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

The mapping between the distributions of the observed galaxy stellar mass and the underlying dark matter halos 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 model (HOD), to solve for this mapping by jointly fitting the galaxy clustering and the galaxy-galaxy lensing measured from the Sloan Digital Sky Survey (SDSS). The method, called the iHOD model, extracts maximum information from the survey by including ∼80% more galaxies than the traditional HOD methods, and takes into account the incompleteness of the stellar mass samples in a statistically consistent manner. The derived stellar-to-halo mass relation not only explains the clustering and lensing of SDSS galaxies over almost four decades in stellar mass, but also successfully predicts the stellar mass functions observed in SDSS. Due to its capability of modelling significantly more galaxies, the iHOD is able to break the degeneracy between the logarithmic scatter in the stellar mass at fixed halo mass and the slope of the stellar-to-halo mass relation at high mass end, without the need to assume a strong prior on the scatter and/or use the stellar mass function as an input. We detect a decline of the scatter with halo mass, from 0.22 −0.01 dex at below 10 12h−1M to 0.18 ± 0.01 dex at 1014h−1M . The model also enables stringent constraints on the satellite stellar mass functions at fixed halo mass, predicting a departure from the Schechter functional form in high mass halos. The iHOD model can be easily applied to existing and future spectroscopic datasets, greatly improving the statistical constraint on the stellar-to-halo mass relation compared to the traditional HOD methods within the same survey.