The effect of population-wide mass-to-radius relationships on the interpretation of Kepler and harps super-earth occurrence rates

The ongoing High Accuracy Radial velocity Planet Search (HARPS) has found that 30%-50% of G and K dwarfs 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 naively 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, given the HARPS occurrence rate, either a population subject to a mass-density relationship extrapolated from our solar system or a population concurrently consisting of dense silicate-iron planets and low-density gaseous worlds can produce total numbers of planet candidates consistent with those actually detected by Kepler. However, these two mass-to-radius relationships (M-Rs) resolve the apparent occurrence rate discrepancy with different mass and period distributions, enabling future observations to rule out M-Rs that do not fully describe the observed planet population in a global sense. Extracting information of this nature from the transit-radial-velocity comparison has significant implications for the interpretation of planet occurrence rates: if a multi-valued M-R, which allows planets of similar mass to have significantly different radii, emerges from observational data, then multiple formation mechanisms are likely at work. In this event, HARPS may be detecting a large population of dense low-mass planets, while Kepler detects a large population of gaseous sub-Neptunes.