On the relationship between the planetary radius and the equilibrium temperature for transiting exoplanets

Scaling laws have always played an important role in astronomy. They can give a general qualitative overview of common behaviors of many astrophysical objects, helping to understand the occurring physical processes. In the context of exoplanets, we study the possible correlation between (i) the planetary radius and the equilibrium temperature, Rp - Teq, and (ii) the planetary radius and the parent-star metallicity, Rp - [Fe/H]. We considered a sample of transiting planets, for which their mass radius and equilibrium temperature are accurately determined. While we do not see any notable evidence of a correlation between Rp and [Fe/H], the existence of a relationship between Rp and Teq is almost clear. We sub-divided our sample in different groups, based on their mass, and performed a least-squares regression of Rp on Teq for each sub-sample of planets. We found that the Rp - Teq relation results very tight for two groups of intermediate-massive gas planets (i.e. for Mp in the range between 0.5-1.0MJup and 1.0-1.5MJup) and that the slope of the best-fitting line gradually increases from the group of very massive to those of less massive planets, up to reverse in the Neptunian-Super-Earth regime, which has a negative correlation.