Reconstructing the IRAS Point Source Catalog Redshift Survey with a generalized PIZA

Abstract

ABSTRA C T We present a generalized version of the path interchange Zel’dovich approximation (PIZA), for use with realistic galaxy redshift surveys. PIZA is a linear particle-based Lagrangian method which uses the present-day positions of galaxies to reconstruct both the initial density field and the present-day peculiar velocity field. We generalize the method by mapping galaxy positions from redshift space to real space in the Local Group frame, and take the selection function into account by minimizing the mass-weighted action. We have applied our new method to mock galaxy catalogues, and find that it offers an improvement in the accuracy of reconstructions over linear theory. We have applied our method to the all-sky IRAS Point Source Catalog Redshift Survey (PSCz). Applying PIZA to PSCz, we are able to obtain the peculiar velocity field, the dipole, bulk velocities, and the distortion parameter. From the dipole, we find that ba 0:51 ^ 0:14: We compare the PSCz bulk velocity with that of the Mark III velocity survey, and conclude that ba 0:5 ^ 0:15: We compare the PSCz dipole with that of the SFI Tully Fisher Survey and find that ba 0:55 ^ 0:1: Cosmological density and velocity fields may be reconstructed using the radial velocity information from a galaxy redshift survey. To do this, assumptions must be made about the way in which the peculiar velocity field is produced, the relations between the velocity and density fields, and the relationship between galaxies and the underlying mass distribution. The reconstructed fields may then be compared with the directly measured fields, e.g. from a peculiar velocity survey, and used to place constraints on cosmological parameters. The structures seen in the Universe today formed by the growth via gravitational instability of small density perturbations present in the early Universe. The growth and evolution of these structures may be studied using methods of two types: Eulerian methods which solve the gravitational instability equations (see Peebles 1980); and Lagrangian methods which follow individual galaxy displacements. These methods may be used to deduce the velocity field from the density field and vice versa. Eulerian methods include those that use linear perturbation theory applied to the gravitational instability equations. The iterative reconstruction methods of Yahil et al. (1991), who studied the 1.2-Jy redshift survey, and Kaiser et al. (1991) and Taylor & Rowan-Robinson (1993), who studied the QDOT redshift survey, use this method to reconstruct the peculiar velocity field from galaxy redshift surveys. Branchini et al. (1999) used a similar method to reconstruct the peculiar velocity of the