Mapping stellar content to dark matter haloes using galaxy clustering and galaxy–galaxy lensing in the SDSS DR7

The mapping between the distributions of the observed galaxy stellar mass and the underlying dark matter haloes provides the crucial link from theories of large-scale structure formation to interpreting the complex phenomena of galaxy formation and evolution. We develop a novel statistical method, based on the halo occupation distribution (HOD) model, to solve for this mapping by jointly fitting the galaxy clustering and the galaxy–galaxy lensing from the Sloan Digital Sky Survey (SDSS). The method, called the iHOD model, extracts maximum information from the survey by including ∼80 per cent more galaxies than the traditional HOD methods, accounting for the incompleteness of the stellar mass samples self-consistently. The derived stellar-to-halo mass relation (SHMR) explains the clustering and lensing of SDSS galaxies over four decades in stellar mass, while successfully predicting the observed stellar mass functions (SMFs). By modelling significantly more galaxies, the iHODbreaks the degeneracy between the logarithmic scatter in the stellar mass at fixed halo mass and the slope of the mean SHMR at high masses, without assuming a strong prior on the scatter and/or using the SMF as an input. We detect a decline of the scatter with halo mass, from dex below 10¹² h⁻¹ M_⊙ to 0.18 ± 0.01 dex at 10¹⁴ h⁻¹ M_⊙. The model predicts a departure of satellite SMFs from the Schechter form in massive haloes and a linear scaling of satellite number with halo mass. The iHOD model can be easily applied to other spectroscopic data sets, greatly improving statistical constraints on the SHMR compared to traditional HOD methods within the same survey.