Reconstructing the IRAS point source catalog redshift survey with a generalized PIZA

We present a generalized version of the path interchange Zel'dovich approxi mation (PIZA), for use with realistic galaxy redshift surveys. PIZA is a li near particle-based Lagrangian method which uses the present-day positions of galaxies to reconstruct both the initial density field and the present-d ay peculiar velocity field. We generalize the method by mapping galaxy posi tions 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 theor y. We have applied our method to the all-sky IRAS Point Source Catalog Reds hift Survey (PSCz). Applying PIZA to PSCz, we are able to obtain the peculi ar velocity field, the dipole, hulk velocities, and the distortion paramete r. From the dipole, we find that beta = 0.51 +/- 0.14. We compare the PSCz bulk velocity with that of the Mark III velocity survey, and conclude that beta = 0.5 +/- 0.15. We compare the PSCz dipole with that of the SFI Tully Fisher Survey and find that beta = 0.55 +/- 0.1.