J/A+A/643/L10 Phoebe Spherical Harmonics decomposition (Rambaux+, 2020)
Phoebe's differentiated interior from refined shape analysis.
Rambaux N., Castillo-Rogez J.C.
<Astron. Astrophys. 643, L10 (2020)>
=2020A&A...643L..10R 2020A&A...643L..10R (SIMBAD/NED BibCode)
ADC_Keywords: Solar system ; Planets
Keywords: planets and satellites: interiors -
planets and satellites: individual: Phoebe - methods: numerical
Abstract:
Phoebe is an irregular satellite of Saturn, and its origin, from
either between the orbits of the giant planets or the Kuiper Belt, is
still uncertain. The extent of differentiation of its interior can
potentially help inform its formation location because it is mainly
determined by heat from 26-aluminium. The internal structure is
reflected in the shape, assuming the body is relaxed to hydrostatic
equilibrium. Although previous data analysis indicates Phoebe is close
to hydrostatic equilibrium, its heavily cratered surface makes it
difficult to tease out its low-order shape characteristics. This paper
aims to extract Phoebe's global shape from the observations returned
by the Cassini mission for comparison with uniform and stratified
interior models under the assumption of hydrostatic equilibrium. The
global shape is derived from fitting spherical harmonics and keeping
only the low-degree harmonics that represent the shape underneath the
heavily cratered surface. The hydrostatic theoretical model for shape
interpretation is based on the Clairaut equation developed to the
third order (although the second order is sufficient in this case). We
show that Phoebe is differentiated with a mantle density between 1900
and 2400kg/m3. The presence of a porous surface layer further
restricts the fit with the observed shape. This result confirms the
earlier suggestion that Phoebe accreted with sufficient 26-aluminium
to drive at least partial differentiation, favoring an origin with
C-type asteroids.
Description:
Phoebe has been observed by the Cassini-Huygens spacecraft in 2004.
From these observations a Digital Terrain Model (DTM) was built by B.
Gaskell. It is accessible at NASA Planetary Data System,
CO-SA-ISSNA-5-PHOEBESHAPE-V2.0. The file Phoebe_SH.dat presents a
spherical harmonics decomposition of the phoebe_quad64q.tab DTM model.
The Spherical Harmonics decomposition uses unnormalized Legendre
polynomials. The uncertainties of each parameters are formal
uncertainties coming from the covariance matrix. A more realistic
uncertainty is about 0.5 km (see the paper). In order to minimize the
degree 1 and off-diagonal degree 2 we translate the DTM by -0.4, 0.4,
0.4 km and rotate it by (0.62, 1.34, 91.98) degrees for the
orientation angles with the rotation matrices in angular sequence
1,2,3.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
tablea1.dat 99 105 Coefficients of the spherical functions
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Byte-by-byte Description of file: tablea1.dat
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Bytes Format Units Label Explanations
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1- 3 I3 --- Degree Degree
5- 7 I3 --- Order Order
9- 30 E22.15 km A Topographic coefficients of the
spherical functions (cosine term)
32- 53 E22.15 km B Topographic coefficients of the
spherical functions (sine term)
55- 76 E22.15 km e_A Formal uncertainty on A (sigmaA)
78- 99 E22.15 km e_B Formal uncertainty on B (sigmaB)
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Acknowledgements:
Nicolas Rambaux, Nicolas.Rambaux(at)imcce.fr
(End) Nicolas Rambaux [IMCCE, France], Patricia Vannier [CDS] 22-Oct-2020