Abstract
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≤9.4Gyr), motivated by characterizing the initial conditions of stars for chemical tagging. Gas within 1kpc of the disc mid-plane is vertically homogeneous to ≲0.008dex at all z ≤ 1.5. We find negative radial gradients (metallicity decreases with galactocentric radius) at all times, which steepen over time from ≈−0.01dexkpc−1 at z = 1 (tlookback=7.8Gyr) to ≈−0.03dexkpc−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 0.14dex at z = 1, reducing to 0.05dex 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≳6.9Gyr). Furthermore, elemental abundances are measurably homogeneous (to ≲0.05 dex) across a radial range of ΔR≈3.5kpc at z ≳ 1 and ΔR≈1.7kpc 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.