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

TL;DR

This study investigates how cosmic variance and observational uncertainties affect the inferred properties of dark matter halos hosting high-redshift Ly-$ ext{alpha}$ emitters, using mock catalogs and MCMC analysis to constrain halo mass and occupation fraction.

Contribution

It introduces a method combining mock catalogs and MCMC to quantify the impact of cosmic variance on galaxy-halo connection parameters at high redshift.

Findings

Wide range of halo masses consistent with observations.

Occupation fraction is tightly linked to minimum halo mass.

Large upcoming surveys can improve constraints on model parameters.

Abstract

In this paper we study the impact of cosmic variance and observational uncertainties in constraining the mass and occupation fraction, $f_{\rm occ}$, 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 $z=3.1$ ($\sim 1 {\rm deg^2}$). In our model a dark matter halo with mass in the range $M_{\rm min}<M_{\mathrm h}<M_{\rm max}$ can only host one detectable LAE at most. We proceed to explore the parameter space determined by $M_{\rm min}$,$M_{\rm max}$ and $f_{\rm occ}$ 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 $10^{10.0}h^{-1}{\rm{M_{\odot}}}\leq M_{\rm min} \leq 10^{11.1}h^{-1}{\rm{M_{\odot}}}$ , $10^{11.0}h^{-1}{\rm{M_{\odot}}}\leq M_{\rm max} \leq 10^{13.0}h^{-1}{\rm{M_{\odot}}}$; followed by a wide range in the occupation fraction $0.02\leq f_{\rm occ} \leq 0.30$. As a consequence the median mass, $M_{50}$, of all the consistent models has a large uncertainty $M_{50} = 3.16^{+9.34}_{-2.37}\times 10^{10}$$h^{-1}{\rm{M_{\odot}}}$. However, we find that the same individual models have a relatively tight $1\sigma$ scatter around the median mass $\Delta M_{1\sigma} = 0.55^{+0.11}_{-0.31}$ dex. We are also able to show that \focc\ is uniquely determined by $M_{\rm min}$, regardless of $M_{\rm max}$. We argue that upcoming large surveys covering at least $25$ deg$^{2}$ should be able to put tighter constraints on $M_{\rm min}$ and $f_{\rm occ}$ through the LAE number density distribution width constructed over several fields of $\sim 1$ deg$^{2}$.