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

Abstract

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