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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.