The Mass-Radius Relation for 65 Exoplanets Smaller than 4 Earth Radii

We study the masses and radii of 65 exoplanets smaller than 4 Earth radii with orbital periods shorter than 100 days. We calculate the weighted mean densities of planets in bins of 0.5 Earth radii and identify a density maximum of 7.6 g/cc at 1.4 Earth radii. Planets with radii up to R = 1.5 Earth radii increase in density with increasing radius. Above 1.5 Earth radii, planet density rapidly decreases with increasing radius, indicating that these planets have a large fraction of volatiles by volume overlying a rocky core. Including the solar system terrestrial planets with the exoplanets below 1.5 Earth radii, we find \rho = 2.43 + 3.39 (R/R_E) g cm^-3 for R < 1.5 Earth radii, which is consistent with rocky compositions. For exoplanets between 1.5 and 4 Earth radii, we find M/M_E = 2.69 (R/R_E)^0.93. The RMS of planet masses to the fit between 1.5 and 4 Earth radii is 4.3 M_E with reduced \chi^2 = 6.2. The large scatter indicates a diversity in planet composition at a given radius. The compositional diversity can be due to planets of a given volume (as determined by their large H/He envelopes) containing rocky cores of different masses or compositions.