Planet Occurrence Rate Correlated to Stellar Dynamical History: Evidence from Kepler Stars

The dynamical history of stars influences the formation and evolution of planets significantly. To explore the influence of dynamical history on the planet formation and evolution from observations, we assume that it's probable that stars with higher relative velocities experienced significant dynamical events. Utilizing the accurate Gaia-Kepler Stellar Properties Catalog, we select single main-sequence stars and divide these stars into three groups according to their relative velocities, i.e. High-V, Median-V, and Normal-V stars. After considering the known biases from Kepler data and adopting prior and posterior correction to minimize the influence of stellar properties on planet occurrence rate, we find that High-V stars have a lower occurrence rate of super-Earths and sub-Neptunes (1--4 R$_{\rm \oplus}$, P<100 days) and higher occurrence rate of sub-Earth (0.5--1 R$_{\rm \oplus}$, P<2 days) than Normal-V stars. Additionally, we discuss two scenarios to explain the results: "High-V stars with initially lower disk fraction", which works before gas disk dissipation, and "High-V stars with extreme dynamical evolution", which works after gas disk dissipation or the formation of planetary systems. After investigating the multiplicity and eccentricity, we find that High-V planet hosts prefer a higher fraction of multi-planets systems and lower average eccentricity, which is consistent with the eccentricity-multiplicity dichotomy of Kepler planetary systems. Therefore, it supports the first scenario. In the future, with data release from Gaia, TESS, and PLATO, more planets can be used to test our statistical results and check different scenarios.