Hot Jupiter dynamos operate in the low Rossby number regime, if they exist

In this work, we model the interior evolutionary tracks of inflated hot Jupiters using MESA, a one-dimensional radial code. Guided by observationally constrained flux-heating efficiency relations, we inject heat into the internal layers of the planet to reproduce the observed radii. Our models assume tidal locking and blackbody radiation from main-sequence stars, and we explore dependencies on orbital distance, planetary and stellar mass, and the type of heat injection.

For most of our models—both inflated and non-inflated—the planetary structure remains broadly similar. Planets typically exhibit a shallow stratified outer layer, which contains the irradiation zone, followed by a deep convective interior where pressure is sufficient for hydrogen metallization and possible dynamo action. Whether heat is injected uniformly, centrally, or throughout the convective region, the structural differences are minimal.

We investigate the internal convective structure by analyzing the Rossby number as a function of depth. Most models yield $\mathrm{Ro}<.1$, indicating fast-rotating convection regime. Only the most massive, distantly orbiting (yet still tidally locked) planets exceed $\mathrm{Ro}>.1$ over significant interior regions, potentially altering the dynamo regime. Thus, massive HJs with orbital periods beyond 20–25 days may host low-Rossby number dynamos that generate weaker, more multipolar magnetic fields despite similar convective power. Inflation primarily affects the outer layers and consistently increases $\mathbf{Ro}$. While this effect is negligible for planets above 8~$\mathrm{M_J}$—especially those already exceeding $\mathrm{Ro}>.1$, lower-mass planets experience have roughly one order of magnitude increase in $Ro$, which could have observable consequences even if they remain within the low-$\mathrm{Ro}$ regime.

We also examine heat injection localized outside the dynamo region. In such cases, internal heat transport is significantly reduced, leading to positive entropy gradients that suppress convection. These scenarios may reflect Ohmic heating or delayed cooling due to high opacity.

We apply the integral form of the magnetic field strength scaling laws from \cite{Christensenetal2009}, suited for fast rotators. When heat is deposited centrally or uniformly, we recover magnetic field strengths around 150~G for the most inflated planets, which is an order of magnitude higher than Jupiter's. In contrast, external heating substantially reduces convective power and yields weaker magnetic fields. This mechanism is consistent with the lack of a dynamo on Venus, which could also be influenced by the low-$\mathbf{Ro}$ regime.

Magnetic fields remain one of the least understood features of exoplanetary systems. While radio emission offers the most direct probe of exoplanetary magnetism, it has yet to be detected. HJs are generally thought to possess strong dynamo-generated fields capable of sustaining star–planet interaction (SPI) radio signals. Such emissions would be compatible with low-Rossby regime field strengths for all but the most massive and distant (20 d $< d <$ 30 d) HJs. Additionally, the absence of observed radio signals could be explained by our externally heated models, where convection—and hence dynamo activity—is significantly reduced.