We report the results of an analysis of the redshift power spectrum P ^ { S } ( k, \mu ) in three typical Cold Dark Matter ( CDM ) cosmological models , where \mu is the cosine of the angle between the wave vector 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

P ^ { S } ( k, \mu ) = P ^ { R } ( k ) [ 1 + \beta \mu ^ { 2 } ] ^ { 2 } D ( k, \mu, \sigma _ { 12 } ( k ) ) , where P ^ { R } ( k ) is the real space power spectrum , and \beta equals \Omega _ { 0 } ^ { 0.6 } / b _ { l } .
The damping function D which should generally depend on k , \mu , and \sigma _ { 12 } ( k ) , is found to be a function of only one variable k \mu \sigma _ { 12 } ( 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 D > 0.1 .
The difference between \sigma _ { 12 } ( k ) and the pairwise velocity dispersion defined by the 3–D peculiar velocity of the simulations ( taking r = 1 / k ) is about 15 \% .
Therefore \sigma _ { 12 } ( 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 .