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The Intrinsic Magnetic Field of Saturn: A Special One or an Averaged One?

H. Cao, C. T. Russell, U. R. Christensen, M. K. Dougherty

Magnetospheres of the Outer Planets14:35, Tuesday, July 12th , 2011

Boston, Massachusetts

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Power Spectrum of Planetary Magnetic Field

• Lowes spectrum

Lowes spectrum of the geomagnetic field (IGRF 2010) at the surface of the Earth and

the CMB

a is the radius of the planet

This is the mean square value of the field of degree n on sphere of radius r(outside the dynamo)

The Lowes spectrum of the geomagnetic field is flat near the geo-dynamo surface (core-mantle boundary), while the dipole power is enhanced

n

m

mn

mn

nra

n hgnR0

22)42( ])()[()()1(

0

222

022 sin)(

4

1ddrrB

rBR nnn

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Planetary Magnetic Field at the Dynamo Surface

• The fact that the Lowes spectrum of the geomagnetic field is flat at the dynamo surface means that the field is characterized by small scale structures at where it is generated

• Intense equatorial flux spots• Reversed flux patches in the

southern hemisphereBr [μT] at the Earth’s surface and CMB(after Hulot et al., 2010)

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Saturn’s Intrinsic Field – Cassini Era

• Study of Cassini Rev 3 – 126 (2.46 Rs – 3.8 Rs)- the field is extremely axisymmetric , dipole tilt < .06 deg- the first three zonal moments remain the same as the Pioneer- Voyager values, while their counterpart at the Earth changes ~ 20 nT/yr- high degree moments (n>3) cannot be identified

|B|<10nT beyond 13 Rs|B|<1nT beyond 28 Rs|B| quad. < 1 nT beyond 7 Rs|B| octu. < 1 nT beyond 5 Rs

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Cassini SOI Reinterpretation

• SOI provides measurements reaching 1.33 Rs

• Residuals from the Cassini (Rev 3-126) model behave as expected until reaches ~2 Rs

• Maximum value of the residuals ~ 100 nT too large to be of external origin

• The steep radial dependence implies high degree moments as the origin Residuals of SOI measurements from

the Cassini (Rev 3 – 126) model inside 30 Rs

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Parameter Space of High Degree Moments

• Due to the limited spatial coverage, a parameter space search would enable a better determination of the high degree moments than inversion

• With the first 3 zonal moments fixed, we search the parameter space (g40, g50) based on the Cassini SOI measurements (1.33 Rs – 2.46 Rs)

• Maximum absolute component residuals and RMS residuals are examined• g40~30 +/- 60, g50~ 230 +/- 100 are found if 24 nT, corresponding to the

uncertainty of the first three zonal moments, is allowed for the residuals

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Fast Decaying Field of High Degree Moments

|B|(g40) < 1nT beyond 2.2 Rs|B|(g50) < 1nT beyond 2.5 Rs

Hardly detectable in any Cassini orbit until now other than SOI

Should show up again in the Cassini proximal orbits

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Saturn’s Magnetic Spectrum and Dynamo Depth

• The power spectrum of the field is zig-zag up to degree 5 at the planet surface

• Spectrum of the odd axial moments is flat ~ 0.4 Rs

• The first two accessible even axial moments are both suppressed

• This deeply seated dynamo is favored by the heat flux scaling law (Christensen, 2010)

• The scaling law is based on the argument that ohmic dissipation of the field generation balanced by the available heat flux from the planet

• “Saturn 1” and “Saturn 2” assume the dynamo depth at 0.64 and 0.4 Rs respectively [Christensen,

2010]

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Molecular-metallic Transition of Hydrogen

• However, Saturn’s dynamo depth is estimated to be 0.64 - 0.5 Rs

• This comes from matching the pressure of the planet interior to the pressure corresponding to the molecular-metallic transition (1.3 - 3 Mbar)

• The molecular-metallic transition pressure is estimated from shock wave experiments and theoretical calculations

• Pressure (0. 4 Rs) ~ 5 Mbar, lies close to the suspected monatomic metallic hydrogen transition with even higher electrical conductivity

Pressure profile for Saturn derived from Cassini observations

(after Anderson & Schubert, 2007)

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A Stable Layer, Acting as a Frequency Filter

• The discrepancy between the two dynamo depth estimations may due to the existence of a conducting stable layer above the dynamo

• This stable layer will act as a frequency filter due to the EM skin effect

• Non-axisymmetric components will be strongly attenuated• With a layer ~ 10,000 km thick, the average difference between

two dynamo depth estimations, the dipole tilt at the planet surface < 0.001 deg from an analytical analysis

• The same effect will also damp the fluctuations of the field • Consistent with no detectable secular variation• Saturn’s intrinsic field, as we observe it “now”, is a filtered

version of the field generated deep down

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Field Geometry at the Dynamo Surface

• Field at the dynamo surface, corresponding to this zig-zag spectrum, is concentrated into two very localized bundles of flux at the rotation poles

• Geostrophic flow in the stable layer could stretch the radial component in the low-middle latitude region, convection would then bring the field to the high latitude

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Summary

• Revisit the Cassini SOI magnetic measurements• Extract the high degree axial magnetic moments• The Lowes spectrum of Saturn’s field has a zig-zag pattern up to

degree 5 at the planet surface• Both g20

and g40, which belong to the quadrupole family solution, are suppressed

• A deeply seated dynamo, ~0.4 Rs, is suggested by this more complete magnetic spectrum

• The field at the dynamo surface is strongly concentrated at the spin poles

• It is possible that Saturn’s field as we observe it is filtered• Surface dipole tilt could be less than 0.001 degree

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Field Geometry at Various Depth

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