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

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-O(g) O that describe the response of the HODs to long-wavelength perturbations O. The linear galaxy bias parameters b(O)(g) are a weighted version of b(O)(h) + R-O(g), where b(O)(h) is the halo bias, but the contribution from R-O(g) is routinely ignored in the literature. We investigate the impact of this by measuring the R-O(g) in separate universe simulations of the IllustrisTNG model for three types of perturbations: total matter perturbations, O = delta(m); baryon-CDM compensated isocurvature perturbations, O = sigma; and potential perturbations with local primordial non-Gaussianity, O proportional to integral (NL)phi. Our main takeaway message is that the R-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 O 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-O(g) recovers the measured b(O)(g) well, which indicates that R-O(g) can be easily added to HM/HOD studies as a new ingredient.

Automated summary

Halo occupation distribution (HOD) models are widely used in galaxy-halo connection studies, and in this study, we introduce and investigate HOD response functions R-O(g) to long-wavelength perturbations. The results show that the impact of HOD response on bias parameters should be estimated case by case, with significant effects on stellar-mass selected galaxies and minor effects on gas distribution bias.