Characterizing the Conditional Galaxy Property Distribution Using Gaussian Mixture Models

Line-intensity mapping (LIM) is a promising technique to constrain the global distribution of galaxy properties. To combine LIM experiments probing different tracers with traditional galaxy surveys and fully exploit the scientific potential of these observations, it is necessary to have a physically motivated modeling framework. As part of developing such a framework, in this work, we introduce and model the conditional galaxy property distribution (CGPD), i.e., the distribution of galaxy properties conditioned on the host halo mass and redshift. We consider five galaxy properties, including the galaxy stellar mass, molecular gas mass, galaxy radius, gas-phase metallicity, and star formation rate (SFR), which are important for predicting the emission lines of interest. The CGPD represents the full distribution of galaxies in the five-dimensional property space; many important galaxy distribution functions and scaling relations, such as the stellar mass function and SFR main sequence, can be derived from integrating and projecting it. We utilize two different kinds of cosmological galaxy simulations, a semi-analytic model and the IllustrisTNG hydrodynamic simulation, to characterize the CGPD and explore how well it can be represented using a Gaussian mixture model (GMM). We find that with just a few (approximately three) Gaussian components, a GMM can describe the CGPD of the simulated galaxies to high accuracy for both simulations. The CGPD can be mapped to LIM or other observables by constructing the appropriate relationship between galaxy properties and the relevant observable tracers, which will be discussed in future works.