ESTIMATION OF PECULIAR VELOCITY FROM THE INVERSE TULLY-FISHER RELATION

We present a method for deriving a smoothed estimate of the peculiar v elocity field of a set of spiral galaxies with measured circular veloc ities eta = log Delta upsilon and apparent magnitudes m. The method is based on minimizing the scatter of a linear inverse Tully-Fisher rela tion eta = eta(M), where the absolute magnitude of each galaxy is infe rred from its redshift z, corrected by a peculiar velocity field, M pr oportional to m - 5 log(z - u). We describe the radial peculiar veloci ty field u(z) in terms of a set of orthogonal functions which can be d erived from any convenient basis set; as an example, we take them to b e linear combinations of low-order spherical harmonic and spherical Be ssel functions. The model parameters are then found by maximizing the likelihood function for measuring a set of observed eta. The predicted peculiar velocities are free of Malmquist bias in the absence of mult istreaming, provided that no selection criteria are imposed on the mea surement of circular velocities. This procedure can be considered as a generalized smoothing algorithm of the peculiar velocity field, and i s particularly useful for comparison with the smoothed gravity field d erived from full-sky galaxy redshift catalogues such as the IRAS surve ys. We demonstrate the tech nique using a catalogue of 'galaxies' deri ved from an N-body simulation.