Shallowness of circulation in hot Jupiters -- Advancing the Ohmic dissipation model

Abstract

The inflated radii of giant short-period extrasolar planets collectively indicate that the interiors of hot Jupiters are heated by some anomalous energy dissipation mechanism. Although a variety of physical processes have been proposed to explain this heating, recent statistical evidence points to the confirmation of explicit predictions of the Ohmic dissipation theory, elevating this mechanism as the most promising candidate for resolving the radius inflation problem. In this work, we present an analytic model for the dissipation rate and derive a simple scaling law that links the magnitude of energy dissipation to the thickness of the atmospheric weather layer. From this relation, we find that the penetration depth influences the Ohmic dissipation rate by an order of magnitude. We further investigate the weather layer depth of hot Jupiters from the extent of their inflation and show that, depending on the magnetic field strength, hot Jupiter radii can be maintained even if the circulation layer is relatively shallow. Additionally, we explore the evolution of zonal wind velocities with equilibrium temperature by matching our analytic model to statistically expected dissipation rates. From this analysis, we deduce that the wind speed scales approximately as $1/\sqrt{T_{\mathrm{eq}}-T_0}$, where $T_0$ is a constant that equals $T_0\sim 1000\mathrm{K}-1800\mathrm{K}$ depending on planet-specific parameters (radius, mass, etc.). This work outlines inter-related constraints on the atmospheric flow and the magnetic field of hot Jupiters and provides a foundation for future work on the Ohmic heating mechanism.

published in A&A, 5 pages, including 5 figures, plus 2 pages appendix, including 2 figures; v2 follows the A&A language guidelines

References in corpus (23)

• On the radiative equilibrium of irradiated planetary atmospheres
• Accurate, Empirical Radii and Masses of Planets and their Host Stars with Gaia Parallaxes
• Can TiO Explain Thermal Inversions in the Upper Atmospheres of Irradiated Giant Planets?
• Inflating Hot Jupiters With Ohmic Dissipation
• Mass-Metallicity Trends in Transiting Exoplanets from Atmospheric Abundances of H${}_2$O, Na, and K
• Constraints on Deep-seated Zonal Winds Inside Jupiter and Saturn
• How drifting and evaporating pebbles shape giant planets I: Heavy element content and atmospheric C/O
• The water abundance in Jupiter's equatorial zone
• Magnetic field strengths of hot Jupiters from signals of star-planet interactions
• Magnetic Effects in Hot Jupiter Atmospheres
• A new equation of state for dense hydrogen-helium mixtures II: taking into account hydrogen-helium interactions
• Seeing double with K2: Testing re-inflation with two remarkably similar planets around red giant branch stars
• Estimating the magnetic field strength in hot Jupiters
• Exploring the Effects of Active Magnetic Drag in a GCM of the Ultra-Hot Jupiter WASP-76b
• Evidence of Three Mechanisms Explaining the Radius Anomaly of Hot Jupiters
• HAT-P-65b and HAT-P-66b: Two Transiting Inflated Hot Jupiters and Observational Evidence for the Re-Inflation of Close-In Giant Planets
• Into the Storm: Diving into the winds of the ultra hot Jupiter WASP-76 b with HARPS and ESPRESSO
• Shallow-water Magnetohydrodynamics for Westward Hotspots on Hot Jupiters
• Slow Cooling and Fast Reinflation for Hot Jupiters
• Theoretical vs. observational uncertainties: composition of giant exoplanets
• Time-resolved rotational velocities in the upper atmosphere of WASP-33 b
• Hot Jupiter Atmospheric Flows at High Resolution
• Indentation of solid membranes on rigid substrates with Van-der-Waals attraction

Cited by in corpus (8)

• The mass-radius relation of intermediate-mass planets outlined by hydrodynamic escape and thermal evolution
• No evidence for radius inflation in hot Jupiters from vertical advection of heat
• Emergent Spectral Fluxes of Hot Jupiters: an Abrupt Rise in Day Side Brightness Temperature Under Strong Irradiation
• Follow-up LOFAR observations of the $\tau$ Boötis exoplanetary system
• In-situ enrichment in heavy elements of hot Jupiters
• Evidence of Radius Inflation in Radiative GCM Models of WASP-76b due to the Advection of Potential Temperature
• Inflated hot Jupiters: Inferring average atmospheric velocity via Ohmic models coupled with internal dynamo evolution
• Ohmic heating in the upper atmosphere of hot exoplanets The influence of a time-varying magnetic field