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

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Abstract
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 on the IRAS galaxy redshift survey and gravitational instability theory, using a rigorous maximum likelihood method called VELMOD. In the first paper in this series, we applied the method to a czLG ≤ 3000 km s-1, 838 galaxy TF sample and found βI = 0.49 ± 0.07, where βI ≡ Ω0.6/bI and bI is the linear biasing parameter for IRAS galaxies. In this paper we increase the redshift limit to czLG = 7500 km s-1, thereby enlarging the sample to 1876 galaxies. The expanded sample now includes the Willick Pisces-Perseus (W91PP) and Courteau-Faber (CF) subsamples of the Mark III Catalog, in addition to the Aaronson et al. (A82) and Mathewson et al. (MAT) subsamples already considered in the first paper in this series. We implement VELMOD using both the forward and inverse forms of the TF relation and allow for a more general form of the quadrupole velocity residual than considered in the first paper in this series. We find βI = 0.50 ± 0.04 (1 σ error) at 300 km s-1 smoothing of the IRAS-predicted velocity field. The fit residuals are spatially incoherent for βI = 0.5, which indicates that the IRAS plus quadrupole velocity field is a good fit to the TF data. If we eliminate the quadrupole we obtain a worse fit but a similar value for βI of 0.54 ± 0.04. Changing the IRAS smoothing scale to 500 km s-1 has almost no effect on the best βI. Thus the data are consistent with a model in which the cosmological density parameter Ω ≈ 0.3, and IRAS galaxies are unbiased, bI = 1. We find evidence for a density dependence of the small-scale velocity dispersion, σv(δg) (100 + 35δg) km s-1. One of the byproducts of the VELMOD method is a self-consistent calibration of the TF relation. We confirm our result from the first paper in this series that the TF relations for the A82 and MAT samples found by VELMOD are consistent with those that went into the published Mark III Catalog. However, the VELMOD TF calibrations for the W91PP and CF samples place objects ~8% closer than their Mark III Catalog distances, which has an important effect on the inferred large-scale flow field at 4000-6000 km s-1. With this recalibration, the IRAS and Mark III velocity fields are consistent with one another at all radii.
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