Ohmic Dissipation in the Interiors of Hot Jupiters

TL;DR

This paper models ohmic heating in hot Jupiters, showing it can slow contraction only under specific conditions and is insufficient to explain observed inflated radii of some planets.

Contribution

It introduces a decoupled model of interior and wind zone effects, providing a detailed analysis of ohmic heating's impact on planetary evolution.

Findings

Ohmic heating affects planetary contraction only after a critical entropy is reached.

The model suggests ohmic heating cannot fully explain the inflated radii of many hot Jupiters.

Magnetic drag prescriptions limit the effectiveness of ohmic heating in inflating planets.

Abstract

We present models of ohmic heating in the interiors of hot jupiters in which we decouple the interior and the wind zone by replacing the wind zone with a boundary temperature Tiso and magnetic field Bphi0. Ohmic heating influences the contraction of gas giants in two ways: by direct heating within the convection zone, and by heating outside the convection zone which increases the effective insulation of the interior. We calculate these effects, and show that internal ohmic heating is only able to slow the contraction rate of a cooling gas giant once the planet reaches a critical value of internal entropy. We determine the age of the gas giant when ohmic heating becomes important as a function of mass, Tiso and induced Bphi0. With this survey of parameter space complete, we then adopt the wind zone scalings of Menou (2012) and calculate the expected evolution of gas giants with different levels of irradiation. We find that,with this prescription of magnetic drag, it is difficult to inflate massive planets or those with strong irradiation using ohmic heating, meaning that we are unable to account for many of the observed hot jupiter radii. This is in contrast to previous evolutionary models that assumed that a constant fraction of the irradiation is transformed into ohmic power.