The Evolution of Jupiter and Saturn as a function of the Parameter R${}_{\rho }$

Abstract

Computed using the APPLE planetary evolution code, we present updated evolutionary models for Jupiter and Saturn that incorporate helium rain, non-adiabatic thermal structures, and "fuzzy" extended heavy-element cores. Building on our previous Ledoux-stable models, we implement improved atmospheric boundary conditions that account for composition-dependent effective temperatures and systematically explore the impact of varying the parameter $R_{\rho }$, which allows one to explore in an approximate way the efficiency of semiconvection. For both Jupiter and Saturn, we construct models spanning from $R_{\rho }=1$ (Ledoux) to $R_{\rho }=0$ (Schwarzschild), and identify best-fit solutions that match each planet's effective temperature, equatorial radius, lower-order gravitational moments, and atmospheric composition at 4.56 Gyr. We find that lower $R_{\rho }$ values lead to stronger convective mixing, resulting in higher surface metallicities and lower deep interior temperatures, while requiring reduced heavy-element masses and lower initial entropies to stabilize the dilute inner cores. Our Saturn models also broadly agree with the observed brunt frequency profile inferred from Cassini ring seismology, with stable layers arising from both the helium rain region and the dilute core. These findings support the presence of complex, compositionally stratified interiors in both gas giants.

13 pages, 6 figures, published in ApJ

References in corpus (29)

• Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core
• Heat transport in giant (exo)planets: a new perspective
• New models of Jupiter in the context of Juno and Galileo
• A new equation of state for dense hydrogen-helium mixtures
• AQUA: A Collection of H${}_2$O Equations of State for Planetary Models
• Saturn Ring Seismology: Evidence for Stable Stratification in the Deep Interior of Saturn
• Layered convection as the origin of Saturn's luminosity anomaly
• The Formation of Jupiter's Diluted Core by a Giant Impact
• A new equation of state for dense hydrogen-helium mixtures II: taking into account hydrogen-helium interactions
• The Challenge of Forming a Fuzzy Core in Jupiter
• An Exploration of Double Diffusive Convection in Jupiter as a Result of Hydrogen-Helium Phase Separation
• Evidence for a Dichotomy in the Interior Structures of Jupiter and Saturn from Helium Phase Separation
• Jupiter's interior from Juno: Equation-of-state uncertainties and dilute core extent
• Double-diffusive erosion of the core of Jupiter
• Bayesian Evolution Models for Jupiter with Helium Rain and Double-diffusive Convection
• Turbulent transport by diffusive stratified shear flows: from local to global models. Part I: Numerical simulations of a stratified plane Couette flow
• Convective boundary mixing in main-sequence stars: theory and empirical constraints
• Evolution of Jupiter and Saturn with helium rain
• Study of Jupiter's Interior: Comparison of 2, 3, 4, 5, and 6 Layer Models
• Schwarzschild and Ledoux are equivalent on evolutionary timescales
• Layer formation in a stably-stratified fluid cooled from above. Towards an analog for Jupiter and other gas giants
• Exoplanet Interior Retrievals: core masses and metallicities from atmospheric abundances
• Convective Mixing in Gas Giant Planets with Primordial Composition Gradients
• Rotation reduces convective mixing in Jupiter and other gas giants
• Evolution of Semi-convective Staircases in Rotating Flows: Consequences for Fuzzy Cores in Giant Planets
• Thermal Evolution and magnetic history of rocky planets
• Unraveling the origin of giant exoplanets: Observational implications of convective mixing
• 3D Simulations of Semiconvection in Spheres: Turbulent Mixing and Layer Formation
• On the origin of Jupiter's fuzzy core: constraints from N-body, impact and evolution simulations

Cited by in corpus (2)

• Further constraints on Jupiter's primordial structure
• How Internal Structure Shapes the Metallicity of Giant Exoplanets