Interior Models of Saturn: Including the Uncertainties in Shape and Rotation

TL;DR

This paper investigates how wind velocities, internal rotation, and shape uncertainties influence Saturn's internal structure models, highlighting the importance of shape and rotation data for constraining planetary composition and core mass.

Contribution

It introduces methods to incorporate shape constraints into Saturn's interior models and analyzes the impact of rotation period uncertainties on inferred composition.

Findings

Saturn's physical shape is insensitive to deep rotation assumptions.

Uncertainty in rotation period significantly affects heavy element estimates.

Core mass depends on helium phase separation pressure, estimated at 5-20 Earth masses.

Abstract

The accurate determination of Saturn's gravitational coefficients by Cassini could provide tighter constrains on Saturn's internal structure. Also, occultation measurements provide important information on the planetary shape which is often not considered in structure models. In this paper we explore how wind velocities and internal rotation affect the planetary shape and the constraints on Saturn's interior. We show that within the geodetic approach (Lindal et al., 1985, ApJ, 90, 1136) the derived physical shape is insensitive to the assumed deep rotation. Saturn's re-derived equatorial and polar radii at 100 mbar are found to be 54,445 $\pm$10 km and 60,365$\pm$10 km, respectively. To determine Saturn's interior we use {\it 1 D} three-layer hydrostatic structure models, and present two approaches to include the constraints on the shape. These approaches, however, result in only small differences in Saturn's derived composition. The uncertainty in Saturn's rotation period is more significant: with Voyager's 10h39mns period, the derived mass of heavy elements in the envelope is 0-7 M$_{\oplus}$. With a rotation period of 10h32mns, this value becomes $<4$ $M_{\oplus}$, below the minimum mass inferred from spectroscopic measurements. Saturn's core mass is found to depend strongly on the pressure at which helium phase separation occurs, and is estimated to be 5-20 M$_{\oplus}$. Lower core masses are possible if the separation occurs deeper than 4 Mbars. We suggest that the analysis of Cassini's radio occultation measurements is crucial to test shape models and could lead to constraints on Saturn's rotation profile and departures from hydrostatic equilibrium.