Low- and high-order gravitational harmonics of rigidly rotating Jupiter

Abstract

The Juno Orbiter has provided improved estimates of the even gravitational harmonics J2 to J8 of Jupiter. To compute higher-order moments, new methods such as the Concentric Maclaurin Spheroids (CMS) method have been developed which surpass the so far commonly used Theory of Figures (ToF) method in accuracy. This progress rises the question whether ToF can still provide a useful service for deriving the internal structure of giant planets in the Solar system. In this paper, I apply both the ToF and the CMS method to compare results for polytropic Jupiter and for the physical equation of state H/He-REOS.3 based models. An accuracy in the computed values of J2 and J4 of 0.1% is found to be sufficient in order to obtain the core mass safely within 0.5 Mearth numerical accuracy and the atmospheric metallicity within about 0.0004. ToF to 4th order provides that accuracy, while ToF to 3rd order does not for J4. Furthermore, I find that the assumption of rigid rotation yields J6 and J8 values in agreement with the current Juno estimates, and that higher order terms (J10 to J18) deviate by about 10% from predictions by polytropic models. This work suggests that ToF4 can still be applied to infer the deep internal structure, and that the zonal winds on Jupiter reach less deep than 0.9 RJup.

arXiv comment8 pages, accepted to A&A

References in corpus (21)

• Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core
• The Interior Structure, Composition, and Evolution of Giant Planets
• Shock Compression of Deuterium and the Interiors of Jupiter and Saturn
• A new vision on giant planet interiors: the impact of double diffusive convection
• A Massive Core in Jupiter Predicted From First-Principles Simulations
• Jupiter models with improved ab initio hydrogen EOS (H-REOS.2)
• Ab Initio Equation of State for Hydrogen-Helium Mixtures with Recalibration of the Giant-Planet Mass-Radius Relation
• Ab initio equations of state for hydrogen (H-REOS.3) and helium (He-REOS.3) and their implications for the interior of Brown Dwarfs
• Planet formation with envelope enrichment: new insights on planetary diversity
• Concentric Maclaurin spheroid models of rotating liquid planets
• The fuzziness of giant planets' cores
• A Preliminary Jupiter Model
• Jupiter internal structure: the effect of different equations of state
• Interior Models of Saturn: Including the Uncertainties in Shape and Rotation
• The Evolution and Internal Structure of Jupiter and Saturn with Compositional Gradients
• An Exploration of Double Diffusive Convection in Jupiter as a Result of Hydrogen-Helium Phase Separation
• Constraining Saturn's Core Properties by a Measurement of Its Moment of Inertia - Implications to the Cassini Solstice Mission
• Bayesian Evolution Models for Jupiter with Helium Rain and Double-diffusive Convection
• Gravity and Zonal Flows of Giant Planets: From the Euler Equation to the Thermal Wind Equation
• The Concentric Maclaurin Spheroid method with tides and a rotational enhancement of Saturn's tidal response
• Predictions on the core mass of Jupiter and of giant planets in general

Cited by in corpus (23)

• Jupiter's evolution with primordial composition gradients
• Saturn's deep atmospheric flows revealed by the Cassini Grand Finale gravity measurements
• Jupiter's inhomogeneous envelope
• Cassini Ring Seismology as a Probe of Saturn's Interior I: Rigid Rotation
• Revelations on Jupiter's Formation, Evolution and Interior: Challenges from Juno Results
• Saturn's Probable Interior: An Exploration of Saturn's Potential Interior Density Structures
• Empirical Structure Models of Uranus and Neptune
• Equilibrium Tidal Response of Jupiter: Detectability by Juno
• Relation of Gravity, Winds, and the Moment of Inertia of Jupiter and Saturn
• A complete study of the precision of the concentric MacLaurin spheroid method to calculate Jupiter's gravitational moments
• Linking Zonal Winds and Gravity: The Relative Importance of Dynamic Self Gravity
• The interior of Uranus: Thermal profile, bulk composition and the distribution of rock, water and hydrogen and helium
• Benchmarking the ab initio hydrogen equations of state for the interior structure of Jupiter
• Connecting gravity field, moment of inertia, and core properties in Jupiter through empirical structure models
• Zonal winds of Uranus and Neptune: Gravitational harmonics, dynamic self-gravity, shape, and rotation
• NeuralCMS: A deep learning approach to study Jupiter's interior
• Tesseral harmonics of Jupiter from static tidal response
• Setting the Stage for Uranian Seismology from Rings and Radial Velocities
• 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 $J_{2n}$
• No dilute core produced in simulations of giant impacts on to Jupiter
• Constraining Saturn's interior with ring seismology: effects of differential rotation and stable stratification
• Lie Group Theory of Multipole Moments and Shape of Stationary Rotating Fluid Bodies