3d Gas-Phase Elemental Abundances Across The Formation Histories Of Milky Way-Mass Galaxies In The Fire Simulations: Initial Conditions For Chemical Tagging

We use FIRE-2 simulations to examine 3D variations of gas-phase elemental abundances of [O/H], [Fe/H], and [N/H] in 11MW and M31-mass galaxies across their formation histories at z <= 1.5 (t(lookback) <= 9.4 Gyr), motivated by characterizing the initial conditions of stars for chemical tagging. Gas within of the disc mid-plane is vertically homogeneous to less than or similar to 0.008 dex at all z <= 1.5. We find negative radial gradients (metallicity decreases with galactocentric radius) at all times, which steepen over time from approximate to -0.01 dex kpc(-1) at z = 1 (t(lookback) = 7.8 Gyr) to approximate to-0.03 dex kpc(-1) at z = 0, and which broadly agree with observations of the MW, M31, and nearby MW/M31-mass galaxies. Azimuthal variations at fixed radius are typically at z = 1, reducing to 0.05 dex at z = 0. Thus, over time radial gradients become steeper while azimuthal variations become weaker (more homogeneous). As a result, azimuthal variations were larger than radial variations at z greater than or similar to 0.8 (t(lookback) greater than or similar to 6.9 Gyr). Furthermore, elemental abundances are measurably homogeneous (to less than or similar to 0.05dex) across a radial range of Delta R approximate to 3.5 kpc at z greater than or similar to 1 and at z = 0. We also measure full distributions of elemental abundances, finding typically negatively skewed normal distributions at z greater than or similar to 1 that evolve to typically Gaussian distributions by z = 0. Our results on gas abundances inform the initial conditions for stars, including the spatial and temporal scales for applying chemical tagging to understand stellar birth in the MW.