New hot-Jupiter magnetic field scaling laws

Hot Jupiters (HJs) are commonly thought to host the strongest dynamo-generated magnetic fields among exoplanets, potentially exceeding Jupiter’s by an order of magnitude. Yet, despite extensive radio and spectroscopic searches for star–planet interactions (SPI), no unambiguous detections have been made. Here, we present new magnetic field estimates for individual HJs together with general magnetic field scaling laws. Assuming their dynamos operate in the fast-rotating regime (Ro < 0.1), we combine one-dimensional evolutionary models with integral magnetic field scaling laws under two heating scenarios: deep and shallow energy deposition within the convective zone. Using interpolators built from the simulation data, we derive optimistic (deep heating) and pessimistic (shallow heating) magnetic field strengths, and construct scaling relations based on observables, i.e., planetary mass, radius, and incident stellar flux. The deep-heating scenario maximizes convective heat flux in the dynamo and predicts strong magnetic fields of up to ~100 G, whereas shallow heating suppresses convection and yields much weaker fields of order ~1 G. These results challenge the standard assumption that inflated HJs necessarily host exceptionally strong magnetic fields because of their large radii and vigorous interiors. Instead, many HJs may generate fields too weak to produce detectable coherent radio emission or strong SPI signatures, naturally explaining the persistent non-detections in radio surveys. Future facilities may distinguish between these interior-heating scenarios through improved magnetic field constraints.