Estimation of Peculiar Velocity from the Inverse Tully-Fisher Relation

Abstract

We present a method for deriving a smoothed estimate of the peculiar velocity field of a set of galaxies with measured circular velocities $\eta \equiv \log \Delta v$ and apparent magnitudes $m$. The method is based on minimizing the scatter of a linear inverse Tully-Fisher relation $\eta =\eta (M)$ where the absolute magnitude of each galaxy is inferred from its redshift $z$, corrected by a peculiar velocity field, $M\propto m-5\log (z-u)$. We describe the radial peculiar velocity field $u(\mathbf{z})$ in terms of a set of orthogonal functions which can be derived from any convenient basis set; as an example we take them to be linear combinations of low order spherical harmonic and spherical Bessel 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 multi-streaming, provided no selection criteria are imposed on the measurement of circular velocities. This procedure can be considered as a generalized smoothing algorithm of the peculiar velocity field, and is particularly useful for comparison to the smoothed gravity field derived from full-sky galaxy redshift catalogs such as the IRAS surveys. We demonstrate the technique using a catalog of ``galaxies" derived from an N-body simulation. Increasing the resolution of the velocity smoothing beyond a certain level degrades the correlation of fitted velocities against the velocities calculated from linear theory methods, which have finite resolution,

17pages+10figures, uuencoded postscript file available by anonymous ftp from pub/marc/itf on magicbean.berkeley.edu, submitted to MNRAS

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