The Occurrence of Earth-Like Planets Around Other Stars

The quantity $\eta_\oplus$, the number density of planets per star per logarithmic planetary radius per logarithmic orbital period at one Earth radius and one year period, describes the occurrence of Earth-like extrasolar planets. Here we present a measurement of $\eta_\oplus$ from a parameterised forward model of the (correlated) period-radius distribution and the observational selection function in the most recent (Q17) data release from the Kepler satellite. We find $\eta_\oplus = 3.9_{-1.6}^{+2.2}\%$ (90% CL). We conclude that each star hosts $3.83_{-0.62}^{+0.76}$ planets with $P \lesssim 3 \mathrm{yr}$ and $R \gtrsim 0.2 R_\oplus$. Our empirical model for false-positive contamination is consistent with the dominant source being background eclipsing binary stars. The distribution of planets we infer is consistent with a highly-stochastic planet formation process producing many correlated, fractional changes in planet sizes and orbits.