Planets Across Space and Time (PAST). III. Morphology of the Planetary
  Radius Valley as a Function of Stellar Age and Metallicity in the Galactic
  Context Revealed by the LAMOST-Gaia-Kepler Sample
  The radius valley, a dip in the radius distribution of exoplanets at ~1.9
Earth radii 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 the Space and Time (PAST) 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
[alpha/Fe]). We find that (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
[alpha/Fe]. (3) The average radius of planets above the valley (2.1-6 Earth
radii) decreases with age but increases with [Fe/H]. (4) In contrast, the
average radius of planets below the valley (R < 1.7 Earth radii) is broadly
independent on age and metallicity. Our results demonstrate that the valley
morphology as well as the whole planetary radius distribution evolves on a long
timescale of giga-years, 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.
