On the Nature of Small Planets around the Coolest Kepler Stars

Abstract

We constrain the densities of Earth- to Neptune-size planets around very cool (Te =3660-4660K) Kepler stars by comparing 1202 Keck/HIRES radial velocity measurements of 150 nearby stars to a model based on Kepler candidate planet radii and a power-law mass-radius relation. Our analysis is based on the presumption that the planet populations around the two sets of stars are the same. The model can reproduce the observed distribution of radial velocity variation over a range of parameter values, but, for the expected level of Doppler systematic error, the highest Kolmogorov-Smirnov probabilities occur for a power-law index alpha ~ 4, indicating that rocky-metal planets dominate the planet population in this size range. A single population of gas-rich, low-density planets with alpha = 2 is ruled out unless our Doppler errors are >= 5m/s, i.e., much larger than expected based on observations and stellar chromospheric emission. If small planets are a mix of gamma rocky planets (alpha = 3.85) and 1-gamma gas-rich planets (alpha = 2), then gamma > 0.5 unless Doppler errors are >=4 m/s. Our comparison also suggests that Kepler's detection efficiency relative to ideal calculations is less than unity. One possible source of incompleteness is target stars that are misclassified subgiants or giants, for which the transits of small planets would be impossible to detect. Our results are robust to systematic effects, and plausible errors in the estimated radii of Kepler stars have only moderate impact.