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 biv ariate brightness distribution (BED) of galaxies in luminosity and sur face brightness and we consider the prospects for deriving such a samp le. First, we note that determinations of the galaxy luminosity functi on can be seriously in error if surface brightness (visibility) select ion 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 surfac e brightness bins. We propose a set of criteria which the sample of ga laxies in each surface brightness bin must satisfy if it is to be reli ably used in such a determination. Each sample should be restricted to a well defined range in morphological type, the measured isophotal si ze and magnitude and the surface brightness of each galaxy should be c orrected to a common galactic inclination, all galaxies should have me asured redshifts and the sample should be complete to a known isophota l size and/or magnitude. We then describe a rigorous method for select ing samples which satisfy these criteria from existing catalogues of g alaxies. We apply this method to the ESO-LV catalogue and find that fr om the intial sample of 11 000 galaxies with a disk component we can o nly find 5 subsamples in half-magnitude wide surface brightness bins w hich satisfy our proposed criteria. The largest derived subsample cont ains only 27 galaxies, far too few to determine a luminosity function at its surface brightness. We suggest that had our proposed criteria b een applied to the samples used in previous determinations of the BED or the galaxy luminosity function then sample sizes would have been gr eatly reduced. For this reason, we suggest that the conclusions of pre vious work should be treated with caution.