HR: 13:40h
AN: P23C-01 INVITED    [Abstracts]
TI: Saturn's Interior and Deep Rotation Rate
AU: * Schubert, G
EM: schubert@ucla.edu
AF: Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics, University of California, 595 Charles E. Young Drive East, Los Angeles, CA 90095-1567, United States
AU: Anderson, J D
EM: jdandy@earthlink.net
AF: John D. Anderson, 121 South Wilson Ave., Pasadena, CA 91106, United States
AB: Temporal changes in the periodicities of Saturn's kilometric radiation and magnetic field show that these signals reflect magnetospheric processes and not the rotation rate of Saturn's deep interior. There is thus no way known at present to directly measure the rotation period of Saturn. We have proposed (Anderson and Schubert, Science 317, 7 September 2007) a plausible, but not definitive, method to infer Saturn's rotation rate. We use Cassini gravitational data (Jacobson et al., 2006, Astron. J. 132, 2520) along with Pioneer and Voyager radio occultation and wind data to simultaneously determine Saturn's rotation rate and internal structure. We hypothesize that Saturn's rotation period can be constrained by minimizing the dynamical height variations with respect to the geoid of the 100~mbar surface of Saturn's atmosphere. The shape of Saturn's 100~mbar isosurface is known, but the shape of the geoid is not because it depends on Saturn's unknown rotation rate. We thus vary the geoid until the 100~mbar isosurface heights measured from the geoid have a minimum variance. There is no dynamical principle that can serve as a basis for this procedure. In a qualitative sense it minimizes the energy and angular momentum of Saturn's winds. It produces a Jovian-like Saturnian wind system with sensible equatorial wind speeds and both eastward and westward jets at higher latitudes. We obtain a rotation period for Saturn of 10~h 32~m 35~s with a standard error of ± 13~s (Anderson and Schubert, Science, 317, 7 September 2007). The corresponding fifth-order reference geoid that best fits the wind and occultation data at the 100~mbar level has a polar radius of 54,438 ± 10~km and an equatorial radius of 60,357 ± 3~km. We represent Saturn's internal density distribution by a single sixth degree polynomial in fractional mean radius r/R, with R equal to 58,256~km, the radius of a sphere with density equal to the mean density of 686.244~kg~m^-3 (mass of Saturn divided by the volume internal to the geoid). By constraining the polynomial such that it goes to zero at the surface, and also such that its derivative goes to zero at both the surface and the center, and by using up all the total available mass, four constraints in all, the polynomial has three degrees of freedom. We use the third-order method of level surfaces (Zharkov and Trubitsyn, Physics of Planetary Interiors, W. B. Hubbard, Ed., Pachart Press, Tucson, 1978) to match this polynomial to the three zonal gravitational harmonics J₂ = 16290.71 ± 0.27, J₄ = - 935.8 ± 2.8 and J₆ = 85.3± 8.5, all in units of 10^-6 and at a reference radius of 60,330~km. The result is a unique sixth degree polynomial that defines an empirical equation of state for Saturn's interior.
DE: 5704 Atmospheres (0343, 1060)
DE: 5714 Gravitational fields (1221)
DE: 5724 Interiors (8147)
DE: 5744 Orbital and rotational dynamics (1221)
DE: 6275 Saturn
SC: Planetary Sciences [P]
MN: 2007 Fall Meeting