Understanding the nature of luminous red galaxies (LRGs): Connecting LRGs to central and satellite subhaloes

We develop a novel abundance matching method to construct a mock catalogue of luminous red galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS), using catalogues of haloes and subhaloes in N-body simulations for a Λ-dominated cold dark matter model. Motivated by observations suggesting that LRGs are passively evolving, massive early-type galaxies with a typical age ≳5 Gyr, we assume that simulated haloes at z = 2 (z2-halo) are progenitors for LRG-host subhaloes observed today, and we label the most tightly bound particles in each progenitor z2-halo as LRG 'stars'. We then identify the subhaloes containing these stars to z = 0.3 (SDSS redshift) in descending order of the masses of z2-haloes until the comoving number density of the matched subhaloes becomes comparable to the measured number density of SDSS LRGs, n̄LRG = 10^-4 h³ Mpc^-3. Once the above prescription is determined, our only free parameter is the number density of haloes identified at z = 2 and this parameter is fixed to match the observed number density at z = 0.3. By tracing subsequent merging and assembly histories of each progenitor z2-halo, we can directly compute, from the mock catalogue, the distributions of central and satellite LRGs and their internal motions in each host halo at z=0.3. While the SDSS LRGs are galaxies selected by the magnitude and colour cuts from the SDSS images and are not necessarily a stellar-mass-selected sample, our mock catalogue reproduces a host of SDSS measurements: the halo occupation distribution for central and satellite LRGs, the projected autocorrelation function of LRGs, the cross-correlation of LRGs with shapes of background galaxies (LRG-galaxy weak lensing) and the non-linear redshift-space distortion effect, the Finger-of-God effect, in the angle-averaged redshift-space power spectrum. The mock catalogue generated based on our method can be used for removing or calibrating systematic errors in the cosmological interpretation of LRG clustering measurements as well as for understanding the nature of LRGs such as their formation and assembly histories.