Evolution of Semi-convective Staircases in Rotating Flows: Consequences for Fuzzy Cores in Giant Planets

Abstract

Recent observational constraints on the internal structure of Jupiter and Saturn suggest that these planets have ``fuzzy" cores, i.e., gradients of the concentration of heavy elements that might span a large fraction of the planet's radius. These cores could be composed of a semi-convective staircase, i.e., multiple convective layers separated by diffusive interfaces arising from double-diffusive instabilities. However, to date, no study has demonstrated how such staircases can avoid layer mergers and persist over evolutionary time scales. In fact, previous work has found that these mergers occur rapidly, leading to only a single convective layer. Using 3D simulations, we demonstrate that rotation prolongs the lifetime of a convective staircase by increasing the timescale for both layer merger and erosion of the interface between the final two layers. We present an analytic model for the erosion phase, predicting that rotation increases the erosion time by a factor of approximately ${\mathrm{Ro}}^{-1/2}$, where $\mathrm{Ro}$ is the Rossby number of the convective flows (the ratio of the rotation period to the convective turnover time). For Jovian conditions at early times after formation (when convection is vigorous enough to mix a large fraction of the planet), we find the erosion time to be roughly $10^9\mathrm{yrs}$ in the non-rotating case and $10^{11}\mathrm{yrs}$ in the rotating case. If these timescales are confirmed with a larger suite of numerical simulations, the existence of convective staircases within the deep interiors of giant planets is a strong possibility, and rotation could be an important factor in the preservation of their fuzzy cores.

Accepted for publication in ApJ Letters

References in corpus (28)

• Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods
• Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core
• A new vision on giant planet interiors: the impact of double diffusive convection
• Saturn Ring Seismology: Evidence for Stable Stratification in the Deep Interior of Saturn
• Layered convection as the origin of Saturn's luminosity anomaly
• A new model for mixing by double-diffusive convection (semi-convection): I. The conditions for layer formation
• The fuzziness of giant planets' cores
• The Formation of Jupiter's Diluted Core by a Giant Impact
• A new model for mixing by double-diffusive convection (semi-convection). II. The transport of heat and composition through layers
• The Challenge of Forming a Fuzzy Core in Jupiter
• Revelations on Jupiter's Formation, Evolution and Interior: Challenges from Juno Results
• Theory and simulations of rotating convection
• Convection and Mixing in Giant Planet Evolution
• Jupiter's interior from Juno: Equation-of-state uncertainties and dilute core extent
• Double-diffusive erosion of the core of Jupiter
• Heat transfer and flow regimes in quasi-static magnetoconvection with a vertical magnetic field
• Semiconvection: numerical simulations
• Semiconvection: theory
• The Primordial Entropy of Jupiter
• Main Sequence Evolution with Layered Semiconvection
• The effect of rotation on oscillatory double-diffusive convection (semiconvection)
• Layer formation in a stably-stratified fluid cooled from above. Towards an analog for Jupiter and other gas giants
• Rotation reduces convective mixing in Jupiter and other gas giants
• The Properties of G-modes in Layered Semi-Convection
• Penetration of a cooling convective layer into a stably-stratified composition gradient: entrainment at low Prandtl number
• Properties of semi-convection and convective overshooting for massive stars
• Layer formation in double-diffusive convection over resting and moving heated plates
• NeuralCMS: A deep learning approach to study Jupiter's interior

Cited by in corpus (11)

• 3D Simulations of Semiconvection in Spheres: Turbulent Mixing and Layer Formation
• Conditions for radiative zones in the molecular hydrogen envelope of Jupiter and Saturn: The role of alkali metals
• Setting the Stage for Uranian Seismology from Rings and Radial Velocities
• On the origin of Jupiter's fuzzy core: constraints from N-body, impact and evolution simulations
• Seven decades of exploring planetary interiors with rotating convection experiments
• The Evolution of Jupiter and Saturn as a function of the Parameter R${}_{\rho }$
• Further constraints on Jupiter's primordial structure
• The impact of rotation on the stochastic excitation of stellar acoustic modes in solar-like pulsators
• An Energy Perspective of Core Erosion in Gas Giant Planets
• 3D Simulations of Convective Entrainment in Gas Giants: Rotation and Decreasing Luminosity as Barriers to Mixing
• Planetary dynamos driven by semiconvection in stably stratified layers