Clustering analysis of BOSS-CMASS galaxies with semi-analytical model for galaxy formation and halo occupation distribution

TL;DR

This paper cross-validates two approaches to modeling galaxy–halo connections by applying both a halo occupation distribution (HOD) and a Galacticus semi-analytical model (SAM) to CMASS galaxy clustering at non-linear scales. An emulator-based inference framework, augmented by a velocity-field parameter $\gamma_{f}$ related to $f\sigma_{8}$, enables joint constraints on cosmology and galaxy formation physics using the same CMASS data and a single cosmology simulation. The results show that the HOD and SAM yield broadly consistent cosmological inferences, though the SAM constraints are weaker due to emulator accuracy and model flexibility; SAM indicates higher satellite fractions and specific parameter sensitivities tied to star formation and cooling processes. The work highlights the value of cross-model comparisons and joint clustering–abundance analyses to robustly constrain galaxy formation physics and cosmic growth, pointing to future gains from expanding training sets, incorporating additional observables, and building cosmology–SAM emulator suites.

Abstract

The spatial distribution of massive and luminous galaxies have provided important constraints on the fundamental cosmological parameters and physical processes governing galaxy formation. In this work, we construct and compare independent galaxy-halo connection models in the application of clustering measurement at non-linear scales of BOSS-CMASS galaxies. In particular, we adopt a halo occupation distribution (HOD) model with 11 parameters and a semi-analytical model (SAM) with 16 parameters to describe the galaxy two point correlation function. With an empirical parameterization for the velocity field to model the redshift space distortion effect and the emulator technique, we can explore the parameter space of both models. We find that the HOD model is able to recover the underlying velocity field of SAM with an accuracy of 3\%, and can be improved to 1\% when the analysis is restricted to scales above 1$h^{-1}$Mpc. The comparison is based on multiple samplings in the parameter space which can verify the convergence of the models. Then we perform constraints on the model parameters using clustering measurement of CMASS galaxies. Although limited by the emulator accuracy and the flexibility of the model, we find that the clustering measurement is capable of constraining a subset of the SAM parameters, especially for components sensitive to the star formation rate. This result leads us to anticipate that a joint analysis of both clustering and abundance measurements can significantly constrain the parameters of galaxy formation physics, which requires further investigation from both theoretical and observational aspects.

Figures (11)

• Figure 1: The 2-point correlation function ($w_{p}, \xi_{0}$ and $\xi_{2}$) predicted from the HOD and SAM model, respectively, compared with the measurement from BOSS-CMASS galaxy sample. The HOD model has 4000 sampling in the parameter space, while the Galacticus SAM has 500 sampling. It is clear that the range of the parameters of both models can produce clustering results to encompass the observed measurement.
• Figure 2: The GP-based emulator error of the two-point correlation function using HOD and SAM models, respectively. The HOD model uses 80% of the mocks for training, while SAM model uses 90% for training, and the rest are used to quantify the emulator error. The lines show the inner 68% of the fractional difference from all the test samples. For comparison, the input training error and the uncertainty from BOSS galaxies are also shown.
• Figure 3: The halo occupation distribution predicted by the Galacticus SAM for central and satellite galaxies. The mocks are selected by stellar mass until the sample reaches the required number density, which is allowed to vary in the range [$1.5\times 10^{-4}, 4.5\times10^{-4}$] ($h^{-1}$Mpc)$^{-3}$.
• Figure 4: Satellite fraction of the galaxy mocks predicted from both HOD and SAM models. The histogram has been normalized by the total number of models.
• Figure 5: The fitting results of all the 500 SAM mocks with the HOD model. $Left:$ distribution of $\chi^{2}_{\mathrm{min}}$ to represent the goodness of fit, $Right:$ distribution of $\gamma_{f}$, the velocity scaling parameter. The top panels show results using 2PCF within scales from 0.1 to 60 $h^{-1}$Mpc, while the bottom panels show results without using the scales below 1$h^{-1}$Mpc.