Statistical Trends in the Obliquity Distribution of Exoplanet Systems

Abstract

Important clues to the formation and evolution of planetary systems can be inferred from the stellar obliquity ψ . We study the distribution of obliquities using the California- Kepler Survey and the TEPCat Catalog of Rossiter–McLaughlin (RM) measurements, from which we extract, respectively, 275 and 118 targets. We infer a “best fit” obliquity distribution in ψ with a single parameter κ . Large values of κ imply that ψ is distributed narrowly around zero, while small values imply approximate isotropy. Our findings are as follows. (1) The distribution of ψ in Kepler systems is narrower than found by previous studies and consistent with κ  ∼ 15 (mean and spread ψ  ∼ 10°). (2) The value of κ 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 ∼2.5 σ significance level). (3) The obliquities of Hot Jupiter (HJ) systems with RM measurements are consistent with κ  ∼ 2, which corresponds to a broader distribution than for the general Kepler population. (4) A separation of the RM sample into cooler ( T eff  ≲ 6250 K) and hotter ( T eff  ≳ 6250 K) HJ hosts results in two distinct distributions, κ cooler  ∼ 4 and κ hotter  ∼ 1 (4 σ 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 dependence on period could be due to primordial disk alignment rather than tidal realignment of stellar spin.