The mass-radius relation of intermediate-mass planets outlined by hydrodynamic escape and thermal evolution

Context. Exoplanets in the mass range between Earth and Saturn show a wide spread in radius, and thus in density, for a given mass. Aims. We aim to understand to which extent the observed radius spread is affected by the specific planetary parameters at formation and by planetary atmospheric evolution. Methods. We employed planetary evolution modeling to reproduce the mass-radius (MR) distribution of the 199 planets that are detected so far whose mass and radius were measured to the <= 45% and <= 15% level, respectively, and that are less massive than 108 M-circle plus. We simultaneously accounted for atmospheric escape, based on the results of hydrodynamic simulations, and thermal evolution, based on planetary structure evolution models. Because high-energy stellar radiation affects atmospheric evolution, we accounted for the entire range of possible stellar rotation evolution histories. To set the planetary parameters at formation, we used analytical approximations based on formation models. Finally, we built a grid of synthetic planets with parameters reflecting those of the observed distribution. Results. The predicted radius spread reproduces the observed MR distribution well, except for two distinct groups of outliers (approximate to 20% of the population). The first group consists of very close-in Saturn-mass planets with Jupiter-like radii for which our modeling underpredicts the radius, likely because it lacks additional (internal) heating similar to the heating that causes inflation in hot Jupiters. The second group consists of warm (similar to 400-700 K) sub-Neptunes, which should host massive primordial hydrogen-dominated atmospheres, but instead present high densities indicative of small gaseous envelopes (<1-2%). This suggests that their formation, internal structure, and evolution is different from that of atmospheric evolution through escape of hydrogen-dominated envelopes accreted onto rocky cores. The observed characteristics of low-mass planets (<= 10-15 M-circle plus) strongly depend on the impact of atmospheric escape, and thus of the evolution of the host star's activity level, while primordial parameters are less relevant. Instead, the parameters at formation play the dominant role for more massive planets in shaping the final MR distribution. In general, the intrinsic spread in the evolution of the activity of the host stars can explain just about a quarter of the observed radius spread.