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 𝒪 g 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 = δ h ; baryon-CDM compensated isocurvature perturbations, 𝒪 = σ; and potential perturbations with local primordial non-Gaussianity, 𝒪 ∝ f NLϕ. 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 𝒪 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 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.

Large-scale dark matter simulations

“…10 Schematic illustration of various kinds of Separate Universe simulations. Structure formation embedded into a large-scale fluctuation d L is equivalent to that of a simulation with a modified background matter parameter, q m ; structure formation with inside large-scale compensated isocurvature fluctuation, r L is equivalent to a modification in the background baryon and cold dark matter densities, q c and q m ; and finally structure formation inside a large potential fluctuation, as originated by primordial non-gaussianity, can be captured in the Separate Universe formalism by a change in the amplitude of fluctuations A s Image reproduced with permission from Voivodic and Barreira (2021), copyright by IOP…”

The local PNG bias of neutral Hydrogen, ${\rm H_I}$

“…The halo model is a useful tool to guide the interpretation of our numerical results. Assuming that all of the H I is inside halos with some mass M h , then b φ can be written as [48] b…”

“…This response function is an ingredient that is often ignored in the literature, but which must be present in general to account for the modulation of M HI (M h ) by f nl φ, in the same way that b h φ accounts for the same modulation of the halo mass function; see Ref. [48] for more details. We have evaluated Eq.…”

“…These separate universe simulations have been presented for the first time in Ref. [37] (to which we refer the reader for more details), and used in previous works already to study galaxy bias [34] and halo occupation distribution responses [48]. In our results below we analyse the simulation outputs at redshifts z = 0, 0.5, 1, 2, 3.…”

“…Similarly to as discussed in the last section for b φ , here too the halo model is a useful tool to interpret our numerical results. The halo model expression for b φδ is given by [48] b HI φδ (z) =…”