Rossby number regime, convection suppression, and dynamo-generated magnetism in inflated hot Jupiters

Abstract

Hot Jupiters (HJs) are commonly thought to host the strongest dynamo-generated magnetic fields among exoplanets, up to one order of magnitude larger than Jupiter. Thus, they have often been regarded as the most promising exoplanets to display magnetic star-planet interaction signals and magnetically-driven coherent radio emission, which unfortunately remains elusive, despite many diversified observational campaigns. In this work, we investigate the evolution of the internal convection and dynamo properties of HJs via one-dimensional models. We explore the dependency on orbital distance, planetary and stellar masses, and types of heat injection. We employ one-dimensional evolutionary models to obtain internal convective structures. Specifically, we obtain the Rossby number $\mathrm{Ro}$ as a function of planetary depth and orbital period, after showing that tidal synchronization is likely valid for all HJs. When the heat is applied uniformly, the convective layers of almost all HJs remain in the fast rotator regime, $\mathrm{Ro} \lesssim 0.1$, except possibly the most massive planets with large orbital distances (but still tidally locked). We recover magnetic field strengths for inflated HJs by applying well-known scaling laws for fast rotators. When strong heat sources are applied mostly in the outer envelope and outside the dynamo region, as realistic Ohmic models predict, convection in the dynamo region often breaks down. Consequently, the heat flux and the derived surface magnetic fields can be greatly reduced to or below Jovian values, contrary to what is commonly assumed, thus negatively affecting estimates for coherent radio emission, and possibly explaining the failure in detecting it so far.