摘要
We explore features of redshift distortion in Fourier analysis of N-body simulations. The phases of the Fourier modes of dark matter density fluctuation are generally shifted by the peculiar motion along the line of sight, the induced phase shift is stochastic and has a probability distribution function （PDF） that is symmetric about the peak at zero shift and whose exact shape depends on the wave vector, except on very large scales where phases are invariant by linear perturbation theory. Analysis of the phase shifts motivates our phenomenological models for the bispectrum in redshift space. Comparison with simulations shows that our toy models are very successful in modeling bispectrum of equilateral and isosceles trian- gles at large scales. In the second part we compare the monopole of the power spectrum and bispectrum in the radial and plane-parallel distortion to test the plane-parallel approximation. We confirm the results of Scoccimarro that difference of power spectrum is at the level of 10%, and, in the reduced bispectrum, the difference is as small as a few percent. However, on the plane perpendicular to the line of sight of kz = 0, the difference in power spectrum be- tween the radial and plane-parallel approximation can be more than - 10%, and even worse on very small scales. Such difference is prominent for bispectrum, especially for configura- tions of tilted triangles. Non-Ganssian signals under the radial distortion on small scales are systematically biased downside than are in the plane-parallel approximation, with amplitudes depending on the opening angle of the sample point to the observer. This observation gives warning to the practice of using the power spectrum and bispectrum measured on the kz = 0 plane as estimates of the real space statistics.
We explore features of redshift distortion in Fourier analysis of N-body simulations. The phases of the Fourier modes of dark matter density fluctuation are generally shifted by the peculiar motion along the line of sight, the induced phase shift is stochastic and has a probability distribution function （PDF） that is symmetric about the peak at zero shift and whose exact shape depends on the wave vector, except on very large scales where phases are invariant by linear perturbation theory. Analysis of the phase shifts motivates our phenomenological models for the bispectrum in redshift space. Comparison with simulations shows that our toy models are very successful in modeling bispectrum of equilateral and isosceles trian- gles at large scales. In the second part we compare the monopole of the power spectrum and bispectrum in the radial and plane-parallel distortion to test the plane-parallel approximation. We confirm the results of Scoccimarro that difference of power spectrum is at the level of 10%, and, in the reduced bispectrum, the difference is as small as a few percent. However, on the plane perpendicular to the line of sight of kz = 0, the difference in power spectrum be- tween the radial and plane-parallel approximation can be more than - 10%, and even worse on very small scales. Such difference is prominent for bispectrum, especially for configura- tions of tilted triangles. Non-Ganssian signals under the radial distortion on small scales are systematically biased downside than are in the plane-parallel approximation, with amplitudes depending on the opening angle of the sample point to the observer. This observation gives warning to the practice of using the power spectrum and bispectrum measured on the kz = 0 plane as estimates of the real space statistics.
基金
Supported by the National Natural Science Foundation of China.
