Open AccessNon‐linear redshift distortions: the two‐point correlation function
Author(s) -
Bharadwaj Somnath
Publication year - 2001
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2001.04738.x
Subject(s) - physics , redshift , astrophysics , correlation function (quantum field theory) , spectral density , distortion (music) , degeneracy (biology) , redshift space distortions , space (punctuation) , cosmology , statistical physics , redshift survey , quantum mechanics , galaxy , statistics , amplifier , bioinformatics , linguistics , philosophy , mathematics , optoelectronics , cmos , dielectric , biology
We consider a situation where the density and peculiar velocities in real space are linear, and we calculate ξ s , the two‐point correlation function in redshift space, incorporating all non‐linear effects which arise as a consequence of the map from real to redshift space. Our result is non‐perturbative and it includes the effects of possible multi‐streaming in redshift space. We find that the deviations from the predictions of the linear redshift distortion analysis increase for the higher spherical harmonics of ξ s . While the deviations are insignificant for the monopole ξ 0 , the hexadecapole ξ 4 exhibits large deviations from the linear predictions. For a COBE normalized , cold dark matter (CDM) power spectrum, our results for ξ 4 deviate from the linear predictions by a factor of two on the scale of ∼10 h −1 Mpc. The deviations from the linear predictions depend separately on f (Ω) and b . This holds the possibility of removing the degeneracy that exists between these two parameters in the linear analysis of redshift surveys which yields only . We also show that the commonly used phenomenological model, where the non‐linear redshift two‐point correlation function is calculated by convolving the linear redshift correlation function with an isotropic pair velocity distribution function, is a limiting case of our result.