Introduction

The luminosity function, usually parameterized as a Schechter function (Schechter, 1976), is often used to describe a population of galaxies. As surface brightness selection effects are not taken into account by this description, there is an implicit assumption that these can be ignored (McGaugh, 1994; Ferguson & McGaugh, 1995). However, optically selected samples are known to suffer from serious selection effects that act against low surface brightness objects (eg. Disney, 1976, Impey & Bothun, 1997). This means that luminosity functions derived from these optical samples really only describe the way the Universe is populated by relatively high surface brightness galaxies (HSBG's) which are near the peak of the `visibility function' (Disney & Phillips, 1983; McGaugh, Bothun & Schombert, 1995). These galaxies can be seen to much further distances than LSBG's and are therefore preferentially selected in optical surveys.

The Bivariate Brightness Distribution (BBD) will determine the luminosity function as a function of surface brightness. This will describe the population of galaxies more fully than possible using the luminosity function alone and will determine if there is a correlation between luminosity and surface brightness. If such a correlation does exist then the number of Schechter (1976) L galaxies has probably been determined quite accurately, as the numbers of giant low surface brightness galaxies (LSBG's) will be insignificant. However this would also suggest that a significant number of dwarf galaxies will have been missed due to SB selection effects, thus adding even greater uncertainty to the poorly determined faint end of the luminosity function. If the correlation is weak or non-existant, then the population of giant LSBG's will be significant and SB selection effects must be taken into account across the whole range of the luminosity function to make an accurate determination.

It is known (Schombert et al., 1992) that LSBG's cover the same range of HImass as HSBG's. This implies that selection using HIwill not be subject to selection effects in the same way as an optical survey. We aim to use HImass measurements to determine our sample and therefore cover a much wider range of surface brightness than possible with an optical survey. The luminosity and surface brightness of the galaxies will then be determined as part of an optical follow-up programme.

Even though we will avoid optical selection effects, there will still be selection effects inherent in using an HIsample. These include possible biases against LSBG's and high velocity-width galaxies due to profile shape. There is a further possibility of resolving large galaxies and removing them during either bandpass subtraction or baseline removal. These are discussed in more detail in §3.

When both HIand optical characteristics of the sample have been determined, we can also investigate relationships other than luminosity - surface brightness. For instance, it has been proposed (McGaugh, Bothun & Schombert, 1995) that luminosity - scale length may be a more important relationship than luminosity - surface brightness in determining optical selection effects, and it will be possible to test this. We can further to examine the Tully Fisher relationship (Tully & Fisher, 1977) for these galaxies and investigate whether it continues to hold true for LSBG's as found by Zwaan et al. (1995).

© Copyright Astronomical Society of Australia 1997