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

We study the masses and radii of 65 exoplanets smaller than 4R⊕ 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−3at 1.4 R⊕. On average, planets with radii up to RP = 1.5R⊕ 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 ρP = 2.43 + 3.39 (RP/R⊕) g cm −3 for RP < 1.5R⊕, which is consistent with rocky compositions. For 1.5 ≤ RP/R⊕ < 4, we find MP/M⊕ = 2.69 (RP/R⊕). The RMS of planet masses to the fit between 1.5 and 4 R⊕ is 4.3 M⊕ with reduced χ 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.