Models of Saturn's Interior Constructed with Accelerated Concentric Maclaurin Spheroid Method

Abstract

The Cassini spacecraft's Grand Finale orbits provided a unique opportunity to probe Saturn's gravity field and interior structure. Doppler measurements yielded unexpectedly large values for the gravity harmonics J_6, J_8, and J_10 that cannot be matched with planetary interior models that assume uniform rotation. Instead we present a suite of models that assume the planet's interior rotates on cylinders, which allows us to match all the observed even gravity harmonics. For every interior model, the gravity field is calculated self-consistently with high precision using the Concentric Maclaurin Spheroid (CMS) method. We present an acceleration technique for this method, which drastically reduces the computational cost, allows us to efficiently optimize model parameters, map out allowed parameter regions with Monte Carlo sampling, and increases the precision of the calculated J_2n gravity harmonics to match the error bars of the observations, which would be difficult without acceleration. Based on our models, Saturn is predicted to have a dense central core of 15-18 Earth masses and an additional 1.5-5 Earth masses of heavy elements in the envelope. Finally, we vary the rotation period in the planet's deep interior and determine the resulting oblateness, which we compare with the value from radio occultation measurements by the Voyager spacecraft. We predict a rotation period of 10:33:34 h +- 55s, which is in agreement with recent estimates derived from ring seismology.

12 color figures, 5 tables, Astrophysical Journal, in press (2019)

References in corpus (9)

• Mass-Radius Relationships for Solid Exoplanets
• Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core
• Hydrogen-Helium Mixtures in the Interiors of Giant Planets
• Nuclear Quantum Effects and Nonlocal Exchange-Correlation Functionals Applied to Liquid Hydrogen at High Pressure
• Phase separation in hydrogen-helium mixtures at Mbar pressures
• Layered convection as the origin of Saturn's luminosity anomaly
• An Exploration of Double Diffusive Convection in Jupiter as a Result of Hydrogen-Helium Phase Separation
• Saturn's fast spin determined from its gravitational field and oblateness
• A complete study of the precision of the concentric MacLaurin spheroid method to calculate Jupiter's gravitational moments

Cited by in corpus (18)

• First-Principles Equation of State Database for Warm Dense Matter Computation
• Evidence for a Dichotomy in the Interior Structures of Jupiter and Saturn from Helium Phase Separation
• The landscape of Saturn's internal magnetic field from the Cassini Grand Finale
• A pole to pole pressure temperature map of Saturn's thermosphere from Cassini Grand Finale data
• Study of Jupiter's Interior: Comparison of 2, 3, 4, 5, and 6 Layer Models
• Saturn's atmospheric response to the large influx of ring material inferred from Cassini INMS measurements
• GASTLI: An open-source coupled interior-atmosphere model to unveil gas giant composition
• Relation of Gravity, Winds, and the Moment of Inertia of Jupiter and Saturn
• The effects of nonlinearities on tidal flows in the convective envelopes of rotating stars and planets in exoplanetary systems
• The complex interplay between tidal inertial waves and zonal flows in differentially rotating stellar and planetary convective regions I. Free waves
• Tidal Response and Shape of Hot Jupiters
• Connecting gravity field, moment of inertia, and core properties in Jupiter through empirical structure models
• Energy deposition in Saturn's equatorial upper atmosphere
• Saturn's rings as a seismograph to probe Saturn's internal structure
• Ab Initio Entropy Calculations of Water Predict the Interiors of Uranus and Neptune to be 15-30% Colder than Previous Models
• The Shape of Jupiter and Saturn Based on Atmospheric Dynamics, Radio Occultations and Gravity Measurements
• Study of Jupiter's Interior with Quadratic Monte Carlo Simulations
• Nested spheroidal figures of equilibrium III. Connection with the gravitational moments $J_{2n}$