3D Parameter Maps of Red Clump Stars in the Milky Way -- Absolute
  Magnitudes and Intrinsic Colors
  Red clump stars (RCs) are useful tracers of distances, extinction, chemical
abundances, and Galactic structures and kinematics. Accurate estimation of the
RC parameters -- absolute magnitude and intrinsic color -- is the basis for
obtaining high-precision RC distances. By combining astrometric data from Gaia,
spectroscopic data from APOGEE and LAMOST, and multi-band photometric data from
Gaia, APASS, Pan-STARRS1, 2MASS, and WISE surveys, we use the Gaussian process
regression to train machine learners to derive the multi-band absolute
magnitudes $M_\lambda$ and intrinsic colors $(\lambda_1-\lambda_2)_0$ for each
spectral RC. The dependence of $M_\lambda$ on metallicity decreases from
optical to infrared bands, while the dependence of $M_\lambda$ on age is
relatively similar in each band. $(\lambda_1-\lambda_2)_0$ are more affected by
metallicity than age. The RC parameters are not suitable to be represented by
simple constants but are related to the Galactic stellar population structure.
By analyzing the variation of $M_\lambda$ and $(\lambda_1-\lambda_2)_0$ in the
spatial distribution, we construct $(R, z)$ dependent maps of mean absolute
magnitudes and mean intrinsic colors of the Galactic RCs. Through external and
internal validation, we find that using three-dimensional (3D) parameter maps
to determine RC parameters avoids systematic bias and reduces dispersion by
about 20% compared to using constant parameters. Based on Gaia's EDR3 parallax,
our 3D parameter maps, and extinction-distance profile selection, we obtain a
photometric RC sample containing 11 million stars with distance and extinction
measurements.
