A theoretical framework for combining techniques that probe the link between galaxies and dark matter

We develop a theoretical framework that combines measurements of galaxy-galaxy lensing, galaxy clustering, and the galaxy stellar mass function in a self-consistent manner. While considerable effort has been invested in exploring each of these probes individually, attempts to combine them are still in their infancy. These combinations have the potential to elucidate the galaxy-dark matter connection and the galaxy formation physics responsible for it, as well as to constrain cosmological parameters and to test the nature of gravity. In this paper, we focus on a theoretical model that describes the galaxy-dark matter connection based on standard halo occupation distribution techniques. Several key modifications enable us to extract additional parameters that determine the stellar-to-halo mass relation and to simultaneously fit data from multiple probes while allowing for independent binning schemes for each probe. We construct mock catalogs from numerical simulations to investigate the effects of sample variance and covariance for each probe. Finally, we analyze how trends in each of the three observables impact the derived parameters of the model. In particular, we investigate various features of the observed galaxy stellar mass function (low-mass slope, "plateau," knee, and high-mass cutoff) and show how each feature is related to the underlying relationship between stellar and halo mass. We demonstrate that the observed "plateau" feature in the stellar mass function at M * 2 × 10¹⁰ M _∞ is due to the transition that occurs in the stellar-to-halo mass relation at M_h 10¹² M _∞ from a low-mass power-law regime to a sub-exponential function at higher stellar mass.