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 [ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>α</mml:mi> </mml:math> /Fe] near <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mrow> <mml:mo stretchy="true" form="prefix" mathvariant="normal">[</mml:mo> <mml:mi mathvariant="normal">F</mml:mi> <mml:mi mathvariant="normal">e</mml:mi> <mml:mi mathvariant="normal">/</mml:mi> <mml:mi mathvariant="normal">H</mml:mi> <mml:mo stretchy="true" form="postfix" mathvariant="normal">]</mml:mo> </mml:mrow> <mml:mo>≈</mml:mo> <mml:mo>−</mml:mo> <mml:mn>1.3</mml:mn> </mml:mrow> </mml:math> , which we previously interpreted as evidence for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>α</mml:mi> </mml:math> -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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> <mml:mo>&lt;</mml:mo> <mml:mrow> <mml:mo stretchy="true" form="prefix" mathvariant="normal">[</mml:mo> <mml:mi mathvariant="normal">F</mml:mi> <mml:mi mathvariant="normal">e</mml:mi> <mml:mi mathvariant="normal">/</mml:mi> <mml:mi mathvariant="normal">H</mml:mi> <mml:mo stretchy="true" form="postfix" mathvariant="normal">]</mml:mo> </mml:mrow> <mml:mo>&lt;</mml:mo> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> ) 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>≃</mml:mo> <mml:mn>0.6</mml:mn> </mml:mrow> </mml:math> –2.0. Comparison with one-zone galactic chemical-evolution (GCE) models that replicated the [ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>α</mml:mi> </mml:math> /Fe]-rise from Paper I shows that shallow tails ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>≃</mml:mo> <mml:mn>0.6</mml:mn> </mml:mrow> </mml:math> ) require a massive initial cold gas reservoir ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>≳</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>9</mml:mn> </mml:msup> <mml:mspace width="0.167em"/> <mml:msub> <mml:mi mathvariant="normal">M</mml:mi> <mml:mo mathvariant="normal">⊙</mml:mo> </mml:msub> </mml:mrow> </mml:math> ), while steeper tails ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>≳</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> ) arise from small reservoirs that built up over time with weak inflow. MDFs with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>≃</mml:mo> <mml:mn>1.0</mml:mn> </mml:mrow> </mml:math> are best reproduced under our GCE framework, which favor a proto-Galaxy with a moderate gas reservoir ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>8</mml:mn> </mml:msup> </mml:math> – <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>9</mml:mn> </mml:msup> <mml:mspace width="0.167em"/> <mml:msub> <mml:mi mathvariant="normal">M</mml:mi> <mml:mo mathvariant="normal">⊙</mml:mo> </mml:msub> </mml:mrow> </mml:math> ) sustained through weak continuous inflow ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>2</mml:mn> <mml:mspace width="0.222em"/> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">M</mml:mi> <mml:mo mathvariant="normal">⊙</mml:mo> </mml:msub> <mml:mspace width="0.222em"/> <mml:mi mathvariant="normal">y</mml:mi> <mml:msup> <mml:mi mathvariant="normal">r</mml:mi> <mml:mrow> <mml:mo mathvariant="normal">−</mml:mo> <mml:mn mathvariant="normal">1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> </mml:math> ) and SFE comparable to today’s value (a few <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>10</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.167em"/> <mml:mrow> <mml:mi mathvariant="normal">y</mml:mi> <mml:msup> <mml:mi mathvariant="normal">r</mml:mi> <mml:mrow> <mml:mo mathvariant="normal">−</mml:mo> <mml:mn mathvariant="normal">1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> </mml:math> ) during the first Gyr. This scenario is reinforced by MDFs of 30 Milky Way analogs in the Auriga simulations, which exhibit similar slopes ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>≈</mml:mo> <mml:mn>1.25</mml:mn> </mml:mrow> </mml:math> ). The metal-poor MDF tail thus provides a quantitative constraint on the Milky Way’s early gas accretion and star formation history.