OPTIMAL GALAXY DISTANCE ESTIMATORS

The statistical properties of galaxy distance estimators corresponding to the Tully-Fisher and D-n-sigma relations are studied, and a rigoro us framework for identifying and removing the effects of Malmquist bia s due to observational selection is developed. The prescription of Sch echter for defining unbiased distance estimators is verified and exten ded to more general-and more realistic-cases. Finally, the derivation of ''optimal'' unbiased estimators of minimum dispersion, by utilizing information from additional suitably correlated observables, is discu ssed and the results applied to a calibrating sample from the Fornax c luster, as used in the Mathewson spiral galaxy redshift survey. In thi s illustrative example the optimal distance estimator derived from app arent magnitude, isophotal diameter, and line width has an intrinsic s catter which is similar to 22% smaller than that of the conventional T ully-Fisher relation.