Causes of Hot Jupiter Inflation from Causal Discovery
Hot Jupiters often have radii larger than predicted by standard cooling--contraction models, but it remains unclear which process supplies or preserves the extra internal heat. We analyze 328 short-period giant planets with measured $M_p$, $R_p$, $P_{\rm orb}$, and host-star $T_{\rm eff}$ using causal discovery, a statistical framework that asks which observed properties remain directly connected to planet radius after the others are accounted for. As a check, the same pipeline recovers the expected mass--radius connection for a super-Earth control sample. For hot Jupiters, the preferred graph links $R_p$ directly to $P_{\rm orb}$ and $T_{\rm eff}$, but not to $M_p$. Since incident flux increases with $T_{\rm eff}$ and decreases with $P_{\rm orb}$ at fixed stellar properties, this paired dependence is naturally interpreted as a population-level signature of irradiation-regulated inflation. Comparing the graph with analytic radius-excess scalings suggests a comparatively important role for Gold--Soter thermal tides, with kinetic/mechanical heating and ohmic dissipation potentially contributing alongside them. Purely period-controlled gravitational tides are disfavored as the sole explanation because they lack a leading dependence on stellar temperature. Distinguishing thermal tides, kinetic/mechanical heating, ohmic dissipation, and mixed scenarios will require radius-excess measurements that control for incident flux, age, composition, stellar properties, and selection effects. More broadly, this work shows how causal discovery can turn population-level exoplanet data into physically interpretable tests of hot-Jupiter inflation. Causal discovery complements parametric Bayesian population models by testing which observables retain direct conditional dependence on $R_p$ without imposing a specific radius relation, although the modest sample size limits the scope of the inferred graph.