We investigate the luminosity and colour dependence of clustering of CMASS galaxies in the Sloan Digital Sky Survey-III Baryon Oscillation Spectroscopic Survey Tenth Data Release, focusing on projected correlation functions of well-defined samples extracted from the full catalog of ∼ 540, 000 galaxies at z ∼ 0.5 covering about 6, 500 deg 2 . The halo occupation distribution framework is adopted to model the measurements on small and intermediate scales (from 0.02 to 60 h −1 Mpc), infer the connection of galaxies to dark matter halos and interpret the observed trends. We find that luminous red galaxies in CMASS reside in massive halos of mass M ∼10 13 -10 14 h −1 M ⊙ and more luminous galaxies are more clustered and hosted by more massive halos. The strong small-scale clustering requires a fraction of these galaxies to be satellites in massive halos, with the fraction at the level of 5-8 per cent and decreasing with luminosity. The characteristic mass of a halo hosting on average one satellite galaxy above a luminosity threshold is about a factor 8.7 larger than that of a halo hosting a central galaxy above the same threshold. At a fixed luminosity, progressively redder galaxies are more strongly clustered on small scales, which can be explained by having a larger fraction of these galaxies in the form of satellites in massive halos. Our clustering measurements on scales below 0.4 h −1 Mpc allow us to study the small-scale spatial distribution of satellites inside halos. While the clustering of luminosity-threshold samples can be well described by a Navarro-Frenk-White (NFW) profile, that of the reddest galaxies prefers a steeper or more concentrated profile. Finally, we also use galaxy samples of constant number density at different redshifts to study the evolution of luminous red galaxies, and find the clustering to be consistent with passive evolution in the redshift range of 0.5 z 0.6.

We study the dependence of galaxy clustering on Hi mass using ∼16,000 galaxies with redshift in the range of 0.0025 < z < 0.05 and Hi mass of M Hi > 10 8 M , drawn from the 70% complete sample of the Arecibo Legacy Fast ALFA survey. We construct subsamples of galaxies with M Hi above different thresholds, and make volume-limited clustering measurements in terms of three statistics: the projected two-point correlation function, the projected cross-correlation function with respect to a reference sample, and the redshift-space monopole moment. In contrast to previous studies, which found no/weak Hi-mass dependence, we find both the clustering amplitudes on scales above a few Mpc and the bias factors to increase significantly with increasing Hi mass for M Hi > 10 9 M . For Hi mass thresholds below ∼ 10 9 M , the inferred galaxy bias factors are systematically lower than the minimum halo bias from mass-selected halo samples. We extend the simple halo model, in which the galaxy content is only determined by halo mass, by including the halo formation time as an additional parameter. A model that puts Hi-rich galaxies into halos that formed late can reproduce the clustering measurements reasonably well. We present the implications of our best-fitting model on the correlation of Hi mass with halo mass and formation time, as well as the halo occupation distributions and Hi mass functions for central and satellite galaxies. These results are compared with the predictions from semi-analytic galaxy formation models and hydrodynamic galaxy formation simulations.

We extend the halo-based group finder developed by Yang et al. (2005c) to use data simultaneously with either photometric or spectroscopic redshifts. A mock galaxy redshift survey constructed from a high-resolution N-body simulation is used to evaluate the performance of this extended group finder. For galaxies with magnitude z ≤ 21 and redshift 0 < z ≤ 1.0 in the DESI legacy imaging surveys (the Legacy Surveys), our group finder successfully identifies more than 60% of the members in about 90% of halos with mass ≳1012.5 h −1 M ⊙. Detected groups with mass ≳1012.0 h −1 M ⊙ have a purity (the fraction of true groups) greater than 90%. The halo mass assigned to each group has an uncertainty of about 0.2 dex at the high-mass end ≳1013.5 h −1 M ⊙ and 0.45 dex at the low-mass end. Groups with more than 10 members have a redshift accuracy of ∼0.008. We apply this group finder to the Legacy Surveys DR8 and find 6.4 million groups with at least three members. About 500,000 of these groups have at least 10 members. The resulting catalog containing 3D coordinates, richness, halo masses, and total group luminosities is made publicly available.

We formulate a model of the conditional colour-magnitude distribution (CCMD) to describe the distribution of galaxy luminosity and colour as a function of halo mass. It consists of two populations of different colour distributions, dubbed pseudo-blue and pseudo-red, respectively, with each further separated into central and satellite galaxies. We define a global parameterization of these four colour-magnitude distributions and their dependence on halo mass, and we infer parameter values by simultaneously fitting the space densities and autocorrelation functions of 79 galaxy samples from the Sloan Digital Sky Survey defined by fine bins in the colour-magnitude diagram (CMD). The model deprojects the overall galaxy CMD, revealing its tomography along the halo mass direction. The bimodality of the colour distribution is driven by central galaxies at most luminosities, though at low luminosities it is driven by the difference between blue centrals and red satellites. For central galaxies, the two pseudocolour components are distinct and orthogonal to each other in the CCMD: at fixed halo mass, pseudo-blue galaxies have a narrow luminosity range and broad colour range, while pseudored galaxies have a narrow colour range and broad luminosity range. For pseudo-blue centrals, luminosity correlates tightly with halo mass, while for pseudo-red galaxies colour correlates more tightly (redder galaxies in more massive haloes). The satellite fraction is higher for redder and for fainter galaxies, with colour a stronger indicator than luminosity. We discuss the implications of the results and further applications of the CCMD model.