Maximum Likelihood Comparison of Tully‐Fisher and Redshift Data. II. Results from an Expanded Sample

This is the second in a series of papers in which we compare Tully-Fisher(TF) data from the Mark III Catalog with predicted peculiar velocities based onthe IRAS galaxy redshift survey and gravitational instability theory, using arigorous maximum likelihood method called VELMOD. In Paper I (Willick et al.1997b), we we applied the method to a $cz_{LG} \leq 3000$ km/sec, 838-galaxy TFsample and found $\beta_I=0.49\pm 0.07,$ where $\beta_I\equiv \Omega^{0.6}/b_I$and $b_I$ is the linear biasing parameter for IRAS galaxies. In this paper weincrease the redshift limit to $cz_{LG}=7500$ km/sec, thereby enlarging thesample to 1876 galaxies. The expanded sample now includes the W91PP and CFsubsamples of the Mark III catalog, in addition to the A82 and MAT subsamplesalready considered in Paper I. We implement VELMOD using both the forward and inverse forms of the TFrelation, and allow for a more general form of the quadrupole velocity residualdetected in Paper I. We find $\beta_I=0.50\pm 0.04$ (1-sigma error) at 300km/sec smoothing of the IRAS-predicted velocity field. The fit residuals arespatially incoherent for $\beta_I=0.5,$ indicating that the IRAS plusquadrupole velocity field is a good fit to the TF data. If we eliminate thequadrupole we obtain a worse fit, but a similar value for $\beta_I$ of $0.54\pm0.04.$ Changing the IRAS smoothing scale to 500 km/sec has almost no effect onthe best $\beta_I.$ We find evidence for a density-dependence of thesmall-scale velocity dispersion, $\sigma_v(\delta_g)\simeq (100 + 35 \delta_g)$km/sec.Comment: Latex, 37 pages, 15 figures, uses modified apjpt4.st