Beyond spectroscopy. I. Metallicities, distances, and age estimates for over twenty million stars from SMSS DR2 and Gaia EDR3

Accurate determinations of stellar parameters and distances for large complete samples of stars are keys for conducting detailed studies of the formation and evolution of our Galaxy. Here we present stellar atmospheric parameters ($T_{\rm eff}$, luminosity classifications, and [Fe/H]) estimates for some 24 million stars determined from the stellar colors of SMSS DR2 and Gaia EDR3, based on training datasets with available spectroscopic measurements from previous high/medium/low-resolution spectroscopic surveys. The number of stars with photometric-metallicity estimates is 4-5 times larger than that collected by the current largest spectroscopic survey to date - LAMOST - over the course of the past decade. External checks indicate that the precision of the photometric-metallicity estimates are quite high, comparable to or slightly better than that derived from spectroscopy, with typical values around 0.05-0.15dex for both dwarf and giant stars with [Fe/H]>$-$1.0, 0.10-0.20dex for giant stars with $-$2.0<[Fe/H]<$-$1.0. and 0.20-0.25dex for giant stars with [Fe/H]<$-$2.0, and include estimates for stars as metal-poor as [Fe/H]~$-$3.5, substantially lower than previous photometric techniques. Photometric-metallicity estimates are obtained for an unprecedented number of metal-poor stars, including a total of over three million metal-poor (MP; [Fe/H] <$-$1.0) stars, over half a million very metal-poor (VMP; [Fe/H]<$-$2.0) stars, and over 25,000 extremely metal-poor (EMP; [Fe/H]<$-$3.0) stars. Moreover, distances are determined for over 20 million stars in our sample. For the over 18 million sample stars with accurate Gaia parallaxes, stellar ages are estimated by comparing with theoretical isochrones. Astrometric information is provided for the stars in our catalog, along with radial velocities for ~10% of our sample stars, taken from completed/ongoing large-scale spectroscopic surveys.