Multiple-streaming and the Probability Distribution of Density in Redshift Space

We examine several aspects of redshift distortions by expressing the redshiftspace density in terms of the eigenvalues and orientation of the local Lagrangian deformation tensor. We explore the importance of multiple-streaming using the Zel’dovich approximation (ZA), and compute the average number of streams in both real and redshift-space. It is found that multiple-streaming can be significant in redshift-space but negligible in real-space, even at moderate values of the linear fluctuation amplitude (σl < ∼ 1). Moreover, unlike their real-space counterparts, redshift-space multiple-streams can flow past each other with minimal interactions. Such nonlinear redshift-space effects, which are physically distinct from the fingers-of-God due to small-scale virialized motions, might in part explain the well-known departure of redshift distortions from the classic linear prediction by Kaiser (1987), even at relatively large scales where the corresponding density field in real-space is well described by linear perturbation theory. We also compute using the ZA the probability distribution function (PDF) of density, as well as S3, in real and redshift-space, and compare it with the PDF measured from N-body simulations. The role of caustics in defining the character of the high density tail is examined. It is found that (non-Lagrangian) smoothing, due to both finite resolution or discreteness and small-scale velocity dispersions, is very effective in erasing caustic structures, unless the initial power spectrum is sufficiently truncated. Subject headings: cosmology: theory — gravitation — large-scale structure of universe NASA/Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, Batavia, IL 60510; e-mail: [email protected] CITA, 60 St. George St., Toronto, M5S 3H8, Canada; e-mail: [email protected] Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045; e-mail: [email protected]