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

Recent analyses of Kepler space telescope data reveal that transiting planets with orbital periods shorter than 2-3 d are generally observed around late-type stars with rotation periods longer than similar to 5-10 d. We investigate different explanations for this phenomenon and favour an interpretation based on secular perturbations in multiplanet 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 similar to 0.05 au, tides shrink and circularize the orbit producing a close-in planet on a time-scale less than or similar to 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 P-orb for 3 less than or similar to P-orb less than or similar to 15 d.