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

TL;DR

This paper identifies a statistically significant correlation between planetary radius and orbital period for small planets using Kepler data, revealing potential insights into planet formation and system evolution.

Contribution

It uncovers a new correlation between radius and period for small planets and analyzes its origins, providing constraints for formation theories.

Findings

Correlation coefficient of 0.5120 between radius and period

Power-law dependence for intermediate periods (3-100 days)

Dearth of larger planets in short periods

Abstract

We suggest the existence of a correlation between the planetary radius and orbital period for planets with radii smaller than 4 R_Earth. 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 days), and the other is a dearth of planets with radii larger than 2 R_Earth in short periods. This correlation may provide important constraints for small-planet formation theories and for understanding the dynamical evolution of planetary systems.