Spatial Variations of Stellar Elemental Abundances in FIRE Simulations of Milky Way-Mass Galaxies: Patterns Today Mostly Reflect Those at Formation

Spatial patterns of stellar elemental abundances encode rich information about a galaxy's formation history. We analyze the radial, vertical, and azimuthal variations of metals in stars, both today and at formation, in the FIRE-2 cosmological simulations of Milky Way (MW)-mass galaxies, and we compare with the MW. The radial gradient today is steeper (more negative) for younger stars, which agrees with the MW, although radial gradients are shallower in FIRE-2. Importantly, this age dependence was present already at birth: radial gradients today are only modestly ($\lesssim$ 0.01 dex kpc$^{-1}$) shallower than at birth. Disk vertical settling gives rise to negative vertical gradients across all stars, but vertical gradients of mono-age stellar populations are weak. Similar to the MW, vertical gradients in FIRE-2 are shallower at larger radii, but they are overall shallower in FIRE-2. This vertical dependence was present already at birth: vertical gradients today are only modestly ($\lesssim$ 0.1 dex kpc$^{-1}$) shallower than at birth. Azimuthal scatter is nearly constant with radius, and it is nearly constant with age $\lesssim$ 8 Gyr ago, but increases for older stars. Azimuthal scatter is slightly larger ($\lesssim$ 0.04 dex) today than at formation. Galaxies with larger azimuthal scatter have a stronger radial gradient, implying that azimuthal scatter today arises primarily from radial redistribution of gas and stars. Overall, spatial variations of stellar metallicities show only modest differences between formation and today; spatial variations today primarily reflect the conditions of stars at birth, with spatial redistribution of stars after birth contributing secondarily.