Redshift space correlations and scale-dependent stochastic biasing of density peaks

الأصل · EN

We calculate the redshift space correlation function and the power spectrum of density peaks of a Gaussian random field. In the linear regime k < 0.1 h/Mpc, the redshift space power spectrum is Pˢpk(k,u) = exp(-f² svel² k² u²) * [bpk(k) + bvel(k) f u²]² * Pₘ(k), where u is the angle with respect to the line of sight, svel is the one-dimensional velocity dispersion, f is the growth rate, and bpk(k) and bvel(k) are k-dependent linear spatial and velocity bias factors. For peaks, the value of svel depends upon the functional form of bvel. The peaks model is remarkable because it has unbiased velocities -- peak motions are driven by dark matter flows -- but, in order to achieve this, bvel is k-dependent. We speculate that this is true in general: k-dependence of the spatial bias will lead to k-dependence of bvel even if the biased tracers flow with the dark matter. Because of the k-dependence of the linear bias parameters, standard manipulations applied to the peak model will lead to k-dependent estimates of the growth factor that could erroneously be interpreted as a signature of modified dark energy or gravity. We use the Fisher formalism to show that the constraint on the growth rate f is degraded by a factor of two if one allows for a k-dependent velocity bias of the peak type. We discuss a simple estimate of nonlinear evolution and illustrate the effect of the peak bias on the redshift space multipoles. For k < 0.1 h/Mpc, the peak bias is deterministic but k-dependent, so the configuration space bias is stochastic and scale dependent, both in real and redshift space. We provide expressions for this stochasticity and its evolution (abridged).