Secular orbital evolution of planetary systems and the dearth of close-in planets around fast rotators

TL;DR

This paper explains the scarcity of close-in planets around fast-rotating stars by modeling secular perturbations in multi-planet systems, showing that high eccentricity and tidal circularization lead to close-in planets over time.

Contribution

It introduces a secular evolution model linking stellar rotation, system age, and the formation of close-in planets, aligning with observed period distributions.

Findings

High eccentricity excitation increases with system age.

Tidal circularization occurs within 50 million years for high-eccentricity planets.

Model matches observed distributions of stellar and orbital periods.

Abstract

Recent analyses of Kepler space telescope data reveal that transiting planets with orbital periods shorter than about 2-3 days are generally observed around late-type stars with rotation periods longer than about 5-10 days. We investigate different explanations for this phenomenon and favor an interpretation based on secular perturbations in multi-planet systems on non-resonant orbits. In those systems, the orbital eccentricity of the innermost planet can reach values close to unity through a process of chaotic diffusion of its orbital elements in the phase space. When the eccentricity of the innermost orbit becomes so high that the periastron gets closer than about 0.05 AU, tides shrink and circularize the orbit producing a close-in planet on a timescale shorter than about 50 Myr. The probability of high eccentricity excitation and subsequent circularization is estimated and is found to increase with the age of the system. Thus, we are able to explain the observed statistical correlation between stellar rotation and minimum orbital period of the innermost planet by using the stellar rotation period as a proxy of its age through gyrochronology. Moreover, our model is consistent with the entire observed distributions of the rotation and orbital periods for orbital periods between 3 and 15 days.