Scaling Properties of the Redshift Power Spectrum: Theoretical Models

We report the results of an analysis of the redshift power spectrum PS(k,μ) in three typical cold dark matter (CDM) cosmological models, where μ is the cosine of the angle between the wavevector and the line of sight. Two distinct biased tracers derived from the primordial density peaks of Bardeen et al. and the cluster-underweight model of Jing, Mo, & Börner are considered in addition to the pure dark matter models. Based on a large set of high-resolution simulations, we have measured the redshift power spectrum for the three tracers from the linear to the nonlinear regime. We investigate the validity of the relation (guessed from linear theory) in the nonlinear regime, PS(k,μ) = PR(k)[1 + βμ2]2D(k,μ,σ12(k)), where PR(k) is the real-space power spectrum and β = Ω/bl. The damping function D, which should generally depend on k, μ, and σ12(k), is found to be a function of only one variable, kμσ12(k). This scaling behavior extends into the nonlinear regime, while D can be accurately expressed as a Lorentz function, well known from linear theory, for values of D > 0.1. The difference between σ12(k) and the pairwise velocity dispersion defined by the three-dimensional peculiar velocity of the simulations (taking r = 1/k) is about 15%. Therefore, σ12(k) is a good indicator of the pairwise velocity dispersion. The exact functional form of D depends on the cosmological model and on the bias scheme. We have given an accurate fitting formula for the functional form of D for the models studied.