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

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 (Wr) radial profile model, tailored for the low-ionization species Mg <ns0:sc>II</ns0:sc> and O <ns0:sc>I</ns0:sc>. Our model provides an excellent match to well-sampled, low-redshift Mg <ns0:sc>II</ns0:sc> 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 <ns0:sc>II</ns0:sc>, 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 Wr2796 ≲ 0.3 Å systems (outermost layers of the model) and, in general, affects O <ns0:sc>I</ns0:sc> more than Mg <ns0:sc>II</ns0:sc>, probably owing to the onset of photoionization by the UV background. The line density of Wr2796 ≳ 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 Wr2796 ≲ 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.