Variability from Thermoresistive Instability in the Atmospheres of Hot Jupiters

Abstract

The atmosphere of a hot Jupiter may be subject to a thermoresistive instability, in which the increasing electrical conductivity with temperature leads to runaway ohmic heating. We introduce a simplified model of the local dynamics in the equatorial region of a hot Jupiter that incorporates the back reaction on the atmospheric flow as the increasing electrical conductivity leads to flux freezing, which in turn quenches the flow and therefore the ohmic heating. We demonstrate a new time-dependent solution that emerges for a temperature-dependent electrical conductivity (whereas a temperature-independent conductivity always evolves to a steady state). The periodic cycle consists of bursts of Alfvén oscillations separated by quiescent intervals, with the magnetic Reynolds number alternating between values smaller than and larger than unity, maintaining the oscillation. We investigate the regions of pressure and temperature in which the instability operates. For the typical equatorial accelerations seen in atmospheric models, we find instability at pressures ∼0.1–1 bar and temperatures ≈1300–1800 K for magnetic fields ∼10 G. Unlike previous studies based on a constant wind velocity, we find that the instability is stronger for weaker magnetic fields. Our results add support to the idea that variability should be a feature of magnetized hot Jupiter atmospheres, particularly at intermediate temperatures. The temperature dependence of the electrical conductivity is an important ingredient that should be included in MHD models of hot Jupiter atmospheric dynamics.