Responses of Halo Occupation Distributions: a new ingredient in the halo model & the impact on 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 \U0001d4aa g that describe the response of the HODs to long-wavelength perturbations \U0001d4aa. The linear galaxy bias parameters b \U0001d4aa g are a weighted version of b \U0001d4aa h + R \U0001d4aa g , where b \U0001d4aa h is the halo bias, but the contribution from R \U0001d4aa g is routinely ignored in the literature. We investigate the impact of this by measuring the R \U0001d4aa g in separate universe simulations of the IllustrisTNG model for three types of perturbations: total matter perturbations, \U0001d4aa = δ h ; baryon-CDM compensated isocurvature perturbations, \U0001d4aa = σ; and potential perturbations with local primordial non-Gaussianity, \U0001d4aa ∝ f NLϕ. Our main takeaway message is that the R \U0001d4aa 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 \U0001d4aa g and R σ g are sizeable and cannot be neglected in HM calculations of the bias parameters b ϕ g and b σ 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 \U0001d4aa 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 \U0001d4aa g recovers the measured b \U0001d4aa g well, which indicates that R \U0001d4aa g can be easily added to HM/HOD studies as a new ingredient.