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

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.