Growth model interpretation of planet size distribution

The radii and orbital periods of 4,000+ confirmed/candidate exoplanets have been precisely measured by the Kepler mission. The radii show a bimodal distribution, with two peaks corresponding to smaller planets (likely rocky) and larger intermediate-size planets, respectively. While only the masses of the planets orbiting the brightest stars can be determined by ground-based spectroscopic observations, these observations allow calculation of their average densities placing constraints on the bulk compositions and internal structures. However, an important question about the composition of planets ranging from 2 to 4 Earth radii (R_⊕) still remains. They may either have a rocky core enveloped in a H₂-He gaseous envelope (gas dwarfs) or contain a significant amount of multicomponent, H₂O-dominated ices/fluids (water worlds). Planets in the mass range of 10-15 M_⊕, if half-ice and half-rock by mass, have radii of 2.5 R_⊕, which exactly match the second peak of the exoplanet radius bimodal distribution. Any planet in the 2- to 4-R_⊕ range requires a gas envelope of at most a few mass percentage points, regardless of the core composition. To resolve the ambiguity of internal compositions, we use a growth model and conduct Monte Carlo simulations to demonstrate that many intermediate-size planets are "water worlds."