Halo model at its best: constraints on conditional luminosity functions from measured galaxy statistics

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 (LF) and clustering statistics from the Sloan Digital Sky Survey (SDSS) at low redshifts, galaxy correlation functions from the Classifying Objects by Medium‐Band Observations 17 (COMBO‐17) survey at a redshift of 0.6, the Deep Extragalactic Evolutionary Probe 2 (DEEP2) survey at a redshift of unity, the Great Observatories Deep Origins Survey (GOODS) at a redshift around 3 and the Subaru/ XMM–Newton Deep Field data at a redshift of 4. The comparison with statistical measurements allows us to constrain certain parameters related to analytical descriptions on 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. With the SDSS r ‐band LF at M r < −17, the lognormal scatter in the central galaxy luminosity at a given halo mass in the central galaxy—halo mass, L c ( M ) , relation is constrained to be 0.17 +0.02 −0.01 , with 1σ errors here and below. For the same galaxy sample, we find no evidence for a low‐mass cut‐off in the appearance of a single central galaxy in dark matter haloes, with the 68 per cent confidence level upper limit on the minimum mass of dark matter haloes to host a central galaxy, with luminosity M r < −17 , is 2 × 10 10   h −1  M ⊙ . If the total luminosity of a dark matter halo varies with halo mass as L c ( M ) ( M / M sat ) β s when M > M sat , using SDSS data, we find that M sat = (1.2 +2.9 −1.1 ) × 10 13 h −1 M ⊙ and power‐law slope β s = 0.56 +0.19 −0.17 for galaxies with M r < −17 at z < 0.1. At z ∼ 0.6, the COMBO‐17 data allows these parameters for M B < −18 galaxies to be constrained as (3.3 +4.9 −3.0 ) × 10 13   h −1  M ⊙ and (0.62 +0.33 −0.27 ) , respectively. At z ∼ 4, Subaru measurements constrain these parameters for M B < −18.5 galaxies as (4.12 +5.90 −4.08 ) × 10 12   h −1  M ⊙ and (0.55 +0.32 −0.35 ) , respectively. The redshift evolution associated with these parameters can be described as a combination of the evolution associated with the halo mass function and the luminosity—halo mass relation. The single parameter well constrained by clustering measurements is the average of the total satellite galaxy luminosity corresponding to the dark matter halo distribution probed by the galaxy sample. For SDSS, 〈 L sat 〉= (2.1 +0.8 −0.4 ) × 10 10   h −2  L ⊙ , while for GOODS at z ∼ 3, 〈 L sat 〉 < 2 × 10 11   h −2  L ⊙ . For SDSS, the fraction of galaxies that appear as satellites is 0.13 +0.03 −0.03 , 0.11 +0.05 −0.02 , 0.11 +0.12 −0.03 and 0.12 +0.33 −0.05 for galaxies with luminosities in the r ′ band from −22 to −21, −21 to −20, −20 to −19 and −19 to −18, respectively. In addition to constraints on central and satellite CLFs, we also determine model parameters of the analytical relations that describe the fraction of early‐ and late‐type galaxies in dark matter haloes. We use our CLFs to establish the probability distribution of halo mass in which galaxies of a given luminosity could be found either at halo centres 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. Our analysis shows how CLFs provide a stronger foundation to built‐up analytical models of the galaxy distribution when compared with models based on the halo occupation number alone.