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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 ($$t_{\rm lookback} \le 9.4 \, \rm {Gyr}$$), motivated by characterizing the initial conditions of stars for chemical tagging. Gas within $$1 \, \rm {kpc}$$ of the disc mid-plane is vertically homogeneous to $$\lesssim 0.008 \, \rm {dex}$$ at all z ≤ 1.5. We find negative radial gradients (metallicity decreases with galactocentric radius) at all times, which steepen over time from $$\approx \! -0.01 \, \rm {dex}\, \rm {kpc}^{-1}$$ at z = 1 ($$t_{\rm lookback} = 7.8 \, \rm {Gyr}$$) to $$\approx \! -0.03 \, \rm {dex}\, \rm {kpc}^{-1}$$ 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 $$0.14 \, \rm {dex}$$ at z = 1, reducing to $$0.05 \, \rm {dex}$$ 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 ($$t_{\rm lookback} \gtrsim 6.9 \, \rm {Gyr}$$). Furthermore, elemental abundances are measurably homogeneous (to ≲0.05 dex) across a radial range of $$\Delta R \approx 3.5 \, \rm {kpc}$$ at z ≳ 1 and $$\Delta R \approx 1.7 \, \rm {kpc}$$ 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.
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