Perturbation theory for modeling galaxy bias: validation with simulations of the Dark Energy Survey

Abstract

We describe perturbation theory (PT) models of galaxy bias for applications to photometric galaxy surveys. We model the galaxy-galaxy and galaxy-matter correlation functions in configuration space and validate against measurements from mock catalogs designed for the Dark Energy Survey (DES). We find that an effective PT model with five galaxy bias parameters provides a good description of the 3D correlation functions above scales of 4 Mpc/h and z < 1. Our tests show that at the projected precision of the DES-Year 3 analysis, two of the non-linear bias parameters can be fixed to their co-evolution values, and a third (the k 2 term for higher derivative bias) set to zero. The agreement is typically at the 2 percent level over scales of interest, which is the statistical uncertainty of our simulation measurements. To achieve this level of agreement, our fiducial model requires using the full non-linear matter power spectrum (rather than the 1-loop PT one). We also measure the relationship between the non-linear and linear bias parameters and compare them to their expected co-evolution values. We use these tests to motivate the galaxy bias model and scale cuts for the cosmological analysis of the Dark Energy Survey; our conclusions are generally applicable to all photometric surveys.

Dark Energy Survey Year 3 Results: Constraints on cosmological parameters and galaxy bias models from galaxy clustering and galaxy-galaxy lensing using the redMaGiC sample

“…We use a five-parameter description of galaxy bias per redshift bin, with three of the parameters fixed based on theoretical considerations. We validated these choices using mock catalogs built on N-body simulations as detailed in our earlier study [87] and Section §IV C. We carry out two analyses: the first using linear bias with more conservative scale cuts, and the second using the full PT bias model going down to smaller scales. Other elements of our model include intrinsic alignments, magnification and "point mass marginalization" (see §II B).…”

“…We use a hybrid 1-loop perturbation theory model for galaxy bias, capturing the non-linear contributions to the overdensity field till third order. We have tested and validated our model using 3dimensional correlation functions from DES-mock catalogs in Pandey et al [87] as well as with projected statistics in DeRose et al [26]; in this study, we validate the bias model with mocks for the 2 × 2pt redMaGiC datavector at scales above 4Mpc/ℎ. This validation presented here, along with results in Pandey et al [87], are then also directly used to validate non-linear bias model for MagLim datavector.…”

“…and 𝑃 s 2 s 2 are described in [95] and are calculable from the linear matter power spectrum. We validated this model in [87] using 3D correlation functions, 𝜉 gg and 𝜉 gm , of redMaGiC galaxies measured in DES-like simulations. These configuration space statistics are the Fourier transforms of the power spectra mentioned above.…”

“…From a joint analysis of 3D galaxy-galaxy and galaxy-matter correlation functions at fixed cosmology in simulations [87], we find that the linear bias model is a good description above 8Mpc/ℎ while the two-parameter non-linear bias model describes the correlations above 4Mpc/ℎ. We convert these physical co-moving distances to angular scale cuts for each tomographic bin and treat them as starting guesses.…”

The PDF perspective on the tracer-matter connection: Lagrangian bias and non-Poissonian shot noise

“…At small scales, this picture of linear bias must be corrected due to halo exclusion and non-linear biasing effects (see e.g. Baldauf et al 2016;Desjacques et al 2018;Ivanov et al 2020;Pandey et al 2020;Baldauf et al 2021). Even the simple linear bias model renders the amplitude of the galaxy clustering correlation function useless for inferring cosmological information.…”