Statistical Trends in the Obliquity Distribution of Exoplanet Systems

Important clues on the formation and evolution of planetary systems can be inferred from the stellar obliquity $\psi$. We study the distribution of obliquities using the California-Kepler Survey and the TEPCat Catalog of Rossiter-MacLaughlin (RM) measurements, from which we extract, respectively, 275 and 118 targets. We infer a "best fit" obliquity distribution in $\psi$ with a single parameter $\kappa$. Large values of $\kappa$ imply that $\psi$ is distributed narrowly around zero, while small values imply approximate isotropy. Our findings are: (1) The distribution of $\psi$ in Kepler systems is narrower than found by previous studies and consistent with $\kappa\sim15$ (mean $\langle\psi\rangle\sim19^\circ$ and spread $\psi\sim10^\circ$). (2) The value of $\kappa$ in Kepler systems does not depend, at a statistically significant level, on planet multiplicity, stellar multiplicity or stellar age; on the other hand, metal-rich hosts, small planet hosts and long-period planet hosts tend to be more oblique than the general sample (at a $\sim$2.5-$\sigma$ significance level). (3) Hot Jupiter (HJ) systems with RM measurements are consistent with $\kappa\sim2$, more broadly distributed than the general Kepler population. (4) A separation of the RM sample into cooler ($T_{\rm eff}\lesssim$6250 K) and hotter ($T_{\rm eff}\gtrsim$6250 K) HJ hosts results in two distinct distributions, $\kappa_{\rm cooler}\sim4$ and $\kappa_{\rm hotter}\sim1$ (4-$\sigma$ significance), both more oblique than the Kepler sample. We hypothesize that the total mass in planets may be behind the increasing obliquity with metallicity and planet radius, and that the period dependence could be due to primordial disk alignment rather than realignment of stellar spin.