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We combine LAMOST DR7 spectroscopic data and Gaia EDR3 photometric data toconstruct high-quality giant (0.7 $< (BP-RP) <$ 1.4) and dwarf (0.5 $< (BP-RP)< $ 1.5) samples in the high Galactic latitude region, with precise correctionsfor magnitude-dependent systematic errors in the Gaia photometry and carefulreddening corrections using empirically determined color- andreddening-dependent coefficients. We use the two samples to buildmetallicity-dependent stellar loci of Gaia colors for giants and dwarfs,respectively. For a given $(BP-RP)$ color, a one dex change in [Fe/H] resultsin about a 5 mmag change in $(BP-G)$ color for solar-type stars. Theserelations are used to determine metallicity estimates from EDR3 colors. Despitethe weak sensitivity, the exquisite data quality of these colors enables atypical precision of about $\delta$\,[Fe/H] = 0.2 dex. Our method is valid forFGK stars with $G \leq 16$, [Fe/H] $\geq -2.5$, and $E(B-V) \leq 0.5$. Starswith fainter $G$ magnitudes, lower metallicities, or larger reddening sufferfrom higher metallicity uncertainties. With the enormous data volume of Gaia,we have measured metallicity estimates for about 27 million stars with 10 $< G\leq 16$ across almost the entire sky, including over 6 million giants and 20million dwarfs, which can be used for a number of studies. These includeinvestigations of Galactic formation and evolution, the identification ofcandidate stars for subsequent high-resolution spectroscopic follow-up, theidentification of wide binaries, and to obtain metallicity estimates of starsfor asteroseismology and exoplanet research.

Stellar Loci V: Photometric Metallicities of 27 Million FGK Stars based on Gaia Early Data Release 3