Responses of Halo Occupation Distributions: a new ingredient in the halo model & the impact on galaxy bias

TL;DR

This paper introduces HOD response functions to long-wavelength perturbations, demonstrating their significant impact on galaxy bias calculations and proposing their inclusion as a new element in halo model analyses.

Contribution

The study develops and measures HOD response functions, showing they are crucial for accurate galaxy bias modeling and should be incorporated into halo model frameworks.

Findings

HOD responses are significant for stellar-mass selected galaxies.

Responses R_φ^g and R_σ^g notably affect bias parameters related to inflation.

R_1^g has a minimal impact on linear galaxy bias.

Abstract

Halo occupation distribution (HOD) models describe the number of galaxies that reside in different haloes, and are widely used in galaxy-halo connection studies using the halo model (HM). Here, we introduce and study HOD response functions $R_\mathcal{O}^g$ that describe the response of the HODs to long-wavelength perturbations $\mathcal{O}$. The linear galaxy bias parameters $b_\mathcal{O}^g$ are a weighted version of $b_\mathcal{O}^h + R_\mathcal{O}^g$, where $b_\mathcal{O}^h$ is the halo bias, but the contribution from $R_\mathcal{O}^g$ is routinely ignored in the literature. We investigate the impact of this by measuring the $R_\mathcal{O}^g$ in separate universe simulations of the IllustrisTNG model for three types of perturbations: total matter perturbations, $\mathcal{O}=\delta_m$; baryon-CDM compensated isocurvature perturbations, $\mathcal{O}=\sigma$; and potential perturbations with local primordial non-Gaussianity, $\mathcal{O}\propto f_{\rm NL}\phi$. Our main takeaway message is that the $R_\mathcal{O}^g$ are not negligible in general and their size should be estimated on a case-by-case basis. For stellar-mass selected galaxies, the responses $R_\phi^g$ and $R_\sigma^g$ are sizeable and cannot be neglected in HM calculations of the bias parameters $b_\phi^g$ and $b_\sigma^g$; this is relevant to constrain inflation using galaxies. On the other hand, we do not detect a strong impact of the HOD response $R_1^g$ on the linear galaxy bias $b_1^g$. These results can be explained by the impact that the perturbations have on stellar-to-total-mass relations. We also look into the impact on the bias of the gas distribution and find similar conclusions. We show that a single extra parameter describing the overall amplitude of $R_\mathcal{O}^g$ recovers the measured $b_\mathcal{O}^g$ well, which indicates that $R_\mathcal{O}^g$ can be easily added to HM/HOD studies as a new ingredient.