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

2.2. Magnitudes

It is of the utmost importance to pay attention to the exact definitions of, and the corrections to, the apparent magnitudes used by various authors to derive the LF. The following parameters must be specified:

1. The passband of the magnitudes. Usually total blue magnitudes B_T are used as defined in Second Reference Catalog of Bright Galaxies (de Vaucouleurs et al. 1976; hereinafter RC2). Frequently, magnitudes must be used that only approximate the B_T system, as for instance Zwicky's magnitudes (Zwicky et al. 1961-68). Infrared workers sometimes follow the example of radio astronomers by using fluxes rather than magnitudes (e.g. Lawrence et al. 1986).

2. The Galactic absorption, which must be corrected for. This correction can be achieved by specific absorption determinations in relevant fields, by following the precepts of the RSA (Sandage & Tammann 1981), by using the maps of Burstein & Heiles (1982), or by any other appropriate method.

3. The internal absorption, which may or may not be corrected for. The internal absorption of E and S0 galaxies is generally neglected. The exact correction for spirals is not well known. The RC2 gives the absorption to face-on orientation, assuming the same absorption for all spiral types and somewhat higher values for Im's. following Holmberg (1958) with slight modifications, the RSA applies inclination-dependent corrections for the total internal absorption, with the highest absorption corrections for Sb's (A_Bⁱ = 1.33 mag for an edge-on Sb galaxy). IRAS data seem to confirm that the internal absorption peaks for Sb's (de Jong & Brink 1987).

Most published LFs have used magnitudes that are uncorrected for internal absorption. Corrected magnitudes Mⁱ were used by Kiang (1961), Tammann et al. (1979), and Kraan-Korteweg (1981). Deciding which procedure is preferable depends on the application of the LF. If spirals are randomly oriented (cf. Djorgovski 1987), uncorrected LFs should be used for the interpretation of galaxy counts and of the cosmic background light. On the other hand, only the LF (Mⁱ) gives correct results if, for example, the total hydrogen consumption or the energy output of a sample of galaxies is required, or if physically meaningful mass-to-light ratios are to be calculated.

Unfortunately, a bulk transformation of (M) into (Mⁱ), or vice versa, is not possible. The exact conversion depends on the specific mixture of galaxy types, which depends upon the environmental density whose average usually varies for subsets of the total sample. Furthermore, in the case of flux-limited samples the two types of LFs are also based on different parent samples; while (M) considers all galaxies brighter than the limiting magnitude m, (Mⁱ) includes in addition all inclined spirals that are brighter than m after the absorption Aⁱ is applied. In some cases, the available data permit both (M) and (Mⁱ) to be determined (cf. Tammann et al. 1979).

4. The K-correction for redshift dimming, which must be applied for distant galaxies. For redshifts z 0.02 the K-correction in optical passbands remains smaller than 0.^m1 for all galaxy types (Whitford 1971, Wells 1972) and may be neglected for the LF. However, at large redshifts the K-correction not only becomes large but also is sensitive to the galaxy type. For instance, at redshift Z = 0.5 the difference in the K-correction may amount to ~ 1.^m5 between different types (Pence 1976, Coleman et al. 1980). If such large effects were neglected, comparison of the LFs of nearby and high-redshift galaxy samples could lead to erroneous conclusions on galaxy evolution.