Connecting Galaxies with Halos Across Cosmic Time: Stellar mass assembly
  distribution modeling of galaxy statistics
  In this work, I explore an empirically motivated model for investigating the
relationship between galaxy stellar masses, star formation rates and their halo
masses and mass accretion histories. The core statistical quantity in this
model is the stellar mass assembly distribution, $P(dM_{*}/dt|\mathbf{X},a)$,
which specifies the probability density distribution of stellar mass assembly
rates given a set of halo properties $\mathbf{X}$ and epoch $a$. Predictions
from this model are obtained by integrating the stellar mass assembly
distribution (SMAD) over halo merger trees, easily obtained from modern,
high-resolution $N$-body simulations. Further properties of the galaxies hosted
by the halos can be obtained by post-processing the stellar mass assembly
histories with stellar population synthesis models. In my particular example
implementation of this model, I use the \citet{behroozi13a} constraint on the
median stellar mass assembly rates of halos as a function of their mass and
redshift to construct an example parameterization of
$P(dM_{*}/dt|\mathbf{X},a)$. This SMAD is then integrated over individual halo
mass accretion histories from $N$-body merger trees starting at z = 4, using
simple rules to account for merging halos. I find that this a simple model can
reproduce qualitatively the bimodal features of the low-redshift galaxy
population, including the qualitative split in the two-point clustering as a
function of specific star formation rate. These results indicate that models
which directly couple halo and galaxy growth through simple efficiency
functions can naturally predict the star formation rate bimodality in
higher-order statistics of the galaxy field, such as its two-point correlations
or galactic conformity signals.
