Electromagnetic periodicities at Saturn
Saturn - University of Toronto - March 2008
Image from Cassini
Jan. 19, 2007 1
Outline
•
•
•
•
Saturn’s spin period: identification and problems.
Identification of drifting periods.
Other people’s models: diagnosis of diseases.
Our model and incontrovertible evidence
supported by typical best case examples of why
we are right.
• Acknowledgement that we don’t know what we
are doing, but it is a fascinating problem.
Saturn - University of Toronto - March 2008
2
Spin rate is of fundamental importance to studies
of planetary structure and evolution
• For the terrestrial planets, whose
surfaces are solid and relatively
unchanging, the period is directly
established.
• The gas giants lack solid surfaces
but we obtain crude estimates of
the rotation rate by observing the
clouds.
• Higher accuracy for Jupiter, Uranus
and Neptune is achieved by
tracking the rotation of their internal
tilted magnetic dipole moments.
• Radio emissions show identical
modulation.
So - measurements modulated by
the changing orientation of the
magnetic dipole moment have
established the rotation period of the
other gas giants. . .
but Saturn’s internal magnetic field
appears to be axially symmetric.
That is no help!
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For Saturn - SKR:
• Saturn’s period, can be
estimated from cloud motion, but
the cloud structure is banded.
Who knows which cloud layer to
follow?
• Periodic increases of radiated
power in the kilometric range
(SKR) at near the cloud rotation
period have been found by
plasma wave/ radio science
investigations on the Saturn
missions: Voyager, Ulysses and,
since 2004, Cassini.
• This periodicity (10.7 hours) was
assumed to be the rotation
period of the planetary interior
and thus to be emitted at some
fixed planetary longitude.
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The official period* of 10 hr 39 min 24 ± 7 sec implies
that all the winds are prograde (i.e. blow in the direction
of planetary rotation). That seemed odd.
SanchezLavega et al.,
2003
speeds relative to
radio period of 639.4
min.
Not the case at Earth or Jupiter
*Desch and Kaiser, Geophys. Res. Lett., 8, 253-256, 1981
Saturn had more
surprises in store
Gurnett, U. Iowa,
The “official” IAU rotation period,
10.66 ± 0.002 hr
is based on1980-81 Voyager SKR.
Ulysses SKR showed other periods:
~10.77 h in March 1995
~10.69 h in May 1996.
Cassini on approach to Saturn
(April 29, 2003, to June 10, 2004),
found
10.76 ± 0.01 hr
In 2004-2005, roughly the same
period was identified by Cassini
in situ measurements of the
magnetic field .
No plausible torques could have
changed the rotation of a planet as
large as Saturn so rapidly!
A puzzle. What fun!
Saturn - University of Toronto - March 2008
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The new period did not endure
Kurth et al., 2007
If the radio power is maximum at a fixed longitude (call it l) and
one knows the period (P), then l = 2p(t-to)/P (mod 2p) and l
should not vary. However, the plot shows that the peaks in
power drift in l by ~ a degree per day.
The period changed by ~1% over ~1 year.
A slowly changing period orders the data
through August 2006
• By fitting a cubic to l
vs. time, Kurth et al.
(2007) find a timevarying P from
2p/P(t) = dl/dt.
• When the SKR power
is plotted against l
based on P(t), the
peak power occurs at
fixed l.
* Kurth refers to l as “longitude”
Saturn - University of Toronto - March 2008
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Something is changing slowly with time
We still don’t know what.
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P(t) orders other data as well.
• Saturn’s magnetosphere
excludes (most of) the fast
flowing solar wind plasma and
shelters an endogenic plasma
population that distorts the
magnetic field configuration.
• Particles and field
measurements within the
magnetosphere also reveal
unanticipated periodicities
related to the nominal planetary
rotation period.
The small moon,
Enceladus, is a
major source of the
internal plasma.
Saturn - University of Toronto - March 2008
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Br
0
B
The magnetic field recorded by Cassini’s
magnetometer shows clear periodic variations.
-8
-16
Br -----Bq -----Bf -----|B| ------
8
night side
Br
B
B
0
|B|
grid marks
at 10.7
hours
r > 15 RS
-8
DOY: 54
2006-Feb-23
R
S
lat
Z_KSO
Loc. Time
17
-0.3
7.7
9.05
057-00
059-00
061-00
9
0.4
-3.8
22.46
25
0.2
-3.3
1.93
35
0.2
-1.4
2.65
-- May 17, 2006 17:52
This orbit lies near the equator. In the r-f plane
(spherical coordinates) the field rotates inside
of 10-15 RS but oscillates outside.
Saturn - University of Toronto - March 2008
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2006-013-11:55-021-01:21
Br
8
0
-8
B
0
-8
B
8
0
-8
Lshell
R
plat
LT
56
60
32.0
32.0
-0.3
7.3
27.3
27.3
-0.3
7.7
64
68
72
76
80
Lecacheux-Kurth predicted SKR phase (units ) adjusted for rotation
21.5
21.5
-0.3
8.2
13.8
13.8
-0.4
9.6
5.6
5.6
-0.0
16.6
13.5
13.5
0.4
23.9
21.2
21.2
0.3
1.4
84
88
27.6
27.6
0.2
2.1
33.0
33.0
0.2
2.5
-- April 17, 2007 00:24
Perturbations are well ordered by the SKR periodicity
corrected for spacecraft motion, i.e. to an effective “longitude”.
Inside of 12 RS, the magnetic signal is rotating.
Saturn - University of Toronto - March 2008
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The periodicity tracks the changing SKR period
Andrews et al., 2007
period (hrs)
solid line from magnetometer periodicities
dashed line from SKR fraction of a percent per year
0
200
400
600
800
1000
time in days from 1 Jan. 2004
The periods from magnetometer and SKR match (to
within uncertainty) and drift at the same rate.
But what imposes periodicity on the
magnetic signature?
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Again consider Jupiter, where a rotating, tilted dipole
makes the magnetic equator seem to nod up and down.
Particle fluxes vs. time
(from Krupp et al., 2005)
Ganymede 8 (s3rh) 10 hour grid
Magnetic
field vs. time
50
Br
0
-50
20
B
0
-20
20
B
0
-20
40
|B| 20
The perturbations resemble
those far from Saturn.
0
DOY: 130 1997-May-11
1997-May-10
R
LAT
LON
local time
31
-0
253
21.69
1997-May-12
1997-May-13
Spacecraft Event Time (UT)
39
-0
112
22.34
46
-0
328
22.77
1997-May-14
53
-0
183
23.09
At Saturn, where the dipole moment is aligned with
the spin axis, this explanation is useless.
• Far from Saturn the magnetic variations behave as
if something is flapping up and down, so a tilt of
the dipole moment would help, but only at large
distance.
• Close to the planet the structure of the periodic
perturbation field is not that of a tilted dipole.
• We need another explanation.
• Several have been offered.
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One model: Goldreich and Farmer, 2007
• They propose that “centrifugally
driven convection
spontaneously breaks the
axisymmetry of the external
magnetic field.” They postulate
that close to the planet the
plasma density varies with
location around the planet and
that the anomalous density
region flows outward, narrowing
in the process Current flows
from the tongue along the field
to Saturn’s ionosphere and that
current generates the SKR.
• Some aspects of this
description are common
to other attempts at
interpreting the periodic
variations of the field and
the radio emissions.
Saturn - University of Toronto - March 2008
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This model should produce signatures in the
magnetic field that are not found in the data
combmdB2004-155-2005-360posrtpnewmodmlatexp
0
The “right-hand rule” says that
across a radial current, the
azimuthal magnetic perturbation
reverses sign. What do the
magnetometer data say?
B
-8
0
-8
-16
6
equator
4
2
B
• As illustrated by
Goldreich-Farmer, the
current system would
produce radial and
azimuthal perturbations
that reverse sign across
the equator.
Br
8
0
-2
-4
DOY: 158
2005-Jun-7
R
MagLat
LT
Zsat(Rs)
158-16:00
159-00:00
159-08:00
159-16:00
160-00:00
160-08:00
11.3
-23.5
11.6
-4.2
7.7
-22.2
12.9
-2.6
4.1
-7.5
16.8
-0.2
5.2
17.1
0.3
1.9
9.0
10.4
2.8
2.0
12.5
5.8
3.9
1.6
• The clearest periodicity is in Bf and it
does not jump by 180 º anywhere
near the equator.
• We need a mechanism that gives Bf
continuous across the equator inside
of 15 RS.
C:\Documents and Settings\David Southwood\My Documents\cass-saturn\data\1temp\filescsv\m\combmdB2004-155-2005-360posrtpnewmodmlatexp -
Saturn - University of Toronto - March 2008
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Gurnett et al. (2007) identified asymmetry in the plasma
density close to the planet and near the equator.
“By following the colored line for a
given orbit, one can see that the
electron densities for the inbound and
outbound portions of the same pass are
often quite different. This hysteresis-like
They also call for a rotating flow
dependence on radial distance strongly
driven by density variations
suggests a longitudinal control.”
The magnetic signatures of the
outward transport are not observed
• Outflow may well be occurring non-uniformly, but, if the
dominant process, it would also produce a 180º phase
jump in Br and Bf across the equator
 this is not
observed
Field lines,
no outflow
Field lines,
equatorial
outflow
Saturn - University of Toronto - March 2008
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• They suggest that there is an
asymmetric ring current (varying
in intensity and rotating with the
planet) enclosing the inner
magnetosphere.
• They are able to account for
“antiphase” variations** of Br
and Bq at relatively large
distances and above the ring
current (relatively high latitudes)
as in the data plotted in the
upper panel.
• The asymmetry arises through
preferential ionization of
neutrals as a result of periodic
enhancements of the flux of
rotating energetic particles
|B| Bf Bq
Br
Khurana et al. (2008) have a creative solution
** meaning one is max when other is min
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KKK et al. expect preferential ionization in the prime sector
of the ring current. Density and inertial asymmetry lead to
rotation phase dependence of field geometry
Saturn - University of Toronto - March 2008
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Correspondingly the prime sector is a favored location
of reconnection/plasma loss and reconnection in the
tail on each rotation resets the clock.
Saturn - University of Toronto - March 2008
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What are my reservations?
1. Reconnection as studied at Earth appears
to have a large stochastic contribution. It
is hard to set clocks by such processes.
2. The energetic particles assumed to
created zones of increased ion density do
not all rotate at the same rate, so how can
they set a clock?
Saturn - University of Toronto - March 2008
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Our (Southwood and Kivelson, 2007) interpretation relies
heavily on the observation that near the equator the
components Br - Bf vary differently through a “rotation”
period at locations close to and far from the planet.
close in
far out
• Close in (and near the equator) the field
looks like a uniform field rotating “with the
planet”.
• Beyond ~15 RS, the magnetic perturbations
look like those imposed by a slightly tilted
dipole, also rotating “with the planet”.
Saturn - University of Toronto - March 2008
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B
ʘ
ʘ
⊗
ʘ
• Currents flowing on the
surface of a rotating
sphere can produce the
fields observed near the
equator.
⊗
⊗
field lines in the
equatorial
plane. . .
Imagine the
whole thing
rotating.
But currents in magnetized
plasmas like to flow along the
background field where
conductivity is very high.
Suppose one indented the
spherical surface.
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An indented sphere resembles a dipole
magnetic shell
• What would happen if the currents were
flowing on a rotating dipolar shell?
The current flows from
ionosphere to ionosphere
through the equator - upward
in regions when Bf <0.
Saturn - University of Toronto - March 2008
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Near the equatorial plane (see A), current
flowing on a spin-axis-aligned dipole L-shell
from ~12 RS with intensity varying as sinf
produces an approximately uniform field inside
12 RS and approximates a dipole field outside.
In the SK07 phenomenological model
(Southwood and Kivelson, 2007), the entire
structure rotates at ~10.7 hours.
equatorial cut
z
x
y
meridional cut (B)
(A)
Z
Y
perturbation
field
X
X
Saturn - University of Toronto - March 2008
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Modeled field lines in the equatorial plane
The whole structure rotates at a rate
close to planetary rotation.
But how
well does it
fit the data?
Field lines of the total field in the XZ plane
When added to the background field, the total field
beyond the current-carrying shell resembles a tilted
rotating dipole. The magnetic equator goes up and down.
Saturn - University of Toronto - March 2008
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Br [nT]
0
0
-0
+7 hrs.
-1
1
Bt [nT]
1
0
-1
+7 hrs.
Bp [nT]
-1
1
0
-1
+7 hrs.
-1
DOY: 315 00:00
2006-Nov-11
r_krtp
theta_kr
phi_krtp
Loc_Time
23.55
47.30
-1.57
0.00
12:00
00:00
12:00
00:00
12:00
25.22
50.47
-2.28
0.00
26.55
53.44
-3.00
0.00
27.56
56.28
2.55
0.00
28.26
59.02
1.81
0.00
28.67
61.72
1.07
0.00
------ Cassini ; ------ Original Traj; ------ Shift z0=-2.5Rs
Equator
dBr_mod[nT]
8
0
-8
8
dBth_mod[nT]
• Compare perturbation
field with data – some
typical best cases!
– above, outside
current shell
– below, inside
current shell near
the equator
• Starting phase was
selected to match the
Bf oscillations
• Amplitudes are off but
are very sensitive to
the position of the
effective magnetic
equator, which is
distorted by external
forces.
• Phases are correct.
1
+9 hrs.
0
-8
8
Bp_krtp[nT]
Data
+9 hrs.
0
-8
DOY: 141
2006-May-21
r_krtp
theta_kr
Loc_Time
+9 hrs.
00:00
09:00
18:00
03:00
7.50
90.42
8.50
5.46
90.36
12.90
7.48
89.82
17.20
11.03
89.65
19.20
The blue trace for the Bq panel has been multiplied by 20.
Saturn - University of Toronto - March 2008
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The SKR emissions are said to be generated by fieldaligned currents flowing out of the ionosphere on the
morning side of the magnetosphere.
Is that connected with the current system we propose?
Zarka et al. (2008 and earlier) argue the SKR power varies in intensity with the
solar wind velocity, and also that it is generated in the 0600-1200 LT sector by
currents flowing upward from the ionosphere.
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• The currents driving the radio emissions are carried by
electrons accelerated into the ionosphere by E parallel to B.
• Cassini, in the southern hemisphere, observes perturbations
of Bf consistent with strong, localized, upward current.
• The current, out of southern ionosphere, on the morning
side, flows where SKR emission is thought to be localized.
• The strong upward current occurs at the point in a rotation
postulated by the SK07 current system.
2006-226-2007-042rtpplatKph
20
60
20
Current from
L=11 to 15
fB
dB
30
0
0
-20
10
1435.00
(2n-1)p
Lshell
R
plat
LT
20
0
½ cycle
Dec-02 03:29
14.36
10.29
-32.01
4.45
1436.00
2np
Dec-02 09:33
15.65
8.02
-44.11
5.93
1437.00
(2n+1)p
Dec-02 16:41
16.13
5.47
-54.14
9.75
1438.00
1439.00
Dec-02 23:55
4.91
4.85
-5.94
13.81
Dec-03 06:38
10.07
6.83
34.78
16.73
2(n+1)p
Planetary Latitude
10
(2n+3)p
-30
C:\Documents and Settings\david southwood\My Documents\cass-saturn\data\2006\2006-226-2007-042rtpplatKph -- December 09, 2007 21:10
Saturn - University of Toronto - March 2008
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We think there is good evidence that the periodic
variations of the magnetic field is driven by
currents flowing external to Saturn, crossing the
equator between 11 and 15 RS.
• The model fits much of the magnetometer data both
inside and outside of the postulated current system.
• What causes the current to flow? There’s the rub!
Saturn - University of Toronto - March 2008
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What is driving the current system
that we propose?
• We don’t know.
• An internal (to Saturn) magnetic anomaly of order m = 1
could, in principal, produce conductivity anomalies, but
that doesn’t seem likely for many reasons, especially
because we find no signatures of such internal moments.
• Asymmetries of the flows of the underlying atmosphere at
the two ends of the high latitude flux tubes could produce
a situation where one ionosphere is trying to accelerate
the one in the other hemisphere, but the shears that this
would produce may be a problem.
• So we do not yet know.
• But if the answer has to do with ionospheric asymmetries,
it becomes plausible to anticipate a period that is not fixed.
• Stay tuned. Propose solutions.
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What is the real internal period?
• Using arguments related to the shape of the gravitational
potential surfaces, Schubert and Anderson (2007) come
up with a period of 10 hours, 32 minutes, and 35 ± 13
seconds, less than the shortest period (10 hours, 39
minutes and 22 seconds) from SKR or the in situ
magnetic field.
• They note: “This more rapid spin implies slower
equatorial wind speeds on Saturn than previously
assumed, and the winds at higher latitudes flow both
east and west, as on Jupiter.” That’s good.
• Other evidence of shorter periods is becoming available.
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Cassini RPWS
instrumentation monitors
radio emissions from
Saturn. Some examples.
2x103
SKR (Saturn kilometric
radiation) is bursty with a
periodicity of close to 10.7
hours.
f = 3x105 Hz if l = 1 km
Note also the (less
common) bursts at lower
frequency (~2x103 Hz) and
roughly the same periodicity
have recently been
reanalyzed by Gurnett et al
and give a period close to
the Schubert and Anderson
period.
From: Louarn, P. et al., (2007).
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Bottom line
• The Schubert-Anderson analysis rests on assumptions
that have not yet been fully confirmed.
• Confirmation from electromagnetic evidence of the
internal period would be comforting, but such evidence is
still weak.
• With confidence we can say that the time varying period
is linked to something other than the planetary interior
but we do not know what.
• Cassini has provided a wonderfully obscure set of riddles
to solve.
• We are discovering aspects of planetary science that no
one predicted.
• It’s a great time to be studying planetary
magnetospheres!
Saturn - University of Toronto - March 2008
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Thank you
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