Velocity Dispersion and the Redshift-Space Power Spectrum

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Abstract
A large (N ~ 17 × 106) high-resolution N-body simulation of a standard cold dark matter (CDM) universe is used to investigate the effects of peculiar velocities on the power spectrum of galaxies in redshift space. The unprecedented dynamical range of the simulation code allows galaxy halos to be resolved in the numerical data while maintaining good statistical sampling on large scales. We present evidence that the redshift-space power spectrum Ps(k) can be related to its real-space counterpart by means of a simple filter function which reflects both small-scale velocity dispersion and large-scale linear flows. After transformation to redshift space, we find that the power spectrum is insensitive to the normalization of the CDM model at scales below 20 h-1 Mpc. Hence Ps(k) does not provide an unambiguous cosmological constraint at small scales. Nonetheless, it is significant that the redshift-space power spectra from CDM models with two different normalizations both compare remarkably well with results from the galaxies in the IRAS 1.2 Jy survey (Fisher et al.) on scales between 1 and 50 h-1 Mpc. By excluding a fraction of the most tightly bound halos, we create a galaxy catalog with 80% of the original objects in the lower normalization model that matches both the IRAS power spectrum and the inferred pairwise velocity dispersion on megaparsec scales. Thus, in contrast to previous reports, we find that the CDM scenario does not produce excess power at small scales.