A possible correlation between planetary radius and orbital period for small planets

We suggest the existence of a correlation between the planetary radius and orbital period for planets with radii smaller than 4 R⊕. Using the Kepler data, we find a correlation coefficient of 0.5120, and suggest that the correlation is not caused solely by survey incompleteness. While the correlation coefficient could change depending on the statistical analysis, the statistical significance of the correlation is robust. Further analysis shows that the correlation originates from two contributing factors. One seems to be a power-law dependence between the two quantities for intermediate periods (3-100 d), and the other is a dearth of planets with radii larger than 2 R⊕ in short periods. This correlation may provide important constraints for small-planet formation theories and for understanding the dynamical evolution of planetary systems.