2018ApJ...856...81R

The most luminous galaxies at high redshift are generally considered to be hosted in massive dark-matter halos of comparable number density, hence residing at the center of over-densities/protoclusters. We assess the validity of this assumption by investigating the clustering around the brightest galaxies populating the cosmic web at redshift z ∼ 8-9 through a combination of semi-analytic modeling and Monte Carlo simulations of mock Hubble Space Telescope WFC3 observations. The innovative aspect of our approach is the inclusion of a log-normal scatter parameter Σ in the galaxy luminosity versus halo mass relation, extending the conditional luminosity function framework extensively used at low redshift to high z. Our analysis shows that the larger the value of Σ, the less likely it is that the brightest source in a given volume is hosted in the most massive halo, and hence the weaker the overdensity of neighbors. We derive a minimum value of Σ as a function of redshift by considering stochasticity in the halo assembly times, which affects galaxy ages and star formation rates in our modeling. We show that Σ_min(z) ∼ 0.15-0.3, with Σ_min increasing with redshift as a consequence of shorter halo assembly periods at higher redshifts. Current observations (m_AB ∼ 27) of the environment of spectroscopically confirmed bright sources at z > 7.5 do not show strong evidence of clustering and are consistent with our modeling predictions for Σ >= Σ_min. Deeper future observations reaching m_AB ∼ 28.2-29 would have the opportunity to clearly quantify the clustering strength and hence to constrain Σ, investigating the physical processes that drive star formation in the early universe.