Evaluating the Evidence for Water World Populations Using Mixture Models

Water worlds have been hypothesized as an alternative to photoevaporation in order to explain the gap in the radius distribution of Kepler exoplanets. We explore water worlds within the framework of a joint mass–radius–period distribution of planets fit to a sample of transiting Kepler exoplanets, a subset of which have radial velocity mass measurements. We employ hierarchical Bayesian modeling to create a range of ten mixture models that include multiple compositional subpopulations of exoplanets. We model these subpopulations—including planets with gaseous envelopes, evaporated rocky cores, evaporated icy cores, intrinsically rocky planets, and intrinsically icy planets—in different combinations in order to assess which combinations are most favored by the data. Using cross-validation, we evaluate the support for models that include planets with icy compositions compared to the support for models that do not, finding broad support for both. We find significant population-level degeneracies between subpopulations of water worlds and planets with primordial envelopes. Among models that include one or more icy-core subpopulations, we find a wide range for the fraction of planets with icy compositions, with a rough upper limit of 50%. Improved data sets or alternative modeling approaches may be able to better distinguish between these subpopulations of planets.