The Kepler telescope has discovered over 4000 planets (candidates) by searching ∼200,000 stars over a wide range of distance (order of kpc) in our Galaxy. Characterizing the kinematic properties (e.g., Galactic component membership and kinematic age) of these Kepler targets (including the planet candidate hosts) is the first step toward studying Kepler planets in the Galactic context, which will reveal fresh insights into planet formation and evolution. In this paper, the second part of the Planets Across the Space and Time (PAST) series, by combining the data from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) and Gaia and then applying the revised kinematic methods from PAST I, we present a catalog of kinematic properties (i.e., Galactic positions, velocities, and the relative membership probabilities among the thin disk, thick disk, Hercules stream, and the halo) as well as other basic stellar parameters for 35,835 Kepler stars. Further analyses of the LAMOST–Gaia–Kepler catalog demonstrate that our derived kinematic age reveals the expected stellar activity-age trend. Furthermore, we find that the fraction of thin (thick) disk stars increases (decreases) with the transiting planet multiplicity (N p = 0, 1, 2 and 3+) and the kinematic age decreases with N p, which could be a consequence of the dynamical evolution of planetary architecture with age. The LAMOST–Gaia–Kepler catalog will be useful for future studies on the correlations between the exoplanet distributions and the stellar Galactic environments as well as ages.

Over 4000 exoplanets have been identified and thousands of candidates are to be confirmed. The relations between the characteristics of these planetary systems and the kinematics, Galactic components, and ages of their host stars have yet to be well explored. To address these questions, we conduct a research project, dubbed Planets Across Space and Time (PAST). To do this, one of the key steps is to accurately characterize the planet host stars. In this paper, Paper I of the PAST series, we revisit the kinematic method for classification of Galactic components and extend the applicable range of velocity ellipsoid from ∼100 pc to ∼1500 pc from the Sun in order to cover most known planet hosts. Furthermore, we revisit the age–velocity dispersion relation (AVR), which allows us to derive kinematic ages with a typical uncertainty of 10–20% for an ensemble of stars. Applying the above revised methods, we present a catalog of kinematic properties (i.e., Galactic positions, velocities, and the relative membership probabilities among the thin disk, thick disk, Hercules stream, and the halo) as well as other basic stellar parameters for 2174 host stars of 2872 planets by combining data from Gaia, LAMOST, APOGEE, RAVE, and the NASA exoplanet archive. The revised kinematic method and AVR, as well as the stellar catalog of kinematic properties and ages, lay the foundation for future studies of exoplanets in space and time in the Galactic context.

The radius valley, a dip in the radius distribution of exoplanets at ∼1.9 R ⊕, separates compact rocky super-Earths and sub-Neptunes with lower density. Various hypotheses have been put forward to explain the radius valley. Characterizing the radius valley morphology and its correlation to stellar properties will provide crucial observation constraints on its origin mechanism and deepen the understanding of planet formation and evolution. In this paper, the third part of the Planets Across Space and Time series, using the LAMOST-Gaia-Kepler catalog, we perform a systematical investigation into how the radius valley morphology varies in the Galactic context, i.e., thin/thick galactic disks, stellar age, and metallicity abundance ([Fe/H] and [α/Fe]). We find the following: (1) The valley becomes more prominent with the increase of both age and [Fe/H]. (2) The number ratio of super-Earths to sub-Neptunes monotonically increases with age but decreases with [Fe/H] and [α/Fe]. (3) The average radius of planets above the valley (2.1–6 R ⊕) decreases with age but increases with [Fe/H]. (4) In contrast, the average radius of planets below the valley (R < 1.7 R ⊕) is broadly independent of age and metallicity. Our results demonstrate that the valley morphology, as well as the whole planetary radius distribution, evolves on a long timescale of gigayears, and metallicities (not only Fe but also other metal elements, e.g., Mg, Si, Ca, Ti) play important roles in planet formation and in the long-term planetary evolution.