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 11 MW and M31-mass galaxies across their formation histories at z ≤ 1.5 (tlookback ≤ 9.4 Gyr), motivated by characterizing the initial conditions of stars for chemical tagging. Gas within 1 kpc of the disc mid-plane is vertically homogeneous 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 -0.01 dex kpc-1 at z = 1 (tlookback} = 7.8 Gyr) 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 0.14 dex 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 ≥ 0.8 (tlookback ≳ 6.9 Gyr). Furthermore, elemental abundances are measurably homogeneous (to ≤0.05 dex) across a radial range of Δ R ≈ 3.5 kpc at z ≥ 1 and Δ R ≈ 1.7 kpc at z = 0. We also measure full distributions of elemental abundances, finding typically negatively skewed normal distributions at z ≥ 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.