Interior Structure of Saturn Inferred from Pioneer 11 Gravity Data

Abstract

The structure of Saturn is studied via a fourth-order theory for rotating planets and equations of state for the envelope which depend parametrically on the helium abundance, on the starting temperature for the adiabat, and on adopted forms of the pressure-density curve in the region of transition from molecular to metallic hydrogen. Models are congtrained by the values of J2 and J4 obtained from the Pioneer-Saturn celestial mechanics experiment. Equations of state are tested by computing Jupiter models, which can now be subjected to a more stringent comparison with observed zonal harmonics. We find that Saturn has a low-density hydrogen-helium envelope with no evidence for enhancement of H20, CH4, or other abundant compounds. Such compounds are presumably located near the core. The helium mass abundance for Saturn's envelope appears to be in the range of--•0.12 to --•0.19, but this result is very model-dependent. The helium abundance in the envelope of Jupiter is apparently very similar to that of Saturn. thermodynamics of the envelope. In the ideal gas region, adiabats are calculated taking into account quantized vibration and rotation of the H: molecule. As discussed by Hubbard and MacFarlane [1980], for p > 0.005 g/½m 3 it is necessary to continue the adiabatic curves by means of analytic fits to Monte Carlo data for the thermodynamic parameters of compressed H:-He mixtures. Data used for this purpose are given in Tables 1 and 2. These data are an extension of the results given by Hubbard and MacFarlane [1980]. We have computed thermodynamics for pure molecular hydrogen and for a ratio of hydrogen molecules to helium atoms of 16/3 (corresponding to Y = 0.27). At these densities, temperatures are high enough for the classical approximation to the vibration and rotation of H: molecules to be valid. The characteristic vibration and rotation temperatures are assumed to be independent of density. Here ¾ is the value of 0 In T/O In p along an adiabat. Procedures for determining adiabats from such data are discussed by Hubbard and MacFarlane. For an arbitrary value of Y the correct adiabat is obtained from an interpolation between the two tables.