Relationship between the threshold mass and the threshold radius. The latter is defined by the radius that the planet with M_thrs would have at 10 Gyr without ever experiencing mass loss ( denoted by R_thrs). The squares, which are connected with a solid line, are M_thrs and R_thrs for 0.1 AU and seven different initial water mass fractions X_wt,0 = 100%, 75%, 50%, 25%, 10%, 5%, 1%, and 0.5%. The dashed and dotted lines represent mass-radius relationships, respectively, for rocky planets and pure-water planets at 0.1 AU. and represent the minimum values of M_thrs and R_thrs, respectively.