Impact of Cosmic Variance on the Galaxy-Halo Connection for Lyman-$\alpha$ Emitters

Abstract

In this paper we study the impact of cosmic variance and observational uncertainties in constraining the mass and occupation fraction, $f_{\mathrm{occ}}$, of dark matter halos hosting Ly-$\alpha$ Emitting Galaxies (LAEs) at high redshift. To this end, we construct mock catalogs from an N-body simulation to match the typical size of observed fields at $z=3.1$ ($\sim 1\mathrm{de}{\mathrm{g}}^2$). In our model a dark matter halo with mass in the range $M_{\min }<M_{\mathrm{h}}<M_{\max }$ can only host one detectable LAE at most. We proceed to explore the parameter space determined by $M_{\min }$,$M_{\max }$ and $f_{\mathrm{occ}}$ with a Markov Chain Monte-Carlo algorithm using the angular correlation function (ACF) and the LAEs number density as observational constraints. We find that the preferred minimum and maximum masses in our model span a wide range $10^{10.0}{h}^{-1}{\mathrm{M}}_{\odot }\le M_{\min }\le 10^{11.1}{h}^{-1}{\mathrm{M}}_{\odot }$ , $10^{11.0}{h}^{-1}{\mathrm{M}}_{\odot }\le M_{\max }\le 10^{13.0}{h}^{-1}{\mathrm{M}}_{\odot }$; followed by a wide range in the occupation fraction $0.02\le f_{\mathrm{occ}}\le 0.30$. As a consequence the median mass, $M_{50}$, of all the consistent models has a large uncertainty $M_{50}=3.16_{-2.37}^{+9.34}\times 10^{10}$$h^{-1}{\mathrm{M}}_{\odot }$. However, we find that the same individual models have a relatively tight $1\sigma$ scatter around the median mass $\Delta M_{1\sigma }=0.55_{-0.31}^{+0.11}$ dex. We are also able to show that \focc\ is uniquely determined by $M_{\min }$, regardless of $M_{\max }$. We argue that upcoming large surveys covering at least $25$ deg${}^2$ should be able to put tighter constraints on $M_{\min }$ and $f_{\mathrm{occ}}$ through the LAE number density distribution width constructed over several fields of $\sim 1$ deg${}^2$.

arXiv comment7 Pages, 5 figures. Accepted for publication in ApJ

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