Annu. Rev. Astron. Astrophys. 1988. 26: 509-560 Copyright © 1988 by Annual Reviews. All rights reserved

2.3. Selection of Galaxies

The selection of galaxies is fundamental for the LF. Ideally, the galaxies are selected by total apparent magnitude. In reality, the galaxies are always drawn from catalogs that are based on photographic surveys. The detection of a galaxy on a photographic plate does not depend on total magnitude but on surface brightness. Both very compact, high-surface-brightness objects and extended, very low-surface-brightness objects have small isophotal diameters and can go undetected. Reaves (1956) and Arp (1965) were the first to draw attention to this potential selection bias by showing that the normal galaxies detected so far populate a narrow strip in the magnitude-log diameter diagram. Galaxies of very low surface brightness may be entirely missed. That such galaxies exist is known from the local dwarf spheroidals (Fornax, Sculptor, et al.), which were detected only because they are sufficiently nearby to be resolved into stars. The possible consequences for the LF are clear: The LF derived from any given sample will usually refer only to normal, easily visible galaxies. A population of luminous galaxies of low surface brightness may go unnoticed, although the LF nominally refers to total magnitudes.

This "tip-of-the-iceberg" bias has been emphasized by Disney (1976). Disney & Phillips (1983) have quantified the visibility of galaxies as a function of central surface brightness and have shown how galaxies of "normal" surface brightness are automatically preferred in any realistic procedure of galaxy sampling. Consequently, these authors have suggested that the "bivariate brightness distribution" be used instead of the (one-dimensional) LF. This is the distribution of galaxies in total magnitude and surface brightness. The recent large-scale photographic survey of the Virgo cluster (Binggeli et al. 1985; hereinafter BST), which should have picked up all Virgo galaxies above a surface brightness threshold of 25.5 B mag arcsec^-2 would appear to be a suitable basis to explore the bivariate brightness distribution of galaxies (cf. also Phillips & Disney 1986). A class of very extended, very low-surface-brightness objects was indeed discovered in the course of this survey, some of which are as bright as M_BT ~ -17 (Sandage & Binggeli 1984). The dominant feature in the magnitude-surface brightness diagram, however, is a strong correlation between absolute magnitude and surface brightness for galaxies fainter than M_BT ~ -19 and of the type dE or Sd-Im (Caldwell 1983, Binggeli et al. 1984, Binggeli 1986, Bothun et al. 1986). This would suggest that most of the galaxies that are missed because of their low surface brightness are also of low total brightness. Galaxies are detected by surface brightness, but (thanks to this relation) they are generally also selected by total absolute magnitude.

However, this simple view is about to be challenged by Impey et al. (1987) who, by using Malin's technique of photographic contrast enhancing, have detected many objects in the Virgo cluster and elsewhere that have a central (peak) surface brightness below 26 B mag arcsec^-2 and that accordingly went undetected by BST. Furthermore, in the course of their survey centered on the Virgo cluster core, these authors (Bothun et al. 1987) accidentally discovered that one of their objects with a very low central surface brightness of 27 B mag arcsec^-2 is a distant spiral with a total magnitude of M_BT -22 (!). This brings new vigor to the question of how many bright galaxies lie hidden below the conventional photographic detection limits (Disney & Phillips 1987) and hence have been missed by all conventional LF studies to date. The answer must await completion of deep surveys like Impey et al.'s. In any case, the galaxy discovered by Bothun et al. is clearly a very rare type. Until its nature and relation to "normal" galaxies are better known, we cannot worry about the expected incompleteness of the LF of galaxies due to this new type of galaxy. Yet it is important to be aware that the LF does use total magnitude for objects that are never strictly selected by total magnitude.