Priors on red galaxy stochasticity from hybrid effective field theory

Abstract

We investigate the stochastic properties of typical red galaxy samples in a controlled numerical environment. We use Halo Occupation Distribution (HOD) modelling to create mock realizations of three separate bright red galaxy samples consistent with datasets used for clustering and lensing analyses in modern galaxy surveys. Second-order Hybrid Effective Field Theory (HEFT) is used as a field-level forward model to describe the full statistical distribution of these tracer samples, and their stochastic power spectra are directly measured and compared to the Poisson shot-noise prediction. While all of the galaxy samples we consider are hosted within haloes with sub-Poisson stochasticity, we observe that the galaxy samples themselves possess stochasticities that range from sub-Poisson to super-Poisson, in agreement with predictions from the halo model. As an application of our methodology, we place priors on the expected degree of non-Poisson stochasticity in cosmological analyses using such samples. We expect these priors will be useful in reducing the complexity of the full parameter space for future analyses using second-order Lagrangian bias models. More generally, the techniques outlined here present the first application of hybrid EFT methods to characterize models of the galaxy-halo connection at the field level, revealing new connections between once-disparate modelling frameworks.

The effective field theory of large-scale structure and multi-tracer

“…By considering two populations of galaxies separated by color and not two populations of halos separated by their masses, we are mixing the masses of the host halos. In that way, we expect to find a non-vanishing stochastic term in the cross spectrum [71].…”

“…to the fact that the halo model [70] predicts a value that is considerably smaller than all other stochastic terms [36], lead us to neglect this term in our main results. We studied the parameter space and concluded that including the cross-stochastic term as free parameter can mildly impact the multi-tracer performance (see figure 6), indicating that one should look for well-motivated priors in order to better leverage the available information, akin done by [71]. We include in appendix C an analysis with galaxies that include the cross-stochastic term, in which we populate our halos using a halo occupation distribution.…”

Cosmological constraints from the tomographic cross-correlation of DESI Luminous Red Galaxies and Planck CMB lensing

“…[99,100]. For the shot-noise term we choose a Gaussian prior on SN, centered on the Poisson value (table 1) with a width of 30% [101]. For the slope of the number counts (s µ ) we use a Gaussian prior centered on the measured value (table 1) with a width of 0.1.…”

Cosmological Analysis of Three-Dimensional BOSS Galaxy Clustering and Planck CMB Lensing Cross Correlations via Lagrangian Perturbation Theory

“…[24] with two exceptions: we have narrowed the counterterm α n priors in the view that they are in any case sufficiently well constrained by the data that the priors are uninformative, and that they should represent only modest corrections to linear theory on scales where perturbation theory is valid. We have also updated the prior on the isotropic stochastic term R 3 h for the higher-redshift sample to better reflect the effective number density of the z3, where n−1 ≈ 6000 h −3 Mpc 3 , such that the priors on R 3 h in both z1 and z3 reflect the latest studies on stochasticity in BOSS-like galaxies [108]. Adopting these new priors shift our constraints on σ 8 by roughly 0.2 σ, with all other parameters essentially unaffected, compared to ref.…”

“…14 we show the fractional change in including higher order bias operators in the model for C gκ for a DESI-like sample of galaxies cross-correlated with Planck and SO CMB lensing. The bias parameters used are derived from the field-level inference of [108] for a DESI-like HOD. The binning adopted uses bins ∆ ≈ 3 √ , and each error bar should be thought of as an independent data point.…”