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

TL;DR

This work presents a statistically grounded framework that connects the incidence of low-ionization metal absorbers to the population of UV-bright galaxies via a radially decreasing $W_r$ profile for Mg II and O I. By combining a redshift-evolving luminosity function with an absorber frequency distribution, the authors predict redshift-dependent equivalent-width profiles, halo extents, and filling factors from the end of reionization through Cosmic Noon. They find that outer Mg II metal envelopes shrink with time due to the rising UV background, while inner, strong Mg II systems track the star-formation rate density and peak near Cosmic Noon; at the end of reionization, halos are largely self-enriched with winds not yet bridging neighbors. The study reconciles statistical metal enrichment with early enrichment scenarios and provides concrete predictions to guide future high-redshift absorption-line analyses (z>6) with next-generation facilities.

Abstract

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 $W_r^{2796}\lesssim 0.3$ Å 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 $W_r^{2796}\gtrsim 1$ Å 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 $W_r^{2796}\lesssim 0.3$ Å 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 $z>6$.

Figures (6)

• Figure 1: Sky-plane representation of a single equivalent width layer illustrating the cases of non-unity (left) and unity covering fraction.
• Figure 2: Rest-frame equivalent width of Mgii vs. projected separation of the absorbing galaxy. Black symbols represent direct data from Huang2021. Olive symbols mark average $W_r$ values weighted by the probability distribution function (PDF) of a Kaplan-Meier estimator of detections and non-detections in the $\rho$-bin (details in the text). The green line shows the statistical prediction of the $\overline{W}_r(R)$ using Eqs. \ref{['eq_hits']} and \ref{['eq_kappa']} for the case $\kappa=1$. The function $f(W)$ is taken from Zhu2013, extrapolated to $\langle z\rangle=0.215$, while $\phi(z,L)$ is from Bouwens2021 with $L_{min}/L^\star=0.03$ and $L_{max}/L^\star=7.5$. The shaded region propagates measurement errors of both statistics. The green dashed portion indicates the weak-Mgii regime where $f(W)$ is incomplete. The dotted blue line shows the statistical prediction of $\overline{W}_r(R_\kappa)$, applying a low-redshift extrapolation of $\kappa=\kappa(\rho)$ proposed by Schroetter2021 to model an independent data set.
• Figure 3: Redshift evolution of the Schechter parameters that fit the ${\rm d}^2N/{\rm d}z{\rm d}W$ data from Mathes2017, Chen2017, Bosman2017, and Sebastian2024. The M17 and S24 data points are published, while the C17 and C17+B17 data points are obtained by us by re-fitting the authors' ${\rm d}^2N/{\rm d}z{\rm d}W$ data (see caption of Fig. \ref{['fig_schechter']}). The solid curves are parametrizations of the form $y=a(1+z)^b /(1+ ((1+z)/c)^d)$ fit to the $W^\star$ data, and $y=a(1+z)^b$ fit to the $N^\star$ and the $\alpha$ data. The best-fit parameters are listed in Table \ref{['table_fit']}. The 1-$\sigma$ bands are computed using bootstrapping over the data ($W^\star$) and covariance-based bootstrapping over the fit parameters ($N^\star$ and $\alpha$).
• Figure 4: Redshift snapshots of the predicted equivalent-width profiles, $\overline{W}_r(R)$, of Mgii $\lambda 2796$ and Oi $\lambda 1302$. The redshifts are selected to match the available $W_r$-$\rho$ data at $z > 2$ for Mgii and the available $f(W)$ parametrization for Oi Becker2019. Model uncertainties are propagated from those of $f$ and $\phi$. The Mgii data points are taken from Bouche2012a and Moller2020 (open circles), and Bordoloi2024 (filled squares), with impact parameters normalized by $(L/L^\star)^\beta$. In the Moller2020 data, $W_r$ is estimated based on the published velocity width, by assuming a simple box profile of a fully saturated line.
• Figure 5: Redshift evolution of various model quantities, shown as following from top to bottom. Panel (a): Statistical prediction of the Mgii comoving line density ${\rm d}N/{\rm d}X$ for three cuts in $W_r^{2796}$ chosen to match published data (colored lines). Data points with the same color codes are from Sebastian2024 and Chen2017. Panel (b): Observed $L>0.01L^\star$ luminosity-weighted space density of UV-bright galaxies Bouwens2021 shown for both fixed and evolving $\beta$. Panel (c): Statistical prediction of the Mgii halo radius. Panel (d): Same as panel (c) but for the volume filling factor. Since $W_r$ is binned, both $R$ and $f_V$ are averages. The magenta line in panels (a), (c), and (d) represents a constant-velocity wind starting at the Big Bang. Model uncertainties are propagated from those of $f$ and $\phi$. A non-evolving $\beta$ would shift $\langle n \rangle_L$ upward by a factor of $\approx 3$, and shift $R$ and $f_V$ downward by $\approx 1.7$ and $\approx 5$, respectively.