Planets Across Space and Time (PAST) IV: The Occurrence and Architecture of Kepler Planetary Systems as a Function of Kinematic Age Revealed by the LAMOST-Gaia-Kepler Sample

One of the fundamental questions in astronomy is how planetary systems form and evolve. Measuring the planetary occurrence and architecture as a function of time directly addresses this question. In the fourth paper of the Planets Across Space and Time (PAST) series, we investigate the occurrence and architecture of Kepler planetary systems as a function of kinematic age by using the LAMOST-Gaia-Kepler sample. To isolate the age effect, other stellar properties (e.g., metallicity) have been controlled. We found the following results. (1) The fraction of stars with Kepler-like planets (F_Kep) is about 50% for all stars; no significant trend is found between F_Kep and age. (2) The average planet multiplicity (Np) exhibits a decreasing trend ( ∼2σ significance) with age, which decreases from N_p ~ 2.6–2.7 for stars younger than 1 Gyr to N_p ∼ 1.8–2.0 for stars older than 8 Gyrs. (3) The number of planets per star (η=F_Kep ×N_p) shows a more pronounced decreasing trend (∼3σ significance), which decreases from η ∼ 1.4–1.5 for young stars to η ∼ 0.9–1.0 for old stars. (4) The median mutual orbital inclination of the planets (σ_i,k) increases from 2.2 to 3.9 as stars aging, and both the Solar System and the Kepler planetary systems fit such a trend. The nearly independence of F_Kep ∼ 50% on age implies that planet formation is robust and stable across the Galaxy history. The age dependence of N_p and σ_i,k demonstrates that planetary architecture is evolving, and planetary systems generally become dynamically hotter with fewer planets as they age.