JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, A12223, doi:10.1029/2005JA011251, 2005
Radial variations in the Io plasma torus
during the Cassini era
P. A. Delamere and F. Bagenal
Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado, USA
A. Steffl
Department of Space Studies, Southwest Research Institute, Boulder, Colorado, USA
Received 2 June 2005; revised 13 September 2005; accepted 22 September 2005; published 28 December 2005.
[1] A radial scan through the midnight sector of the Io plasma torus was made by the
Cassini Ultraviolet Imaging Spectrograph on 14 January 2001, shortly after closest
approach to Jupiter. From these data, Steffl et al. (2004a) derived electron temperature,
plasma composition (ion mixing ratios), and electron column density as a function of
radius from L = 6 to 9 as well as the total luminosity. We have advanced our homogeneous
model of torus physical chemistry (Delamere and Bagenal, 2003) to include latitudinal and
radial variations in a manner similar to the two-dimensional model by Schreier et al.
(1998). The model variables include: (1) neutral source rate, (2) radial transport
coefficient, (3) the hot electron fraction, (4) hot electron temperature, and (5) the neutral
O/S ratio. The radial variation of parameters 1–4 are described by simple power laws,
making a total of nine parameters. We have explored the sensitivity of the model results to
variations in these parameters and compared the best fit with previous Voyager era
models (Schreier et al., 1998), Galileo data (Crary et al., 1998), and Cassini observations
(Steffl et al., 2004a). We find that radial variations during the Cassini era are consistent
with a neutral source rate of 700–1200 kg/s, an integrated transport time from L = 6 to 9 of
100–200 days, and that the core electron temperature is largely determined by a
spatially and temporally varying superthermal electron population.
Citation: Delamere, P. A., F. Bagenal, and A. Steffl (2005), Radial variations in the Io plasma torus during the Cassini era,
J. Geophys. Res., 110, A12223, doi:10.1029/2005JA011251.
1. Introduction
[2] The Io plasma torus is produced by the ionization of
roughly 1 ton/s of neutral material from Io’s atmosphere. In
situ and remote observations of the torus have largely
characterized the density, temperature and composition of
the torus (see review by Thomas et al. [2004]). The issue of
temporal variability of the Io plasma torus has been debated
for many years [Mekler and Eviatar, 1980; Eviatar, 1987;
Thomas et al., 2004]; however, recent observations of the
torus made by the Ultraviolet Imaging Spectrograph (UVIS)
on the Cassini spacecraft during the flyby of Jupiter
(October 2000 to March 2001) have yielded new insights
into the temporal variability of the torus using a homogeneous model for mass and energy flow through the torus
[Delamere and Bagenal, 2003]. The combined data analysis
efforts by Steffl et al. [2004b] and modeling by Delamere et
al. [2004] suggest that a significant change in the neutral
source occurred near the beginning of the Cassini observing
period, decreasing from >1.8 tons/s to 0.7 tons/s. Concurrent iogenic dust measurements made during the Galileo
G28 orbit by Krüger et al. [2003] suggest that the obserCopyright 2005 by the American Geophysical Union.
0148-0227/05/2005JA011251$09.00
vations are consistent with signficant volcanic activity on
Io. While much of the UVIS data does not have sufficient
resolution to address the issue of spatial variations in the
torus, a full radial scan through the midnight sector was
made on 14 January 2001, shortly after closest approach.
The observed radial variations are described by Steffl et al.
[2004a] and provide electron temperature, plasma composition (ion mixing ratios), and electron column density as a
function of radial distance from L = 6 to L = 9. We have
advanced our homogeneous model to address radial variations in a manner similar to the two-dimensional model by
Schreier et al. [1998]. The goal of this study is to model the
radial variations of the torus during the Cassini era and to
compare the results with previous models (e.g., Voyager era
model by Schreier et al. [1998]).
[3] The torus plasma stems from two primary source
regions: (1) ionization of Io’s extended neutral clouds, and
(2) ionization of material within 5 RIo of the satellite
[Bagenal, 1997]. The contribution from the second region
(local source) ranges between 20 and 50% of the canonical
ton/s of new plasma based on estimates by Bagenal [1997]
and Saur et al. [2003]. The plasma is then modified by the
effects of physical chemistry as it is transported outward.
Electron impact ionization is the primary source of new
material (mass and energy) and populates the higher
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ionization states. Neutral-ion charge exchange modifies the
energy flow and removes neutral material from the system
and numerous ion-ion charge exchange reactions generally
make modifications to torus composition and ion temperature. Efficient radiative loss from the core electron
population rapidly cools the torus and the roughly 5 –
10 eV electron temperature is maintained by thermal input
from the hotter ion population (70– 100 eV) and the
ubiquitous superthermal electron population (40 – 100 eV).
A key observation seen in both the Voyager and Cassini
data sets is the steady rise in the core electron temperature
with radius [Sittler and Strobel, 1987; Steffl et al., 2004a,
2004b]. Schreier et al. [1998] describe three mechanisms
for heating the electrons, namely: (1) an increase in
thermal temperature of the ions resulting in heating via
Coulomb collisions, (2) hot (10s of keV) ions of ring
current origin diffusing inward and heating the electrons,
and (3) an increasing flux of superthermal electrons.
[Schreier et al., 1998] conclude that mechanism 2 is the
most likely.
[4] Radial transport is understood to be driven by centrifugally driven interchange motions of magnetic flux tubes
[Richardson and Siscoe, 1981; Siscoe and Summers, 1981].
The interchange rate is regulated by several factors including Jupiter’s Pedersen conductivity [Hill, 1986], ringcurrent impoundment [Siscoe et al., 1981], and velocity
shear impoundment [Pontius et al., 1998] (see discussion by
Thomas et al. [2004]). The standard treatment of the
transport physics is handled with a radial Fokker-Planck
diffusion equation [Dungey, 1965], where the transport
timescale is parameterized by a diffusion coefficient which
varies as a power of L (i.e., DLL = Do Ln). While the detailed
physics of radial transport mechanisms are not fully understood, observational constraints suggest that the transport
timescale is roughly 60 days (for 1 RJ).
[5] The first constraints on the timescales for radial
transport were provided by analysis of the high-energy
particle (MeV) data from the Pioneer 10 and 11 flybys
[Thomsen et al., 1977a, 1977b]. Thomsen et al. [1977a]
estimated that the upper limit for the diffusion coefficient,
Do(L 6), is roughly 6 107 s1 (t 20 days) with n =
2.3 ± 0.5. Analysis of the Voyager 1 and 2 data of
>0.5 MeV ions by Armstrong et al. [1981] indicated a best
value of n 7.5. On the basis of analysis of the Voyager I
low-energy plasma data, the wide range in n deduced from
the energetic particle data was attributed to a marked
transition (discontinuity) between plasma transport rates
inside and outside of Io’s orbit [Bagenal et al., 1980;
Richardson et al., 1980]. For the region outside of Io’s orbit
(the region of interest in this paper), Siscoe and Summers
[1981] determined that the diffusion coefficient varies as
L4+p, where the parameter p was in the range 2 p 4.
[6] The empirical torus model by Bagenal [1994] shows a
‘‘ramp’’ region between L = 7.5 and 8.0, where the slope of
the flux tube content profile steepens. Siscoe et al. [1981]
suggested that inward transport of radiation belt particles
might be impounding the torus plasma. While this prompted
various attempts to model the flux tube content profile with
radial variations in the rate of diffusive transport [Herbert,
1996; P. L. Matheson and D. E. Shemansky, Chemistry and
transport in the Io torus ramp, unpublished manuscript,
1993], it is not clear whether the Voyager ramp region
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might be due, at least in part, to the latitudinal excursion of
the spacecraft or to temporal variability of the plasma
production.
[7] In this paper we compare the radial profiles (L = 6 to
9) of mixing ratios of the five major ion species (S+, S++,
S+++, O+, and O++) and the total torus extreme ultraviolet
(EUV) luminosity (PEUV) provided by the Cassini UVIS
analysis of Steffl et al. [2004b, 2004a] to our modeled
profiles and luminosity. The model contains the following
variables: (1) neutral source rate, (2) radial transport coefficient, (3) the hot electron fraction, (4) hot electron temperature, and (5) the neutral O/S ratio. The radial variation
of variables 1 – 4 are described by simple power laws,
making a total of nine parameters. Most importantly, we
explore the sensitivity of model results to variations in these
parameters and compare the models matching the Cassini
data with previous models (e.g., Voyager era model by
Schreier et al. [1998]).
2. Cassini Data Set
[8] During the Cassini spacecraft’s Jupiter flyby (October
2000 to March 2001), the UVIS instrument produced an
extensive data set of spectrally dispersed images of the Io
plasma torus. The UVIS instrument consists of two independent, coaligned spectrographs (EUV 561– 1181 Å; FUV
1115– 1913 Å) having a point-source spectral resolution of
3 Å FWHM [McClintock et al., 1993; Esposito et al., 1998].
The major ion species present in the torus all have spectral
features in the wavelength range covered by the EUV
channel. The field of view of the EUV channel of the
instrument was such that for the first and last 2 months of
the Jupiter encounter, the entire torus could be observed
simultaneously. During the approach phase of the encounter, the total EUV power radiated by the torus decreased by
25% [Steffl et al., 2004b]. UVIS continued to make observations of the Io torus during the months of December 2000
and January 2001, but the spacecraft’s proximity to Jupiter
precluded simultaneous measurement of the total radiated
EUV power. When total power measurements resumed after
closest approach, the torus EUV luminosity remained relatively constant. On the basis of the observed inbound and
outbound luminosity, we estimate the total EUV power for
the 14 January radial scan to be 1.45 ± 0.25 terawatts.
[9] The spectral analysis method described by Steffl et al.
[2004a] was used to derive the ion composition and electron
temperature of the torus plasma at the ansa. This model
assumes a uniform torus along the line-of-sight and uses the
CHIANTI database [Dere et al., 1997; Young et al., 2003] to
determine radiative emission rates. The assumption of a
uniform column through the torus does not significantly
affect the results for radial distances greater than 6 RJ.
Spectra from October and November can be found in the
work of Steffl et al. [2004b]; spectra from January can be
found in the work of Steffl et al. [2004a].
[10] Historically, it has been difficult to determine the
relative abundance of O II and O III in the Io torus [e.g., see
McGrath et al., 1993, and references therein]. The observational setup of UVIS on 14 January 2001 (i.e., the long
axis of the UVIS entrance slit oriented approximately
parallel to Jupiter’s rotation axis with the field of view
being scanned radially inward from 10 to 4 RJ) allowed the
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inclusion of the FUV channel in the analysis of the spectra.
The observed brightness of the O III lines at 1661 and 1666,
a wavelength region covered by the FUV channel, places a
firm upper limit the amount of O III in the torus [Steffl et al.,
2004b].
3. Model of Torus Chemistry and Emissions
[11] We have developed a homogeneous, time-dependent
model of torus physical chemistry for the purpose of
investigating the sensitivity of torus composition to the
following parameters: neutral source rate (S n), O/S source
ratio (O/S), convective transport loss (t), hot electron
fraction (feh), and hot electron temperature (Teh). A detailed
description of the model is provided by Delamere and
Bagenal [2003]. The model is based largely upon several
earlier models [i.e., Shemansky, 1988; Barbosa, 1994;
Schreier et al., 1998; Lichtenberg and Thomas, 2001] but
uses the latest CHIANTI atomic physics database for
computing radiative loss [Dere et al., 1997].
[12] The model calculates the time rate of change of mass
and energy for both ions and the core electrons based on the
determination of mass and energy sources and losses until a
steady state solution is reached. The primary sources of
mass and energy are electron impact ionization and charge
exchange reactions involving neutral gas. Charge exchange
reactions determine the allocation of energy among the ion
species and their respective ionization states. Charge
exchange reactions involving neutrals also contribute
significantly to the energy budget due to the pickup energy
of plasma into the corotating plasma torus (see Table 1 for
reactions). The velocity distribution for each species is
approximated as Maxwellian. The electrons have a nonthermal component and a ‘‘Kappa’’ distribution is known to
best match torus observations [Meyer-Vernet et al., 1995].
We approximate this nonthermal distribution with two
Maxwellians for the core and hot populations. The hot
electrons, through Coulomb coupling with the core electrons, provide significant energy input into the torus (20–
60%). Major losses of mass include radial transport and fast
neutral escape due to charge exchange reactions with
thermalized ions (Ti = 60– 100 eV). Radiation in the UV
and optical is the major energy sink as roughly 50% of the
input energy is transferred from the ions to the electrons via
Coulomb coupling. The combination of these sources and
sinks of mass and energy lead to an equilibration timescale
of roughly 60 days.
3.1. Radial Transport
[13] Following Schreier et al. [1998], we use the radial
Fokker-Planck equation to describe the radial diffusion in
the torus. For each species, the radial transport equation is
of the form
@Y
@ DLL @Y
¼ L2
;
@t
@L L2 @L
ð1Þ
where Y is any quantity conserved as a flux tube moves
under interchange motion, L is the radial coordinate, and
DLL is the diffusion coefficient. For the case of mass, the
conserved quantity is the total number of ions per unit
magnetic flux, NL2, and for thermal energy density of an
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Table 1. Charge Exchange Reactions, L = 6.0, k0 [Smith and
Strobel, 1985], k1 k16 [McGrath and Johnson, 1989]
k, cm3s1
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++
k0 = 8.1 109
k1 = 2.4 108
k2 = 3 1010
k3 = 7.8 109
k4 = 1.32 108
k5 = 1.32 108
k6 = 5.2 1010
k7 = 5.4 109
k8 = 6 1011
k9 = 3.1 109
k10 = 2.34 108
k11 = 1.62 108
k12 = 2.3 109
k13 = 1.4 109
k14 = 1.92 108
k15 = 9 1010
k16 = 3.6 1010
isotropic plasma, adiabatic changes (i.e., T / V2/3) requires
that Y = NL2TL8/3, where T is the ion temperature and where
the volume of a dipole flux tube of constant flux varies as
L4. We note that this form of the conserved thermal quantity
assumes that the plasma is free to expand into the entire flux
tube volume and does not consider the affects of centrifugal
confinement. Richardson and Siscoe [1983] assume that the
scale height of the torus is small compared to L such that the
effective volume / L3 H (rather than L4), where H is
the plasma scale height. The conservedpthermal
quantity is
ffiffiffiffi
therefore Y = NL2TL2T1/3, where H / T . The centrifugal
confinement reduces the volume to roughly 80% of the flux
tube for H = 1 RJ. The two expressions can be considered
limiting cases of hot [Schreier et al., 1998] and
cold [Richardson and Siscoe, 1983] plasma. The
obvious generalization would be an intermediate case
(V. Vasyliunas, personal communication, 2005). We are
adopting the Schreier et al. [1998] expression for the
purpose of comparison, but note in advance that a model
comparison of these two expressions yielded only small
differences in the transport parameters.
[14] For the diffusion coefficient we assume a power law
of the form DLL = K (L/Lo)m, where Lo = 6.0. Density is
updated in the equatorial plane subject to the latitudeaveraging scheme described below and the equatorial densities are converted to total flux tube content (NL2) by
determining the variation in number density along the
magnetic field. The distribution of plasma along the magnetic field can be determined by considering the balance
between plasma pressure, centrifugal force, and the ambipolar electric field on a dipole magnetic field line. Specification of density at a given point on the magnetic field, So,
determines the density at all other points, S, according to
T?
BðS Þ 1 mi W2 ½r2 ðS Þ r2 ðSo Þ
log
þ
ni ðS Þ ¼ ni ðSo Þ exp 1 Tk
BðSo Þ 2
Tk
Zi q½FðS Þ FðSo Þ
;
ð2Þ
þ
Tk
where W is the angular velocity of the corotating plasma, r
is the perpendicular distance to the spin axis, and F is the
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ambipolar potential [Bagenal and Sullivan, 1981]. The total
flux tube content for a dipole field is given by
NL2 ¼ 4pR3J L4
Z
qmax
n cos7 qdq:
ð3Þ
q¼0
An iterative scheme is used to convert between the updated
flux tube mass content and the equatorial densities. We
assume isotropic Maxwellian particle distributions so that
the temperature of each species is constant along the
magnetic field and the effects of thermal anisotropy are
ignored.
[15] The transport equation is subject to boundary conditions. At L = 6.0 we use @(NL2)/@L = 0 to determine mass
flux across in the inner simulation domain boundary, and for
large L (i.e., >30) we require that NL2 = 0. To justify our
inner boundary condition, we note that Io resides at L = 5.9
and steep (positive) gradients in flux tube content occur
inside of the ribbon region at L = 5.7. The Voyager analysis
of Bagenal [1994] shows a fairly flat profile in flux tube
content between L = 5.7 and 6.0 with small-scale variations
not resolved on our 0.25 RJ model grid. For the energy
update we fix the temperature on the inner boundary (L =
6.0) to 60 eV and for large L the temperature is fixed at
100 eV (consistent with Voyager ion temperatures in the
plasma sheet). Chemistry is only calculated for L = 6.0 to L =
11.0 using the latitudinally averaged chemistry model for
each radial grid cell (0.25 RJ grid resolution).
3.2. Latitudinal Averaging
[16] The rapid rotation of Jupiter and its magnetic field
tightly confines torus plasma to the centrifugal equator. To
calculate the torus chemistry, we assume that mass and
energy flow are largely determined by plasma density in the
centrifugal equator plane. The scale heights of the different
ion species are comparable (1– 2 RJ); however, the neutral
clouds are largely confined to the orbital plane of Io with a
much smaller scale height [Smyth and Marconi, 2000].
Therefore the ion/neutral chemistry in the torus could be
significantly influenced by the latitudinal distribution of
ions and neutrals.
[17] Io moves 7 in latitude with respect to the
centrifugal equator plane of the plasma torus (i.e., above
and below the torus) in the 13 hours of Jupiter’s rotation
(and System III longitude) in Io’s reference frame. We
assume that the neutral clouds are tightly confined to Io’s
orbital plane and likewise are subject to significant
latitudinal excursions (directly correlated with longitude)
with respect to the plasma. To approximate the longitudinally varying neutral source, we fixed the neutral cloud
offset to 3.5 in latitude with a fixed scale height of
0.1 RJ. We argue that it is reasonable to assume longitudinal symmetry because the chemistry timescales are
significantly longer than the System III period and thus
small deviations from rigid corotation ( few km/s) will
smear out longitudinal variations [Brown, 1994; Steffl et
al., 2005]. The total neutral source rate was converted to
an equatorial volumetric quantity for each grid cell
by multiplying the source rate by an approximate volume,
V zdA = (p1/2Hn)p [(L + dL/2)2 (L dL/2)2], where
Hn is the neutral scale height (assumed identical for S
and O).
Figure 1. Sample flux tube distribution with offset neutral
clouds (dark solid lines). In this example the neutrals are
offset by 7 with a 0.1 RJ scale height. The density of the
oxygen neutral cloud is typically 4– 5 greater than the
neutral sulfur cloud.
[18] For a rapidly rotating magnetosphere with dipolar
magnetic field, the density of a single ion species plasma
has a Gaussian distribution about the centrifugal equator
with the same scale height for ions and electrons. With
multiple ion species one can approximate the distribution of
their densities using separate Gaussians with separate scale
heights. The difference between this Gaussian approximation and a self-consistent treatment of a multiple species
plasma is minor (within ±1 RJ). Furthermore, since most
chemical reactions depend on the product of two densities,
the contribution of high-latitude densities has very little
effect. The separate Gaussian approximation facilitates
simple analytical expressions for determining flux tube
averaged quantities. In addition, all distributions are treated
as simple Maxwellians so that the temperature for any given
species is constant along the magnetic field line. The
density of the hot electron component is assumed to be
constant along the magnetic field. Figure 1 illustrates the
distribution of plasma along the magnetic field with respect
to the centrifugal equator plane. The dark solid lines show
the O and S neutral distributions for the limiting case where
Io makes its largest excursion from the centrifugal equator
plane of the plasma torus (i.e., lIII 20 or 200).
[19] In the Gaussian approximation the total number of
ions of each species on a given flux tube will be defined as
Z
Z
þ1
þ1
nð zÞdz ¼ nð0Þ
N
1
2
ez
=H 2
dz ¼
pffiffiffi
pnð0ÞH;
ð4Þ
1
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
where H 2Ti ð1 þ Zi Te =Ti Þ=3mi W2 is the plasma scale
height, W is the angular frequency of Jupiter’s rotation (1.76 104 rad/s) and n(0) is the density in the centrifugal equator
plane, and Zi is the ion charge number. Given the flux tube
total, N, the density in the equator plane is
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N
nð0Þ ¼ pffiffiffi :
pH
ð5Þ
DELAMERE ET AL.: RADIAL VARIATIONS OF THE IO PLASMA TORUS
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Now consider a reaction involving two ion species. The total
flux tube integrated source rate for species g due to a reaction
between species a and b is
dNg
¼
dt
Z
þ1
pffiffiffi 0
kna ð zÞnb ð zÞdz ¼ kna ð0Þnb ð0Þ pH ;
where na/b is the thermal equilibration rate between species
a and b and the flux tube averaged contribution is
determined by evaluating
Z na=b na na nb ð zÞdz
Z
:
hna=b na i ¼
na nb dz
ð6Þ
1
where
k is the reaction rate coefficient and H 0 =
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r
Ha2 Hb2 = Ha2 þ Hb2 . The updated equatorial density
for species g over a time interval, dt, is
Ng þ dNg
ng ð0Þ ¼ pffiffiffi
:
pHg
Z þ1
2
dNg
2
2
2
ez =Hi eðzzo Þ =Hn dz
¼ kni ð0Þnn ð0Þ
dt
r1
ffiffiffi
p ðb2 4acÞ=4a
e
;
¼ kni ð0Þnn ð0Þ
a
ð8Þ
ð9Þ
where H0 = (H2b + H2a)/(H2b H2a) and Za is the charge number.
The hot electron chemistry is simply determined by
pffiffiffi
dNg
¼ kna ð0Þfeh ne ð0Þ pHa ;
dt
ð10Þ
where feh is the hot electron fraction in the centrifugal
equator plane, and ne(0) is the electron density determined
by the quasi-neutrality condition.
[22] It is relatively simple to calculate the mass flow
through the torus when the Gaussian approximation is used
for determining the latitudinally averaged chemistry. Energy
flow calculations are somewhat more complicated. The
basic problem for calculating energy flow is that the change
in energy (due to chemical reactions, radiation, collisions,
etc.) for a given species is a function of z; therefore the best
approach should provide a flux tube weighted average for
the temperature updates. For instance, the Coulomb collision rates are functions of density for both species, so the
energy change due to Coulomb interactions is of the form
dðnT Þa
¼ na=b na Tb Ta ;
dt
*
X
Z "X
+
ra;l ðne ; Te ; zÞna
¼
a
a
#
ra;l ðne ; Te ; zÞna ne ð zÞdz
Z
;
ne ð zÞdz
ð13Þ
where ra,l are the radiative rate coefficients of species a at
wavelength l. We then compare the flux tube averaged
composition with those derived from the Cassini UVIS data
[Steffl et al., 2004b].
4. Results and Discussion
where a = (H2i + H2n)/(H2i H2n), b = 2zo/H2n, and c = z2o/H2n.
[21] For ion/electron chemistry the condition of quasineutrality gives
X
pffiffiffi
pffiffiffi
dNg
Za na ð0Þ pH 0 ¼ knb ð0Þne ð0Þ pHe ;
¼ knb ð0Þ
dt
a
ð12Þ
Radiation can be handled in a similar manner where the
radiation contribution from each species is calculated along
the magnetic field and the latitudinally averaged rates are
given by
ð7Þ
[20] Chemistry involving ion/neutral reactions can be
calculated in a similar manner; however, in this case the
neutral clouds lie in Io’s orbital plane rather than the
centrifugal equator plane of the plasma torus. Thus
the spatial location of the neutral distribution is a function
of System III. The location of the neutral cloud can be
treated as a simple offset, zo, from the centrifugal equator
plane which we take to be a constant value of 3.5 in this
initial azimuthally symmetric model. So
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ð11Þ
[23] The coupled radial transport of mass and energy has
nine parameters: hot electron fraction (feh), hot electron
temperature (Teh), neutral source (S n), transport coefficient
(DLL) and respective power laws, and the O/S neutral source
ratio. A six-dimensional parameter space search using the
downhill simplex method of Nelder and Mead [1965] was
used to find the set of model input parameters that provided
the best model fit to the observed radial Cassini profiles
(specifically, the mixing ratios of major ion species and total
EUV power radiated). Preliminary results were fairly insensitive to the hot electron temperature and the O/S ratio, so
these parameters remained fixed during subsequent parameter searches. We adopted an expression for the hot electron
temperature of the form 42 eV (L/Lo)5.5, where Lo = 6 and
O/S was fixed at 1.8. The increase in the hot electron
temperature with radius was motivated by the Sittler and
Strobel [1987] analysis of the Voyager I electron data which
showed a 500 eV superthermal tail, but we note that the
results are insensitive to the exact radial dependence of the
hot electron temperature as the ionization rates are weakly
dependent on temperature above 100 eV. We constrained the
parameter search with the end points (L = 6 and 9) of the
radial profiles of the five major ion species and the total
EUV power radiated from Steffl et al. [2004a]. Given that
we are modeling the radiated power between L = 6 to 9 and
that a significant fraction (i.e., 20%) of the total power
radiated originates inside of L = 6 (i.e., near Io), we
approximated this additional radiation in the L = 5.75 to
6.0 interval as equal to the modeled value in the L = 6 to
6.25 interval. On the basis of the time history of the
observed power radiated (total power is not available during
the period of closest approach, including the 14 January
radial scan) we constrained our fits using 1.4 ±
0.25 terawatts based on interpolation of the October – April
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Figure 2. Sensitivity of radial profiles to variations in transport rate. The top left panel shows the
integrated transport time for three cases (DLL = 4.2 107 (L/6)4.6, 4.2 107(L/6)5.6, and 4.2 107(L/6)3.6 s1) as well as the results of Schreier et al. [1998] (plus symbols). The remaining panels
compare the mixing ratios of the model (lines) with the Cassini data (cross symbols).
torus EUV luminosity profile. Improved fits were obtained
by including mid points (i.e. L = 7.0) for the S+ and S+++
profiles as constraints.
[24] Figures 2 to 4 show the best fit model results to the
Cassini UVIS radial profiles and the sensitivity of the best
fit to variations in the radial power law dependence of
transport time, hot electron fraction, and neutral source. In
this simple model we have not attempted to address smallscale radial variations seen in the data (i.e., bump between
L = 7.5 and 8.0). These sensitivity studies represent a small
subset of the total nine-dimensional parameter space but
represent the most important parameters for determining the
radial profiles. Sensitivity to variations of parameters at L =
6.0 are similar to our previous sensitivity studies presented
by Delamere and Bagenal [2003] and Delamere et al.
[2004] for the homogenous model. In Figure 2 we show
in the top left panel the integrated transport time for
diffusion coefficients of the form DLL(Lo)(L/Lo) with a =
3.6, 4.6, and 5.6. Following Cheng [1986] and Schreier et
al. [1998], an estimate of the radial transport timescale, t,
can made by integrating the radial transport equation,
d DLL d ð NL2 Þ
N
¼ :
dL L2
dL
t
ð14Þ
For comparison we show the Schreier et al. [1998] results
as plus symbols. For our best fit, the integrated transport
time from L = 6 to L = 9 is roughly 140 days, though the
modeled times ranging between 100 and 200 days are all
consistent with the data. The total power radiated for the
respective short, best fit, and long transport times is 1.1,
1.4, and 1.7 terawatts.
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Figure 3. Sensitivity of radial profiles to variations in hot electron fraction. The top left panel shows
the core electron temperature for three cases (feh = 2.5 103(L/6)4.4, 2.5 103(L/6)5.4, and 2.5 103(L/6)3.4) as well as the Cassini results of Steffl et al. [2004a] (plus symbols). The remaining
panels compare the mixing ratios of the model (lines) with the Cassini data (cross symbols).
[25] In Figure 3 we show in the top left panel the core
electron temperature as a function of radius and compare
with the Cassini-derived result of Steffl et al. [2004a]. The
total power radiated for the low, best fit, and high cases is
1.3, 1.4, and 1.6 terawatts, and we thus conclude that the
model is consistent with the data for these hot electron
profiles. With the exception of the Cassini-derived electron
temperature beyond L = 8.5 (see discussion below regarding
radial variations in the hot electron fraction), the modeled
core electron temperatures are consistent with the data.
[26] Figure 4 compares the sensitivity of the radial profiles
to variations in the extended neutral source. The best fit uses
a fairly steep power law of the form S n(Lo)(L/Lo)a with a =
12. For the considerably higher power, a = 20, the results do
not change significantly, indicating that the radial profiles are
strongly determined by chemistry near L = 6. In the case of a
strong extended source (a = 4) the results change considerably and do not match the data. The total mass loading rates
and radiated power for the respective low, best fit, and high
power of L cases are 2100, 900, and 700 kg/s and 4.2, 1.4,
and 1.0 terawatts. Clearly, the radiated power provides an
important constraint in fitting the neutral source parameters
and we conclude that a mass loading rate of 700– 1200 kg/s
matches the data.
[27] Figure 5 shows the latitudinally integrated O and S
neutral column densities for the a = 12 (solid lines) and a =
20 (dotted lines) cases shown in Figure 4. These profiles
compare favorably with the Voyager-based neutral cloud
models of Smyth and Marconi [2003] at L = 6; however, our
best fit profiles require substantially higher neutral density
in the extended clouds. Our a = 20 case is the best match to
the Smyth and Marconi [2003] model but the total power
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Figure 4. Sensitivity of radial profiles to variations in neutral source. The top left panel shows the
neutral source strength, S n, for three cases (S n = 6.8 1027(L/6)12, 6.8 1027(L/6)20, and 6.8 1027(L/6)4 s1). The remaining panels compare the mixing ratios of the model (lines) with the Cassini
data (cross symbols).
radiated is significantly lower than the Cassini observations,
illustrating once again the importance of the radiated power
constraint. Given the time-variable nature of the neutral
source during the Cassini observing period, it is worth
considering the possibility that the radial profiles contain
a residual imprint of the inferred enhanced neutral source
associated with the September 2000 dust outburst
[Delamere et al., 2004; Krüger et al., 2003]. The integrated
transport time of >100 days from L = 6 to 9 is comparable to
the 100+ days since the beginning of the Cassini observing
period and the inferred dust outburst. The model results are
steady-state solutions for a known time variable problem
and the time variable nature of the coupled interaction
between neutral clouds and the plasma torus is left for
future study.
[28] Figure 6 compares the modeled NL2 profiles with the
total flux tube content from the Voyager era [Bagenal,
1994] and Galileo era [Crary et al., 1998]. The total flux
tube content for our Cassini model is roughly 50% higher
than the Voyager era and comparable to the Galileo era. The
primary difference is in the higher S++ densities observed
during the Cassini era. As expected, the short lifetime of S+
due to electron impact ionization leads to a rapid decrease in
S+ while the higher ionization states increase initially with
radius. The slopes for the Voyager and Cassini total NL2
profiles are initially similar, but our model does not attempt
to reproduce the so-called Voyager ramp region. We feel
that the Cassini radial profiles do not provide definitive
evidence for such a ramp region. Although the Cassini
radial profiles do show fluctuations outside of L = 7.0, these
variations could be explained with a variety of mechanisms
including a fluctuating hot electron population or possibly a
residual imprint of the time varying neutral source. We note
that it is difficult to radially propagate a coherent compo-
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Figure 5. Modeled neutral cloud column density as a
function of radius. The solid lines are the average column
density of the respective O and S neutral clouds for the best
fit case, (L/6)12, and the dotted lines for the (L/6)20 case.
Both neutral cloud profiles generate radial profiles that are
consistent with the Cassini data.
sitional variation because the chemistry effectively smears it
out; however, we cannot dismiss the possibility that the
enhanced flux tube content and extended neutral clouds
from the Cassini model reflect residual plasma at large L
(i.e., L > 8) associated with the September 2000 dust
outburst.
[29] Figure 7 shows the radial variation in the modeled
ion temperature. At L = 6, the average ion temperature is
roughly 100 eV. The initial increase is due to pick up from
an extended neutral source. The solid lines in the top left
corner show the pickup temperatures for S and O as a
function of radius (i.e., the relative velocity of the corotating
plasma with respect to the local Keplerian velocity). Without an additional energy source, the ions cool adiabatically
as the plasma is transported radially outward. The modeled
ion temperatures are somewhat higher than those deter-
Figure 6. Comparison of total flux tube content for the
Cassini model (solid line) with the total flux content from
the Voyager era [Bagenal, 1994] and the Galileo era [Crary
et al., 1998].
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Figure 7. Model ion temperature versus radial distance.
The pickup temperature for S and O are indicated by the
solid lines.
mined for the Voyager (60 eV) and Galileo (<60 eV) eras
[Crary et al., 1998]. Note that this model temperature is
really an average energy and the 100 eV value from the
model is consistent with Voyager measurements of 60 eV
core ion temperature averaged with 20% hot (500 eV)
ions [Bagenal, 1994].
[30] Figure 8 shows the mass source and loss timescales
for each species as a function of radius for the best fit case.
The source/loss timescale for species a interacting with
species b (i.e., ionization or charge exchange) is given by
knb, where k is the reaction rate coefficient. The charge
exchange reactions are labeled k0– k16 and are identified in
Table 1. Electron impact ionization is labeled ‘‘EI’’ and
impact ionization by the hot electron component is labeled
‘‘HEI.’’ The solid lines show the integrated transport time
for each species which differ in accordance with variations
in the NL2 profiles for each species. The peak in the NL2
profiles for O++ and S+++ result in a peak in the integrated
transport time at L = 7, indicating that the primary source of
these higher ionization states is located radially outward
from the primary Io mass loading region near L = 6. These
figures illustrate the relative importance of chemistry versus
transport as a function of radius. Much of the chemistry is
only important near L = 6 with the exception of electron
impact ionization of S, S+, and O+. Chemistry involving
S+++ and O++ becomes important between L = 7 and 8 where
the transport timescales effectively become very long as
d(NL2)/dL = 0. Charge exchange losses for S+++, particularly k14, are important throughout our radial interval.
[31] We provide an initial assessment of the affect of
Europa’s oxygen source on the radial profiles. Estimates of
Europa’s oxygen source have been provided by Schreier et
al. [1993], Saur et al. [1998], and Mauk et al. [2004] based
on Voyager plasma measurements, observations of Europa’s
atmosphere, and results of Galileo ENA (energetic neutral
atom) imaging, respectively. These studies all indicate an
oxygen neutral source of roughly 2 1027 s1. As a
limiting case, we introduce the entire Europa oxygen source
in the interval L = 9.0 to 9.25. Figure 9 compares our best fit
Io-only radial profile with the Europa + Io oxygen source.
The primary difference is an increased abundance of O+ and
a decreased abundance of S+++. However, these differences
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Figure 8. Timescales for transport and chemistry. The integrated transport time for each species is
indicated by the solid lines. Chemistry timescales are indicated by the symbols and the various reactions
are identified on the left. Electron impact ionization is labeled ‘‘EI’’ and hot electron impact ionization is
labeled ‘‘HEI.’’ The charge exchange reactions k0 –k16 are given in Table 1.
are still contained within the error bars of the Cassini
analysis and we cannot conclude that the signature of an
Europa oxygen source is seen in the Cassini data. The final
four data points for the O+ abundance do increase, but we
cannot conclude whether this is due to Europa or due to
other factors including time variations in hot electrons and/
or Io’s neutral source. Charge exchange between Europa’s
neutral hydrogen clouds and O+ (not included in our model)
will further decrease the O+ abundance. On the basis of the
rate coefficients of Kingdon and Ferland [1996] (for <1 eV
plasma) we do not expect the additional O+ loss (due to H
charge exchange) to significantly alter the Europa + Io
radial profiles. Charge exchange between hydrogen and
sulfur ions is expected to be insignificant. So, we conclude
that even a substantial cloud of neutral hydrogen does not
make a significant effect on the plasma chemistry. Figure 10,
however, shows significant modification to the radial ion
temperature profiles due to the pickup of europagenic
oxygen.
[32] Finally, Schreier et al. [1998] reported three mechanisms for heating electrons from 3.6 eV to 5 eV to provide
the Voyager-observed electron temperature and torus emis-
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Figure 9. Radial profiles with Europa oxygen source.
sions: (1) an increase in the temperature of thermal ions,
(2) hot ions diffusing inward, and (3) a flux of superthermal
electrons. Mechanism 2 was most strongly supported by the
Schreier et al. [1998] model. We argue that superthermal
electrons are the most likely candidate. First, measurements
of the hot ion populations made by the Galileo EPD
(Energetic Particle Detector) [Mauk et al., 2004] show that
hot (20 keV) inward diffusing ion densities peak near
Eurora’s orbit at <1 cm3 and decline to insignificant levels
inside of L = 7.5. Our model requires a 20 keV hot ion
population of roughly 10 cm3 to significantly alter (i.e., 1 –
2 eV) the electron temperature. For the densities observed
by Mauk et al. [2004], the heating is insignificant. Second,
the Voyager I electron measurements reported by Sittler and
Strobel [1987] showed a superthermal electron component
(500 eV) and the measured fraction of hot electrons is
consistent with the required abundance for our model
(<0.01).
Figure 10. Ion temperature profiles with Europa oxygen
source.
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[33] Figure 11 compares the Voyager core electron temperature and hot electron fraction with our Cassini model
and shows not only a comparable abundance but also a
similar radial dependence. Both Voyager and Cassini observations show an increase in core electron temperature with
radius and significant variation in core electron temperature
for L > 7.5. To illustrate the sensitivity of the core electron
temperature to the hot electron fraction, we have added
perturbations to the hot electron fraction for our best fit
Cassini profiles. For the Voyager case we used a Gaussian
perturbation centered at L = 8.0 to approximate the bump
seen in the Voyager analysis of Sittler and Strobel [1987]
and for the Cassini case we added a step function at L = 8.5.
Both cases yield the observed radial profiles for core
electron temperature. The hot electron fraction in our
Cassini model is consistently higher than the Voyager data,
but this might be expected for a two-Maxwellian treatment
of what is probably closer to a ‘‘Kappa’’ distribution
[Meyer-Vernet et al., 1995] where the affect on composition
of the midrange temperatures (i.e., 30– 70 eV) may be more
significant than a single superthermal 500 eV tail. Electron
impact ionization rates are roughly independent of temperature above 100 eV and thus composition may be strongly
dependent on an accurate description of the midrange
Kappa electrons. The apparent radial variation in the electron profiles between the Voyager and Cassini eras suggest,
perhaps, additional evidence of temporal variability. Possible physical mechanisms that result in a greater abundance
of hot electrons may include enhanced radial transport and/
or variations in the neutral source. We note that the Voyager
hot electron enhancement coincides with the so-called ramp
region in the NL2 profiles, suggesting a possible connection
between time-variable radial transport and hot electron
abundance. A similar ramp region could exist for the
Cassini era, but the model and data cannot confirm this.
A more detailed analysis of the superthermal electron
population is left for future study.
5. Conclusions
[34] On 14 January 2001, the Cassini UVIS instrument
made a radial scan of the Io plasma torus. Plasma
composition for the five major ion species as a function
of radius as well as total torus luminosity were provided
by Steffl et al. [2004a]. Using a steady-state, twodimensional model of plasma transport and chemistry,
we have modeled the Cassini radial composition profiles
and total luminosity. The model is subject to five primary
parameters: hot electron fraction, hot electron temperature,
neutral source rate, transport coefficient, and the neutral
O/S ratio. Simple power laws for the radial variation of
the hot electron fraction, hot electron temperature, neutral
source rate, and transport coefficients complete our ninedimensional parameter space. A comprehensive search of
a six-dimensional parameter space (fixed O/S ratio and
hot electron temperature profile) yielded the following
best fit parameters: DLL(L) = 4.2 107(L/6)4.6 s1,
S n(L) = 6.8 1027(L/6)12 s1, and feh(L) = 2.5 103(L/6)4.4. These best fit parameters yield an integrated
transport time from L = 6 to 9 of 140 days, a total
neutral source supply rate of roughly 900 kg/s, and a
total luminosity of 1.4 terawatts.
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Figure 11. Comparison of the core electron temperature
and the hot electron fraction as a function of radius for the
Voyager analysis of Sittler and Strobel [1987] (solid lines),
Cassini model (dashed line), and a Voyager model (dotdashed lines). The plus symbols are the core electron
temperatures derived from Cassini UVIS by Steffl et al.
[2004a].
[35] The major findings of this paper are summarized
below.
[36] 1. The integrated transport timescale for plasma
diffusing from L = 6 to L = 9 ranges between 100 and
200 days, slightly longer than the diffusion timescales of
Schreier et al. [1998] (100 days).
[37] 2. Chemistry is largely determined inward of L = 6.5.
The transport rate is fast compared to collision and
Coulomb coupling timescales for L > 6.5.
[38] 3. The core electron temperature is highly sensitive
to the specification of the hot electron fraction due to
efficient thermal coupling between hot and cold electrons.
The hot electron fraction increases with radius and shows
significant spatial variability. Comparison with the Voyager
era profiles of Sittler and Strobel [1987] suggests possible
temporal variability.
[39] 4. Observed hot ion densities [Mauk et al., 2004]
(>20 keV) are not sufficient to heat the core electron
population. The increase in the electron temperature with
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radius is likely due to thermal coupling with an increasingly
abundant hot electron population as seen in the Voyager
results of Sittler and Strobel [1987].
[40] 5. A neutral source of roughly 1 ton/s is necessary to
provided the total radiated power observed by Cassini UVIS
(1.45 ± 0.25 1012 W).
[41] 6. A preliminary assessment of Europa’s neutral
source suggests that the radial profiles of composition are
relatively insensitive to the additional oxygen and hydrogen
at Europa because of the rapid radial transport beyond
9 RJ. However, the additional mass loading at Europa
will significantly alter the ion temperature profiles.
[42] Acknowledgments. Peter Delamere and Fran Bagenal are supported by NASA grants NAG5-12994 and NNG04GQ85G. Andrew Steffl’s
analysis of the Cassini UVIS data is supported under contract JPL 961196.
[43] Arthur Richmond thanks Aharon Eviatar and Edward C. Sittler for
their assistance in evaluating this paper.
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