significantly lower value of σ̄. Again, since this image was
used to create the LISM flatfield, this is hardly surprising.
The last quantitative comparison is of the difference between the summed lowresolution image of the LISM and the summed high-resolution image of the LISM. Again,
both flatfields show an improvement over the simple bad pixel removal. However, the
Spica flatfield produces a slightly lower value of σ̄ than the LISM flatfield, even though
the LISM flatfield was created from the sum of these two images.
Subtracting the high-resolution LISM image from the low-resolution LISM image
will remove 1/2 of the signal from the difference image (the width of the low-resolution
slit is 1.5 mrad, while the width of the high resolution slit is 0.75 mrad). However,
subtracting the two LISM images will completely remove any spatially non-uniform
pattern in the background. The fact that the Spica flatfield performs slightly better in
removing the flatfield variations of the LISM difference image than the LISM-derived
flatfield suggests that the LISM flatfield may be contaminated by variations in the
detector background. (By detector background, I mean whatever counts are generated
from processes other than UV light entering the telescope. The primary source of
background are the spacecraft’s RTGs.) In the LISM images, the count rate due to
197
scattered Lyman-α in the long wavelength regions of the detector is only 2–3 times
the background count rate. In the Spica images, however, the count rate from the
Spica spectrum is several orders of magnitude larger than the background count rate.
Therefore, it seems as though the low count rate of the LISM images introduces structure
into the LISM flatfield that is not due to the instrument radiometric sensitivity (i.e.
FUV photons incident on the detector), but rather to some other mechanism, perhaps
the RTG background.
Spectra from row 41 of the H2 lamp data are presented in Fig. A.4. The top
panel shows the raw spectrum. Much of the high-frequency noise in this panel is due
to bad pixels. The second panel shows the spectrum after the Spica flatfield has been
applied and the resulting spectrum has been 14641 smoothed. The third panel show the
spectrum which has been 14641 smoothed before being corrected by the LISM flatfield.
Both flatfields are a clear improvement over the raw data. The main difference between
the Spica flatfielded spectrum and the LISM flatfielded spectrum is in near 1210Å. The
LISM flatfielded spectrum shows a sharp dip around 1210Å that is not present in the
raw data or the Spica flatfielded spectrum. This feature is an artifact introduced by
the LISM flatfield. There is also ever-so-slightly less high-frequency variation in the
spectrum that has been flatfielded with the Spica flatfield.
The raw and flatfielded spectra from row 43 of one of the images from the May
2003 Spica observations is shown in Fig. A.5. The flatfield correction derived from the
spica observations produces a much cleaner-looking spectrum than the flatfield derived
from the LISM observations. Again, the LISM flatfield correction introduces an artifact
that looks like an absorption line near 1210Å. This feature is present in neither the raw
data nor the spica flatfielded data.
Figure A.6 shows the raw and flatfielded spectra from row 43 of the sum of the
low-resolution slit LISM observations. All flux in this spectrum is due to Lyman-α
emission at 1216Å, either imaged onto the detector, or scattered internally. The bad
H2 Lamp Image
Spica Image
LISM Image
LISM Difference Image
Raw Data
1.95
16.9
20.6
4.9
14641-Smoothed Raw Data
1.84
21.5
16.1
3.8
Raw Data w/ Bad Pixel Mask
1.61
13.1
9.5
2.8
Table A.2: Quantitative comparison of flatfielding methods (χ2ν )
Spica FF
1.59
1.3
3.5
1.6
LISM FF
1.79
9.9
1.3
1.5
198
Counts
Counts
Counts
0
100
200
300
400
500
600
0
100
200
300
400
500
600
0
100
200
300
400
500
600
1200
1200
1200
1300
1300
1300
1500
Wavelength (Å)
1600
1500
Wavelength (Å)
1600
1500
Wavelength (Å)
1600
1700
1700
1700
1800
1800
1800
1900
1900
1900
Figure A.4: Comparison of raw and flatfielded H2 lamp spectra
1400
14641 smoothed H2 Lo−Res Raw Data x LISM FF
1400
14641 smoothed (H2 Lo−Res Raw Data x Spica FF)
1400
H2 Lo−Res Raw Data Row 41
199
Counts
Counts
Counts
2000
0
4000
6000
8000
10000
2000
0
4000
6000
8000
10000
2000
0
4000
6000
8000
10000
1200
1200
1200
Wavelength (Å)
1600
1800
Wavelength (Å)
1600
Wavelength (Å)
1600
1800
1800
Figure A.5: Comparison of raw and flatfielded spectra of Spica
1400
May 2003 14641 smoothed Raw Spica x LISM FF Row 43
1400
May 2003 (Raw Spica x Spica FF) smoothed by 14641 Row 43
1400
May 2003 Raw Spica Row 43
200
201
pixels can be clearly seen in the raw data. Again, both flatfield corrections represent a
marked improvement over the raw data. However, the LISM flatfield correction does a
noticeably better job of removing the high-frequency noise in the spectrum. Since the
LISM spectrum was created from this dataset, it is not surprising that it produces a
cleaner spectrum.
Visible in all three spectra is a bump around 1320Å. This is an instrumental
artifact. In the full two-dimensional image, this artifact appears as a series of discrete
arcs. The cause of this artifact is unknown.
Spectra of the Jovian aurora before and after flatfielding are shown in Fig. A.7.
Aside from the 1210Å artifact in the LISM-flatfielded spectrum, there are few obvious qualitative differences between the between the Spica-flatfielded spectrum and the
LISM-flatfielded spectrum.
Figure A.8 shows reflectance spectra of Jupiter before and after flatfielding. The
Spica flatfield produces smoother spectra than the LISM flatfield. This is probably due
to the relatively low number of counts longward of 1500Å in the summed LISM image.
Counts
Counts
Counts
102
103
104
10
5
102
103
104
105
102
103
104
10
5
1200
1200
1200
Wavelength (Å)
1600
Wavelength (Å)
1600
Wavelength (Å)
1600
1800
1800
1800
Figure A.6: Comparison of raw and flatfielded spectra of the LISM
1400
14641 smoothed LISM x LISM FF Row 43
1400
(Raw LISM x Spica FF) Smoothed 14641 Row 43
1400
1999 Post−Earth LISM lo−res Row 43
202
Counts
Counts
Counts
0
500
1000
1500
2000
0
500
1000
1500
2000
0
500
1000
1500
2000
1200
1200
1200
1400
1500
Wavelength (Å)
1600
1700
1400
1500
Wavelength (Å)
1600
1700
1300
1500
Wavelength (Å)
1600
1700
1800
1800
1800
1900
1900
1900
Figure A.7: Comparison of raw and flatfielded spectra of the Jovian aurora
1400
14641 smoothed 29Dec2000 Jupiter Raw Data x LISM FF
1300
14641 smoothed (29Dec2000 Jupiter Raw Data x Spica FF)
1300
29Dec2000 Jupiter Raw Data Row 25
203
Counts
Counts
Counts
200
0
400
600
1000
800
200
0
400
600
1000
800
200
0
400
600
1000
800
1200
1200
1200
1400
1500
Wavelength (Å)
1600
1700
1400
1500
Wavelength (Å)
1600
1700
1400
1500
Wavelength (Å)
1600
1700
1800
1800
1800
1900
1900
1900
Figure A.8: Comparison of raw and flatfielded reflectance spectra from Jupiter
1300
14641 smoothed 29Dec2000 Jupiter Raw Data x LISM FF
1300
14641 smoothed (29Dec2000 Jupiter Raw Data x Spica FF)
1300
29Dec2000 Jupiter Raw Data Row 29
204