DETERMINING THE BIVARIATE BRIGHTNESS DISTRIBUTION OF GALAXIES

In this paper we describe a set of criteria which we propose a sample of galaxies must satisfy if it is to be useful for determining the bivariate brightness distribution (BED) of galaxies in luminosity and surface brightness and we consider the prospects for deriving such a sample. First, we note that determinations of the galaxy luminosity function can be seriously in error if surface brightness (visibility) selection effects are ignored. We suggest that a determination of the BED is a more physically useful aim. A straightforward way to obtain the BED would be to determine a luminosity function in a set of narrow surface brightness bins. We propose a set of criteria which the sample of galaxies in each surface brightness bin must satisfy if it is to be reliably used in such a determination. Each sample should be restricted to a well defined range in morphological type, the measured isophotal size and magnitude and the surface brightness of each galaxy should be corrected to a common galactic inclination, all galaxies should have measured redshifts and the sample should be complete to a known isophotal size and/or magnitude.

We then describe a rigorous method for selecting samples which satisfy these criteria from existing catalogues of galaxies. We apply this method to the ESO-LV catalogue and find that from the intial sample of 11 000 galaxies with a disk component we can only find 5 subsamples in half-magnitude wide surface brightness bins which satisfy our proposed criteria. The largest derived subsample contains only 27 galaxies, far too few to determine a luminosity function at its surface brightness. We suggest that had our proposed criteria been applied to the samples used in previous determinations of the BED or the galaxy luminosity function then sample sizes would have been greatly reduced. For this reason, we suggest that the conclusions of previous work should be treated with caution.