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.

arXiv comment12 color figures, 5 tables, Astrophysical Journal, in press (2019)

References in corpus (23)

• Mass-Radius Relationships for Solid Exoplanets
• Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core
• Shock Compression of Deuterium and the Interiors of Jupiter and Saturn
• A Comparison of the Interiors of Jupiter and Saturn
• Solar System Abundances of the Elements
• Hydrogen-Helium Mixtures in the Interiors of Giant Planets
• Nuclear Quantum Effects and Nonlocal Exchange-Correlation Functionals Applied to Liquid Hydrogen at High Pressure
• Ab Initio Equation of State for Hydrogen-Helium Mixtures with Recalibration of the Giant-Planet Mass-Radius Relation
• Sequestration of noble gases in giant planet interiors
• Phase separation in hydrogen-helium mixtures at Mbar pressures
• Layered convection as the origin of Saturn's luminosity anomaly
• Concentric Maclaurin spheroid models of rotating liquid planets
• Cassini Ring Seismology as a Probe of Saturn's Interior I: Rigid Rotation
• Interior Models of Saturn: Including the Uncertainties in Shape and Rotation
• Saturn layered structure and homogeneous evolution models with different EOSs
• 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
• Gravity and Zonal Flows of Giant Planets: From the Euler Equation to the Thermal Wind Equation
• A full, self-consistent, treatment of thermal wind balance on oblate fluid planets
• The Concentric Maclaurin Spheroid method with tides and a rotational enhancement of Saturn's tidal response
• The properties of heavy elements in giant planet envelopes
• An adjoint based method for the inversion of the Juno and Cassini gravity measurements into wind fields
• A complete study of the precision of the concentric MacLaurin spheroid method to calculate Jupiter's gravitational moments

Cited by in corpus (32)

• The New Generation Planetary Population Synthesis (NGPPS). II. Planetary population of solar-like stars and overview of statistical results
• First-Principles Equation of State Database for Warm Dense Matter Computation
• Uranus and Neptune: Origin, Evolution and Internal Structure
• Comparison of the deep atmospheric dynamics of Jupiter and Saturn in light of the Juno and Cassini gravity measurements
• 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
• Saturn's Probable Interior: An Exploration of Saturn's Potential Interior Density Structures
• 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
• GASTLI: An open-source coupled interior-atmosphere model to unveil gas giant composition
• Saturn's atmospheric response to the large influx of ring material inferred from Cassini INMS measurements
• The effect of pre-impact spin on the Moon-forming collision
• Equilibrium Tidal Response of Jupiter: Detectability by Juno
• 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
• A Global Simulation of the Dynamo, Zonal Jets, and Vortices on Saturn
• 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
• The impact of tidal friction evolution on the orbital decay of ultra-short period planets
• TOI-5344 b: A Saturn-like planet orbiting a super-Solar metallicity M0 dwarf
• Strong resemblance between surface and deep zonal winds inside Jupiter revealed by high-degree gravity moments
• 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
• NeuralCMS: A deep learning approach to study Jupiter's interior
• 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
• Isolating the gravitational influence of Uranus's winds requires close passages inward of the rings
• Nested spheroidal figures of equilibrium III. Connection with the gravitational moments $J_{2n}$
• Retention of primordial atmospheres through giant impacts
• Lie Group Theory of Multipole Moments and Shape of Stationary Rotating Fluid Bodies