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 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 find 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 ( N over bar p ) exhibits a decreasing trend (similar to 2 sigma significance) with age. It decreases from N over bar p similar to 3 for stars younger than 1 Gyr to N over bar p similar to 1.8 for stars of about 8 Gyr. (3) The number of planets per star (eta = F Kepx N over bar p ) also shows a decreasing trend (similar to 2 sigma-3 sigma significance). It decreases from eta similar to 1.6-1.7 for young stars to eta similar to 1.0 for old stars. (4) The mutual orbital inclination of the planets (sigma i,k ) increases from 1.degrees 2-0.5+1.4 to 3.degrees 5-2.3+8.1 as the stars age from 0.5 to 8 Gyr with a best fit of log sigma i,k=0.2+0.4xlogAge1Gyr . Interestingly, the solar system also fits such a trend. The fact that F Kep remains relatively constant at approximately similar to 50% across different ages suggests the robustness of planet formation throughout the history of the Galaxy. The age dependence of N over bar p and sigma i,k demonstrates that the planetary architecture is evolving, and planetary systems generally become dynamically hotter with fewer planets as they age.