Stellar Metallicities from SkyMapper Photometry II: Precise photometric metallicities of $\sim$280,000 giant stars with [Fe/H] $< -0.75$ in the Milky Way

The Milky Way's metal-poor stars are nearby ancient objects that are used to study early chemical evolution and the assembly and structure of the Milky Way. Here we present reliable metallicities of $\sim280,000$ stars with $-3.75 \lesssim$ [Fe/H] $\lesssim -0.75$ down to $g=17$ derived using metallicity-sensitive photometry from the second data release (DR2) of the SkyMapper Southern Survey. We use the dependency of the flux through the SkyMapper $v$ filter on the strength of the Ca II K absorption features, in tandem with SkyMapper $u,g,i$ photometry, to derive photometric metallicities for these stars. We find that metallicities derived in this way compare well to metallicities derived in large-scale spectroscopic surveys, and use such comparisons to calibrate and quantify systematics as a function of location, reddening, and color. We find good agreement with metallicities from the APOGEE, LAMOST, and GALAH surveys, based on a standard deviation of $\sigma\sim0.25$dex of the residuals of our photometric metallicities with respect to metallicities from those surveys. We also compare our derived photometric metallicities to metallicities presented in a number of high-resolution spectroscopic studies to validate the low metallicity end ([Fe/H] $< -2.5$) of our photometric metallicity determinations. In such comparisons, we find the metallicities of stars with photometric [Fe/H] $< -2.5$ in our catalog show no significant offset and a scatter of $\sigma\sim$0.31dex level relative to those in high-resolution work when considering the cooler stars ($g-i > 0.65$) in our sample. We also present an expanded catalog containing photometric metallicities of $\sim720,000$ stars as a data table for further exploration of the metal-poor Milky Way.