Non-linear redshift distortions: the two-point correlation function |
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| Authors: | Somnath Bharadwaj |
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| Institution: | Department of Physics and Meteorology and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur 721 302, India |
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| Abstract: | 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. |
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| Keywords: | galaxies: clusters: general galaxies: distances and redshifts cosmology: observations cosmology: theory dark matter large-scale structure of Universe |
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