Objects in Kepler's Mirror May be Larger Than They Appear: Bias and Selection Effects in Transiting Planet Surveys

Statistical analyses of large surveys for transiting planets such as the Kepler mission must account for systematic errors and biases. Transit detection depends not only on the planet's radius and orbital period, but also on host star properties. Thus, a sample of stars with transiting planets may not accurately represent the target population. Moreover, targets are selected using criteria such as a limiting apparent magnitude. These selection effects, combined with uncertainties in stellar radius, lead to biases in the properties of transiting planets and their host stars. We quantify possible biases in the Kepler survey. First, Eddington bias produced by a steep planet radius distribution and uncertainties in stellar radius results in a 15%-20% overestimate of planet occurrence. Second, the magnitude limit of the Kepler target catalog induces Malmquist bias toward large, more luminous stars and underestimation of the radii of about one-third of candidate planets, especially those larger than Neptune. Third, because metal-poor stars are smaller, stars with detected planets will be very slightly (<0.02 dex) more metal-poor than the target average. Fourth, uncertainties in stellar radii produce correlated errors in planet radius and stellar irradiation. A previous finding, that highly irradiated giants are more likely to have "inflated" radii, remains significant, even accounting for this effect. In contrast, transit depth is negatively correlated with stellar metallicity even in the absence of any intrinsic correlation, and a previous claim of a negative correlation between giant planet transit depth and stellar metallicity is probably an artifact.