[Paper Review] Connecting Galaxies with Halos Across Cosmic Time: Stellar mass assembly distribution modeling of galaxy statistics

M. R. Becker|arXiv (Cornell University)|Jul 13, 2015

Data Visualization and Analytics22 citations

TL;DR

This paper introduces a statistical model—stellar mass assembly distribution (SMAD)—that links galaxy stellar mass growth to dark matter halo properties across cosmic time. By integrating SMAD over N-body halo merger trees and applying stellar population synthesis models, the framework qualitatively reproduces the bimodal clustering of galaxies by specific star formation rate, demonstrating that halo mass accretion history correlations naturally produce galactic conformity and higher-order statistics without ad hoc assumptions.

ABSTRACT

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.

Motivation & Objective

• To develop a statistically grounded, empirically motivated model for galaxy-halo connection across cosmic time.
• To investigate how halo mass accretion histories influence galaxy stellar mass assembly and observed clustering patterns.
• To test whether simple coupling of stellar mass growth to halo evolution can reproduce observed bimodal galaxy statistics like sSFR bimodality and galactic conformity.
• To provide a framework for fitting SMAD parameters directly to observational data, such as clustering and lensing.
• To enable predictions of galaxy colors, spectra, SN rates, and star formation rate density using SPS models.

Proposed method

• Define the stellar mass assembly distribution (SMAD), $ P(dM_{*}/dt|\mathbf{X},a) $, as a probability density function for stellar mass growth rates given halo properties $ \mathbf{X} $ and redshift $ a $.
• Use the median stellar mass assembly rate from Behroozi et al. (2013a) as a constraint to parameterize the SMAD, assuming it applies to individual halo histories.
• Integrate the SMAD over individual halo merger trees from high-resolution N-body simulations starting at $ z = 4 $, accounting for halo mergers via simple rules.
• Apply stellar population synthesis (FSPS) models with Chabrier IMF and solar metallicity to convert star formation histories into observable colors and spectra.
• Post-process the resulting stellar mass and SFR histories to compute galaxy colors and clustering statistics, comparing to SDSS mock catalogs.
• Use projected correlation functions and color distributions to validate model predictions against local galaxy population statistics.

Experimental results

Research questions

• RQ1 Can a statistical model that directly couples galaxy stellar mass assembly to halo mass accretion histories reproduce the observed bimodal clustering of galaxies by specific star formation rate?
• RQ2 To what extent can halo mass accretion history correlations with large-scale environment naturally explain galactic conformity signals?
• RQ3 How well does a simple SMAD model, parameterized from median assembly rates, reproduce the color and clustering properties of low-redshift galaxies?
• RQ4 What are the limitations of this approach when compared to observed SDSS data, particularly in reproducing the star-forming sequence and color bimodality?
• RQ5 Can this framework be extended to model stochasticity, post-peak mass evolution, or merger-induced starbursts to improve agreement with observations?

Key findings

• The model qualitatively reproduces the bimodal clustering of galaxies as a function of specific star formation rate, indicating that halo mass accretion history correlations can naturally produce higher-order statistics like galactic conformity.
• The model produces color bimodality, with the strength increasing at lower stellar masses, though low-mass central galaxies are too red compared to SDSS mock catalogs.
• The star-forming sequence in the model appears too quenched, suggesting that the current SMAD parameterization underestimates star formation rates in low-mass halos.
• The model consistently produces red satellites across all stellar masses, consistent with environmental quenching effects.
• The framework successfully predicts galaxy colors and spectra using FSPS, demonstrating its utility for broad-band photometry and SNe rate modeling.
• Future work to directly fit SMAD parameters to observational clustering, lensing, and redshift-space distortion data is expected to significantly improve model accuracy.