MAXIMUM-LIKELIHOOD COMPARISONS OF TULLY-FISHER AND REDSHIFT DATA - CONSTRAINTS ON OMEGA AND BIASING

We compare Tully-Fisher (TF) data for 838 galaxies within cz = 3000 km s(-1) from the Mark III catalog with the peculiar velocity and densit y fields predicted from the 1.2 Jy IRAS redshift survey. Our goal is t o test the relation between the galaxy density and velocity fields pre dicted by gravitational instability theory and linear biasing, and the reby to estimate beta(I)=Omega(0.6)/b(I) where b(I) is the linear bias parameter for IRAS galaxies on a 300 km s(-1) scale. Adopting the IRA S velocity and density fields as a prior model, we maximize the likeli hood of the raw TF observables, taking into account the full range of selection effects and properly treating triple-valued zones in the red shift-distance relation. This method is more general and correct than simply minimizing TF residuals with respect to the velocity field mode l. Extensive tests with realistic, simulated galaxy catalogs demonstra te that the method produces unbiased estimates of beta(I) and its erro r. When we apply the method to the real data, we model the presence of a small but significant velocity quadrupole residual (similar to 3.3% of Hubble flow), which we argue is due to density fluctuations incomp letely sampled by IRAS. The method then yields a maximum likelihood es timate beta(I) = 0.49 +/- 0.07 (1 sigma error). We discuss the constra ints on Omega and biasing that follow from this estimate of beta(I) if we assume a COBE-normalized, cold dark matter power spectrum. Our mod el also yields the one-dimensional noise in the velocity field, includ ing IRAS prediction errors, which we find to be 125 +/- 20 km s(-1). W e define a chi(2)-like statistic, chi(xi)(2), that measures the cohere nce of residuals between the TF data and the IRAS model. In contrast t o maximum likelihood, this statistic can identify poor fits but is rel atively insensitive to the best beta(I). As measured by chi(xi)(2), th e IRAS model does not fit the data well without accounting for the res idual quadrupole; when the quadrupole is added, the fit is acceptable for 0.3 less than or equal to beta(I) less than or equal to 0.9. We di scuss this in view of the Davis, Nusser, & Willick analysis that quest ions the consistency of the TF data and IRAS-predicted velocity field.