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, the proportionality factor being the mean absorbing cross section. In this paper we use redshift parameterizations 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 with well-sampled, low-redshift Mg II equivalent-width/impact-parameter pairs from the literature. We then focus on the evolution of various quantities between the Reionization and Cosmic Noon eras. Our findings are: (1) The extent of Mg II and hence the amount of cool ($T\sim 10^4$ K), enriched gas in the average halo decreases continuously with cosmic time after $z \approx 6$--$8$. This effect is more pronounced in $W_r^{2796}\lesssim 0.3$ {\AA} systems (outermost layers of the model) and, in general, affects O I more than Mg II, probably due to the onset of photoionization by the UV background. (2) The line density of $W_r^{2796}\gtrsim 1$ {\AA} systems (model inner layers) constantly increases in synchrony with the star formation rate density until it reaches a peak at Cosmic Noon. The line density of $W_r^{2796}\lesssim 0.3$ {\AA} systems, on the other hand, remains constant or decreases over the same period. (3) At the end of Reionization, the filling factor is low enough that the winds have not yet reached neighboring halos. This implies that the halos are self-enriched, as suggested by semi-analytic models. We discuss how these statistical predictions can be reconciled with early metal enrichment models and offer a practical comparison point for future analyses of quasar absorption lines at $z>6$.