Combining Kepler and HARPS Exoplanet Occurrence Rates to Infer the Period-Mass-Radius Distribution of Super-Earths/Sub-Neptunes

The ongoing High Accuracy Radial velocity Planet Search (HARPS) has found that 30-50% of FGK stars in the solar neighborhood host planets with M_pl < M_Nep in orbits of P < 50 days. At first glance, this high overall occurrence rate seems at best to be marginally consistent with the planet frequency measured during Q0-Q2 of the Kepler Mission, whose 1235 detected planetary candidates imply that ∼ 15% of main sequence dwarfs harbor a short-period planet with R_pl < 4 R_⊕ . A rigorous comparison between the two surveys is difficult, however, as they observe different stellar populations, measure different planetary physical properties, and are subject to radically different sampling plans. In this article, we report the results of a Monte Carlo study which seeks to partially overcome this apparent discrepancy by identifying plausible planetary population distributions which can jointly conform to the results of the two surveys. We find that a population concurrently consisting of (1) dense silicate-iron planets and (2) low-density volatile and gas-dominated worlds provides a natural fit to the current data. In this scenario, the fraction of dense planets decreases with increasing mass, from f_rocky = 90% at M = 1 M_⊕ to f_rocky = 10% at M = M_Nep. Our best fit population has a total occurrence rate of 40% for 2 ≤ P ≤ 50 days and 1 ≤ M ≤ 17 M_⊕ , and is characterized by simple power-law indices of the form N(M)dM ∝ M^α dM and N(P)dP ∝ P^β dP with α = -1.0 and β = 0.0. Our model population therefore contains four free parameters and is readily testable with future observations. Furthermore, our model's insistence that at least two distinct types of planets must exist in the survey data indicates that multiple formation mechanisms are at work to produce the population of planets commonly referred to as ``super-Earths".