Study on the mapping of halo clustering from real space to redshift space

Abstract

The mapping of galaxy clustering from real space to redshift space introduces the anisotropic property to the measured galaxy density power spectrum in redshift space, known as the redshift space distortion (RSD) effect. The mapping formula is intrinsically non-linear, which is complicated by the higher order polynomials due to indefinite orders of cross correlations between density and velocity fields, and the Finger-of-God (FoG) effect due to the randomness of the galaxy peculiar velocity field. In previous works, we have verified the robustness of advanced TNS mapping formula in our hybrid RSD model in dark matter case, where the halo bias models are not taken into account for the halo mapping formula in redshift space. Using 100 realizations of halo catalogs in N-body simulations, we find that our halo RSD model with the known halo bias model and the effective FoG function accurately predicts the halo power spectrum measurements, within 1∼2% accuracy up to k ∼ 0.2 h Mpc −1 , depending on different halo masses and redshifts. Theoretical RSD model for halo clusteringUnderstanding the halo clustering in redshift space is a key stepstone towards theoretically describing the observed galaxy clustering in the Universe. In our previous work [96], the RSD model for dark matter clustering in redshift space was studied in detail. The model has been proved to accurately reconstruct the linear growth rate within 1% at k < 0.18 h Mpc −1 for simulations of different cosmologies with different Hubble parameters [97]. This theoretical RSD model will be applied to the halo clustering case in this manuscript. We will describe the RSD model in this section. Besides, the halo density bias model [108] and halo velocity bias model [105] adopted in this paper will be presented as well. The advanced TNS model for halosMatter distribution in the universe is inhomogeneous at small scales. The gravitational attraction arising from this inhomogeneity perturbs galaxies and causes their motions deviating from the Hubble flow. These deviations, named peculiar velocities of galaxies, disturb the galaxy redshifts and hence the galaxy distribution in redshift space in an anisotropic way.

Assessing non-linear models for galaxy clustering III: theoretical accuracy for stage IV surveys

“…Further, loop corrections in the perturbative part can be added to improve its modelling of the small scales at the considered redshifts. Alternatively, these corrections can be calibrated by simulations [43,44]. The model has also been already extended to general theories of gravity and dark energy [22,23].…”

Quantification of the multi-streaming effect in redshift space distortion

“…Meanwhile, one of the authors has tested the TNS-based [33] dark matter clustering mapping formula from real to redshift space in [58]. The halo density bias and the halo clustering mapping formula of this model will be tested in [59]. However, these investigations so far overlook an important physical process of non-linear structure formation, namely the shell crossing and the resultant multi-streaming effect.…”

Expansion series of the pairwise velocity generating function and its implications on redshift space distortion modeling

“…The above results are widely known in the literature (e.g., Scoccimarro 2004). Several models of RSD are based upon Equation ( 6), or Equation ( 5) or its equivalent forms (e.g., Scoccimarro 2004;Matsubara 2008;Taruya et al 2010;Seljak & McDonald 2011;Okumura et al 2012a;Zhang et al 2013;Zheng et al 2013;Zheng & Song 2016;Song et al 2018;Zheng et al 2019).…”