WIENER RECONSTRUCTION OF DENSITY, VELOCITY AND POTENTIAL FIELDS FROM ALL-SKY GALAXY REDSHIFT SURVEYS

We present a new method for recovering the cosmological density, veloc ity and potential fields from all-sky redshift catalogues. The method is based on an expansion of the fields in orthogonal radial (Bessel) a nd angular (spherical harmonic) functions. In this coordinate system, peculiar velocities introduce a coupling of the radial harmonics descr ibing the density field in redshift space but leave the angular modes unaffected. In the harmonic transform space, this radial coupling is d escribed by a distortion matrix which can be computed analytically wit hin the context of linear theory; the redshift space harmonics can the n be converted to their real space values by inversion of this matrix. Statistical or 'shot' noise is mitigated by regularizing the matrix i nversion with a Wiener filter (roughly speaking, the ratio of the vari ance in the signal to the variance of the signal plus noise). The meth od is non-iterative and yields a minimum variance estimate of the dens ity field in real space. In this coordinate system, the minimum varian ce harmonics of the peculiar velocity and potential fields are related to those of the density field by simple linear transformations. Tests of the method with simulations of a cold dark matter universe and com parison with previously proposed methods demonstrate it to be a very p romising new reconstruction method for the local density and velocity. A first application to the 1.2-Jy IRAS redshift survey is presented.