ON THE VALIDITY OF THE STREAMING MODEL FOR THE REDSHIFT-SPACE CORRELATION-FUNCTION IN THE LINEAR REGIME

The relation between the galaxy correlation functions in real-space an d redshift-space is derived in the linear regime by an appropriate ave raging of the joint probability distribution of density and velocity. The derivation recovers the familiar linear theory result on large sca les but has the advantage of clearly revealing the dependence of the r edshift distortions on the underlying peculiar velocity field; streami ng motions give rise to distortions of O(Omega(0.6)/b) while variation s in the anisotropic velocity dispersion yield terms of order O(Omega( 1.2)/b(2)). This probabilistic derivation of the redshift-space correl ation function is similar in spirit to the derivation of the commonly used ''streaming'' model, in which the distortions are given by a conv olution of the real-space correlation function with a velocity distrib ution function. The streaming model is often used to model the redshif t-space correlation function on small, highly nonlinear, scales. There have been claims in the literature, however, that the streaming model is not valid in the linear regime. Our analysis confirms this claim, but we show that the streaming model can be made consistent with linea r theory provided that the model for the streaming has the functional form predicted by linear theory and that the velocity distribution is chosen to be a Gaussian with the correct linear theory dispersion.