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

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, hulk velocities, and the distortion parameter. 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.