How far have metals reached? Reconciling statistical constraints and enrichment models at reionization

¹ Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago, Chile
² French-Chilean Laboratory for Astronomy, IRL 3386, CNRS and U. de Chile, Casilla 36-D, Santiago, Chile
³ Centre de Recherche Astrophysique de Lyon, Université de Lyon 1, UMR5574, 69230 Saint-Genis-Laval, France

^⋆ Corresponding author: slopez@das.uchile.cl

Received: 16 May 2025
Accepted: 6 September 2025

Abstract

The incidence of quasar absorption systems and the space density of their galaxies are proportional, with the proportionality factor given by the mean absorbing cross section. In this paper, we use redshift parametrizations of these two statistics to predict the cosmic evolution of an equivalent-width (W_r) radial profile model, tailored for the low-ionization species Mg II and O I. Our model provides an excellent match to well-sampled, low-redshift Mg II equivalent-width and impact-parameter pairs from the literature. We then focus on the evolution of various quantities between the reionization and cosmic noon eras. We find that the extent of Mg II, and hence the amount of cool (T ∼ 10⁴ K), enriched gas in the average halo, decreases continuously with cosmic time, suggesting that the expected growth of metal-enriched bubbles before reionization experienced a turnover in its low-ionization phase at around z ≈ 6–8. This effect is more pronounced in W_r²⁷⁹⁶ ≲ 0.3 Å systems (outermost layers of the model) and, in general, affects O I more than Mg II, probably owing to the onset of photoionization by the UV background. The line density of W_r²⁷⁹⁶ ≳ 1 Å systems (model inner layers) continuously increases in synchrony with the star-formation rate density until it reaches a peak at cosmic noon. In contrast, the line density of W_r²⁷⁹⁶ ≲ 0.3 Å systems remains constant or decreases over the same period. (3) At the end of reionization, the filling factor is low enough so that the winds have not yet reached neighboring halos. This implies that the halos are self-enriched, as suggested by semi-analytic models, through a process combined with the constant replenishment of the intergalactic medium. We discuss how these statistical predictions can be reconciled with early metal enrichment models and argue that they offer a practical comparison point for future analyses of quasar absorption lines at z > 6.