  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.
