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

Abstract

Abstract The pairwise velocity generating function G has a deep connection with both the pairwise velocity probability distribution function and modeling of redshift space distortion (RSD). Its implementation into RSD modeling is often faciliated by expansion into a series of pairwise velocity moments 〈 v 12 n 〉 . Motivated by the logrithmic transformation of the cosmic density field, we investigate an alternative expansion into series of pairwise velocity cumulants 〈 v 12 n 〉 c . We numerically evaluate the convergence rate of the two expansions, with three 30723 particle simulations of the CosmicGrowth N-body simulation series. (1) We find that the cumulant expansion performs significantly better, for all the halo samples and redshifts investigated. (2) For modeling RSD at k ∥ < 0.1h Mpc−1, including only the n = 1,2 cumulants is sufficient. (3) But for modeling RSD at k ∥ = 0.2h Mpc−1, we need and only need the n = 1,2,3,4 cumulants. These results provide specific requirements on RSD modeling in terms of m-th order statistics of the large-scale structure.