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 $M_p$, $R_p$, $P_{\mathrm{o}\mathrm{r}\mathrm{b}}$, and host-star $T_{\mathrm{e}\mathrm{f}\mathrm{f}}$ 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 $P_{\mathrm{o}\mathrm{r}\mathrm{b}}$ and $T_{\mathrm{e}\mathrm{f}\mathrm{f}}$, but not to $M_p$. Since incident flux increases with $T_{\mathrm{e}\mathrm{f}\mathrm{f}}$ and decreases with $P_{\mathrm{o}\mathrm{r}\mathrm{b}}$ 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.