The effect of the perturbation of the local velocity field by Virgo on the calculation of differential luminosity functions.

The determination of phi(M) for galaxies in the Revised Shapley-Ames Catalog (1981) has been repeated using Virgo-centric perturbation fields of different strength to counter criticism that past calculations of the luminosity functions for galaxies of various Hubble types and van den Bergh luminosity classes are significantly in error as a result of neglect of this local velocity perturbation. Differential luminosity functions are given for 18 different Hubble types and luminosity classes for perturbation models, with infall velocities of the Galaxy to Virgo of zero (the null model for comparison), 220, and 440 km/s. The results, presented both by Hubble cosmological velocity, M(B-zero)-diagrams and by diagrams for the luminosity functions themselves, show (1) that the change of shape of the upper envelope to the Hubble cosmological velocity, M(B-zero) distributions is negligible compared with the null case, even for the extreme model with an infall velocity of 440 km/s, and (2) the luminosity functions do not become significantly tighter in the perturbed models as the perturbation strengthens. The conclusion is that any realistic perturbation of the local velocity field does not introduce large enough errors in the calculation of phi(M) to change the earlier result that a very large dispersion exists in M(B-zero) within any given Hubble type and/or luminosity class.