The dawn is quiet II: Gaia XP constraints on the Milky Way's proto-Galaxy from very metal-poor MDF tails

Abstract

The earliest phase of the Milky Way's evolution involved a transition from a dispersion-supported proto-galaxy to a rotationally supported disk. A key chemical signature of this transition is the moderate rise in [$\alpha$/Fe] near $\mathrm{[Fe/H]}\approx-1.3$, which we previously interpreted as evidence for $\alpha$-enhanced gas accretion fueling early disk formation. However, this trend alone does not uniquely constrain the trade-off between initial gas mass, inflow rate, and star formation efficiency (SFE), leaving the physical condition of the proto-Milky Way uncertain. To break this degeneracy, we analyze the metal-poor tail ($-3<\mathrm{[Fe/H]}<-2$) of the Milky Way's metallicity distribution function (MDF) using Gaia DR3 BP/RP (XP) metallicities from ten catalogs. After applying recommended quality cuts, all catalogs exhibit a single-slope exponential tail with slopes $k\simeq0.6$--$2.0$. Comparison with one-zone galactic chemical-evolution (GCE) models that replicated the [$\alpha$/Fe]-rise from Paper I shows that shallow tails ($k\simeq0.6$) require a massive initial cold gas reservoir ($\gtrsim10^9\, \mathrm{M_\odot}$), while steeper tails ($k\gtrsim1$) arise from small reservoirs that built up over time with weak inflow. MDFs with $k \simeq 1.0$ are best reproduced under our GCE framework, which favor a proto-Galaxy with a moderate gas reservoir ($10^{8}$--$10^{9}\, \mathrm{M_\odot}$) sustained through weak continuous inflow ($\sim 2 \ \mathrm{M_\odot \ yr^{-1}}$) and SFE comparable to today's value (a few $\times 10^{-10}\,\mathrm{yr^{-1}}$) during the first Gyr. This scenario is reinforced by MDFs of 30 Milky Way analogs in the Auriga simulations, which exhibit similar slopes ($k\approx1.25$). The metal-poor MDF tail thus provides a quantitative constraint on the Milky Way's early gas accretion and star formation history.