Multiple streaming and the probability distribution of density in redshiftspace

We examine several aspects of redshift distortions by expressing the redshi ft-space density in terms of the eigenvalues and orientation of the local L agrangian deformation tensor. We explore the importance of multiple streami ng using the Zeldovich approximation (ZA), and compute the average number o f streams in both real and redshift space. We find that multiple streaming can be significant in redshift space but negligible in real space, even at moderate values of the linear fluctuation amplitude (sigma(l) less than or similar to 1). Moreover, unlike their real-space counterparts, redshift-spa ce multiple streams can how past each other with minimal interactions. Such nonlinear redshift-space effects, which are physically distinct from the f ingers-of-God due to small-scale virialized motions, might in part explain the well-known departure of redshift distortions from the classic linear pr ediction by Kaiser, even at relatively large scales where the corresponding density held in real space is well described by linear perturbation theory . We also compute, using the ZA, the probability distribution function (PDF ) of the density, as well as S-3, in real and redshift space, and compare i t with the PDF measured from N-body simulations. The role of caustics in de fining the character of the high-density tail is examined. We find that (no n-Lagrangian) smoothing, due to both finite resolution or discreteness and small-scale velocity dispersions, is very effective in erasing caustic stru ctures, unless the initial power spectrum is sufficiently truncated.