ON THE PREDICTION OF VELOCITY-FIELDS FROM REDSHIFT SPACE GALAXY SAMPLES

We present a new method for recovering the underlying velocity field f rom an observed distribution of galaxies in redshift space. The method is based on a kinematic Zel'dovich relation between the velocity and density fields in redshift space. This relation is expressed in a diff erential equation slightly modified from the usual Poisson equation an d which depends nontrivially on beta = Omega(0.6)/b. The linear equati on can be readily solved by standard techniques of separation of varia bles by means of spherical harmonics. One can also include a term desc ribing the ''rocket effect'' discussed by Kaiser (1987). From this red shift space information alone, one can generate a prediction of the pe culiar velocity held for each harmonic (l, m) as a function of distanc e. We note that for the quadrupole and higher order moments, the equat ion is a boundary value problem with solutions dependent on both the i nterior and exterior mass distribution. However, for a shell at distan ce r, the dipole, as well as the monopole, of the velocity field in th e Local Group frame is fully determined by the interior mass distribut ion. This implies that the shear of the measured velocity field, when fitted to a dipole distortion, should be aligned and consistent with t he gravity field inferred from the well determined local galaxy distri bution. As a preliminary application we compute the velocity dipole of distant shells as predicted from the 1.2 Jy IRAS survey compared to t he measured velocity dipole on shells, as inferred from a recent POTEN T analysis. The coherence between the two fields is good, yielding a b est estimate of beta = 0.6 +/- 0.2.