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

We study the masses and radii of 65 exoplanets smaller than 4 R _⊕ with orbital periods shorter than 100 days. We calculate the weighted mean densities of planets in bins of 0.5 R _⊕ and identify a density maximum of 7.6 g cm^-3 at 1.4 R _⊕. On average, planets with radii up to R _P = 1.5 R _⊕ increase in density with increasing radius. Above 1.5 R _⊕, the average 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 R _⊕, we find ρ_P = 2.43 + 3.39(R _P/R _⊕) g cm^-3 for R _P < 1.5 R _⊕, which is consistent with rocky compositions. For 1.5 <= R _P/R _⊕ < 4, we find M _P/M _⊕ = 2.69(R _P/R _⊕)^0.93. The rms of planet masses to the fit between 1.5 and 4 R _⊕ is 4.3 M _⊕ with reduced χ² = 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.