Spright: a probabilistic mass–density–radius relation for small planets

Abstract

ABSTRACT We present spright, a python package that implements a fast and lightweight mass–density–radius relation for small planets. The relation represents the joint planetary radius and bulk density probability distribution as a mean posterior predictive distribution of an analytical three-component mixture model. The analytical model, in turn, represents the probability for the planetary bulk density as three generalized Student’s t-distributions with radius-dependent weights and means based on theoretical composition models. The approach is based on Bayesian inference and aims to overcome the rigidity of simple parametric mass–radius relations and the danger of overfitting of non-parametric mass–radius relations. The package includes a set of pre-trained and ready-to-use relations based on two M-dwarf catalogues, one catalogue containing stars of spectral types F, G, and K (FGK stars), and two theoretical composition models for water-rich planets. The inference of new models is easy and fast, and the package includes a command line tool that allows for coding-free use of the relation, including the creation of publication-quality plots. Additionally, we study whether the current mass and radius observations of small exoplanets support the presence of a population of water-rich planets positioned between rocky planets and sub-Neptunes. The study is based on Bayesian model comparison and shows somewhat strong support against the existence of a water-world population around M dwarfs. However, the results of the study depend on the chosen theoretical water-world density model. A more conclusive result requires a larger sample of precisely characterized planets and community consensus on a realistic water-world interior structure and atmospheric composition model.