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.