Constraints on the relationship between stellar mass and halo mass at
  low and high redshift
  We use a statistical approach to determine the relationship between the
stellar masses of galaxies and the masses of the dark matter halos in which
they reside. We obtain a parameterized stellar-to-halo mass (SHM) relation by
populating halos and subhalos in an N-body simulation with galaxies and
requiring that the observed stellar mass function be reproduced. We find good
agreement with constraints from galaxy-galaxy lensing and predictions of
semi-analytic models. Using this mapping, and the positions of the halos and
subhalos obtained from the simulation, we find that our model predictions for
the galaxy two-point correlation function (CF) as a function of stellar mass
are in excellent agreement with the observed clustering properties in the SDSS
at z=0. We show that the clustering data do not provide additional strong
constraints on the SHM function and conclude that our model can therefore
predict clustering as a function of stellar mass. We compute the conditional
mass function, which yields the average number of galaxies with stellar masses
in the range [m, m+dm] that reside in a halo of mass M. We study the redshift
dependence of the SHM relation and show that, for low mass halos, the SHM ratio
is lower at higher redshift. The derived SHM relation is used to predict the
stellar mass dependent galaxy CF and bias at high redshift. Our model predicts
that not only are massive galaxies more biased than low mass ones at all
redshifts, but the bias increases more rapidly with increasing redshift for
massive galaxies than for low mass ones. We present convenient fitting
functions for the SHM relation as a function of redshift, the conditional mass
function, and the bias as a function of stellar mass and redshift.
