Panchromatic Hubble Andromeda Treasury XII. Mapping Stellar Metallicity Distributions in M31

We present a study of spatial variations in the metallicity of old red giant branch stars in the Andromeda galaxy. Photometric metallicity estimates are derived by interpolating isochrones for over seven million stars in the Panchromatic Hubble Andromeda Treasury (PHAT) survey. This is the first systematic study of stellar metallicities over the inner 20 kpc of Andromeda's galactic disk. We see a clear metallicity gradient of $-0.020\pm0.004$ dex/kpc from $\sim4-20$ kpc assuming a constant RGB age. This metallicity gradient is derived after correcting for the effects of photometric bias and completeness and dust extinction and is quite insensitive to these effects. The unknown age gradient in M31's disk creates the dominant systematic uncertainty in our derived metallicity gradient. However, spectroscopic analyses of galaxies similar to M31 show that they typically have small age gradients that make this systematic error comparable to the 1$\sigma$ error on our metallicity gradient measurement. In addition to the metallicity gradient, we observe an asymmetric local enhancement in metallicity at radii of 3-6 kpc that appears to be associated with Andromeda's elongated bar. This same region also appears to have an enhanced stellar density and velocity dispersion.