Constraining the Stellar-to-Halo Mass Relation with Galaxy Clustering and Weak Lensing from DES Year 3 Data

We develop a framework to study the relation between the stellar mass of a galaxy and the total mass of its host dark matter halo using galaxy clustering and galaxy-galaxy lensing measurements. We model a wide range of scales, roughly from \(\sim 100 \; {\rm kpc}\) to \(\sim 100 \; {\rm Mpc}\), using a theoretical framework based on the Halo Occupation Distribution and data from Year 3 of the Dark Energy Survey (DES) dataset. The new advances of this work include: 1) the generation and validation of a new stellar mass-selected galaxy sample in the range of \(\log M_\star/M_\odot \sim 9.6\) to \(\sim 11.5\); 2) the joint-modeling framework of galaxy clustering and galaxy-galaxy lensing that is able to describe our stellar mass-selected sample deep into the 1-halo regime; and 3) stellar-to-halo mass relation (SHMR) constraints from this dataset. In general, our SHMR constraints agree well with existing literature with various weak lensing measurements. We constrain the free parameters in the SHMR functional form \(\log M_\star (M_h) = \log(\epsilon M_1) + f\left[ \log\left( M_h / M_1 \right) \right] - f(0)\), with \(f(x) \equiv -\log(10^{\alpha x}+1) + \delta [\log(1+\exp(x))]^\gamma / [1+\exp(10^{-x})]\), to be \(\log M_1 = 11.506^{+0.325}_{-0.404}\), \(\log \epsilon = -1.632^{+0.306}_{-0.181}\), \(\alpha = -1.638^{+0.108}_{-0.099}\), \(\gamma = 0.596^{+0.251}_{-0.210}\) and \(\delta = 3.810^{+2.045}_{-1.811}\). The inferred average satellite fraction is within \(\sim 5-35\%\) for our fiducial results and we do not see any clear trends with redshift or stellar mass. Furthermore, we find that the inferred average galaxy bias values follow the generally expected trends with stellar mass and redshift. Our study is the first SHMR in DES in this mass range, and we expect the stellar mass sample to be of general interest for other science cases.