Left panel: synthetic M − R relationship with analytical approximations for the mean radius . Blue dots: synthetic planets with 0.1  <  a/AU. Thick blue line: analytical fit. Thin blue line: running mean. Red dots: synthetic planets with 0.1  <  a/AU  ≤  1. Thick red line: analytical fit. Thin red line: running mean. Black lines: M − R relationship for β = 1/3 and 0.485, for solid planets with an Earth-like composition, and for planets with a composition as expected beyond the ice line. Right panel: power-law exponent β for the  relationship as function of mass.