3.1 Luminosity Function

Perhaps one of the most basic statistic that can be measured from redshift surveys is the luminosity function (LF). It not only provides information about the galaxy population but it is a key ingredient in the analysis of magnitude-limited samples. The importance of determining the local LF is that its overall normalization and faint-end slope directly impact the interpretation of the excess observed in the faint number counts and the amount of evolution required to explain them. Furthermore, the local LF has been used to calibrate or to verify the consistency of semi-analytical galaxy evolution models, which have become a powerful tool for detailed comparisons between data and theory (e.g., Kauffmann et al. 1993, Lacey et al. 1993). However, despite the innumerous estimates of the local LF, there still is considerable debate over its shape and normalization. The nature of the problem is reviewed below using results from the most recent surveys.

The local LF has been independently computed for the CfA2 (Marzke et al. 1994a) and SSRS2 (da Costa et al. 1994a, Marzke et al. 1998) north and south sub-samples, which altogether probe four different regions of the sky. Comparison of these LFs shows that the shapes are in relative good agreement, especially at the faint-end. However, the derived normalization of the CfA2 north LF is significantly higher than the rest, suggesting a mean galaxy density a factor of two larger in that region. By contrast, the LF measured for the SSRS2 south and north are essentially identical, presenting very similar shapes and normalizations, even though they probe distinct volumes and largely independent structures. Their normalization is also consistent with that derived for CfA2 south. There are two possible interpretations for the observed discrepancy: 1) there are significant fluctuations of the galaxy distribution on scales of ~ 100 h^-1 Mpc; 2) there are systematic errors in the magnitude-scale, in particular those given in the Zwicky catalog from which the CfA2 sample is drawn.

The same disagreement is seen when comparing the LF of more distant samples (Ellis et al. 1996, Lin et al. 1996a, Zucca et al. 1997, Geller et al. 1997). In general, the derived luminosity functions fall into two broad categories - those with high (Autofib, CfA2, CS, ESP) and low normalizations (SSRS2, Stromlo-APM, LCRS). Again, with the exception of the CfA2 (at the bright end) and LCRS (at the faint end) the shapes are, by and large, very similar. These results are puzzling since there is no clear correlation between the samples used and the direction in space or the way the parent catalogs for these samples were created. Possible explanations for the conflicting results include: the existence of a large underdense region in the local Universe, an underestimate of a population of low luminosity galaxies nearby or a rapid evolution of the blue luminosity function at low redshifts (z ~ 0.1).

The local LF has also been examined as a function of morphology (Figure 2) and color using the CfA2 (morphology) and SSRS2 (morphology and color) samples. Analyzes of these samples show that even locally one observes an excess of blue galaxies at faint magnitudes. It is estimated that the faint-end slope of blue galaxies is -1.3 (Marzke & da Costa 1997). In addition, using the complete morphological information available for the SSRS2, one finds that early and late-type galaxies have very similar, flat LFs (Marzke et al. 1998), while the irregular/peculiar galaxy LF is very steep ( ~ -1.81). These results are in good agreement with earlier findings based on the CfA data (Marzke et al. 1994b) but in clear disagreement with the results of Loveday et al. (1995), probably because of inadequacies in the identification of ellipticals at faint magnitudes. Similar studies are currently underway at moderate redshifts.

A clear resolution of some of the problems mentioned above will have to await the completion of SDSS which will provide a homogeneous, multi-color photometric data set of the northern sky with complete redshift information.

Recent surveys such as Autofib and CFRS, and now CNOC2. with an extended redshift baseline, have provided for the first time, the means to directly study the evolution of the luminosity function. The CFRS sample has been subdivided into several redshift bins and into two colors. Analysis of these subsamples shows that the redder galaxies exhibit remarkably little evolution, while strong evolution is observed for the bluer galaxies. It is important to note that this evolution is independent of the normalization of the ``local'' LF since it is determined from the sample itself. Strong evolution of blue galaxies has also been observed in the B-selected sample of Autofib.