On the patterns observed in Kepler multi-planet systems

Recent studies claimed that planets around the same star have similar sizes and masses and regular spacings, and that planet pairs usually show ordered sizes such that the outer planet is usually the larger one. Here I show that these patterns can be largely explained by detection biases. The \emph{Kepler} planet detections are set by the transit signal-to-noise ratio (S/N). For different stellar properties and orbital period values, the same S/N corresponds to different planetary sizes. This variation in the detection threshold naturally leads to apparent correlations in planet sizes and the observed size ordering. The apparently correlated spacings, measured in period ratios, between adjacent planet pairs in systems with at least three detected planets are partially due to the arbitrary upper limit that the earlier study imposed on the period ratio, and partially due to the varying stability threshold for different planets. After these detection biases are taken into account, we do not find strong evidence for the so-called "intra-system uniformity" or the size ordering effect. Instead, the physical properties of \emph{Kepler} planets are largely independent of the properties of their siblings and the parent star. It is likely that the dynamical evolution has erased the memory of \emph{Kepler} planets about their initial formation conditions. In other words, it will be difficult to infer the initial conditions from the observed properties and the architecture of \emph{Kepler} planets.