Halo Model at Its Best: Constraints on Conditional Luminosity Functions from Measured Galaxy Statistics

Abstract

(Summary) Using the conditional luminosity function (CLF) -- the luminosity distribution of galaxies in a dark matter halo -- as the fundamental building block, we present an empirical model for the galaxy distribution. The model predictions are compared with the published luminosity function and clustering statistics from Sloan Digital Sky Survey (SDSS) at low redshifts, and galaxy correlation functions from COMBO-17 survey at a redshift of 0.6, DEEP2 survey at a redshift of unity, and Great Observatories Deep Origins Survey (GOODS) at a redshift around 3. The comparison with statistical measurements allows us to constrain certain parameters related to analytical descriptions that describe the relation between a dark matter halo and its central galaxy luminosity, its satellite galaxy luminosity, and the fraction of early- and late-type galaxies of that halo. The single parameter best constrained by clustering measurements is the total satellite galaxy luminosity averaged over the halo mass distribution probed by the galaxy sample. For SDSS, $ =(2.1^{+0.8}_{-0.4}) \times 10^{10}$ h${-2}$ L$_{\sun}$, while for GOODS at $z \sim 3$, $ < 2 \times 10^{11}$ h$^{-2}$ L$_{\sun}$. Quantities such as the fraction of satellite galaxies at a given galaxy luminosity are not strongly constrained with SDSS data. We use our CLFs to establish probability distribution of halo mass in which galaxies of a given luminosity could be found either at halo centers or as satellites. Finally, to help establish further properties of the galaxy distribution, we propose the measurement of cross-clustering between galaxies divided into two distinctly different luminosity bins.