We constrain the densities of Earth- to Neptune-size planets around very cool ( T _ { e } =3660-4660 K ) 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 \approx 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 \geq 5 m s ^ { -1 } , 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 \geq 4 m s ^ { -1 } .
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 .