1 Introduction

The galaxy luminosity function (hereafter LF) measures the relative frequency of galaxies as a function of luminosity per unit co-moving volume. Thus, the LF is the zero-order statistic of galaxy samples and provides the natural weighting of most statistical quantities. For instance, the luminosity evolution is often inferred by the variation with redshift of the LF; the metal production rate is the integral of the luminosity weighted against the LF; the fraction of blue galaxies, crucial for the Butcher-Oemler effect (Butcher & Oemler 1984), is given by the ratio between the color distribution, averaged over the LF, and the total number of galaxies (i.e. the integral of the LF). The LF is, therefore, central to many cosmological issues (Binggeli et al. 1988; Koo & Kron 1992; Ostriker 1993).

The determination of the cluster LF is observationally less expensive than the analogous determination of the field LF. In fact, the cluster LF can be determined as the statistical excess of galaxies along the cluster line of sight, with respect to the control field direction, due to the fact that clusters appear as overdensities with respect to the intracluster field. Therefore we do not need to know the redshift of each cluster member but only the mean cluster redshift, provided that we treat the sampled volume as a free parameter. This approach assumes implicitly that the background contribution along the cluster line of sight is equal to the "average'' background, a hypothesis that a non-zero correlation function for galaxies shows to be only approximate: there are galaxies near the cluster line of sight, but not belonging to the cluster itself, in excess of the value expected by assuming a uniform "average'' galaxy density. In other words, it happens very often that a nearby group, cluster or supercluster contaminates the control field counts or the cluster counts thus affecting the determination of the cluster LF. This problem is even more relevant when sampling the cluster outskirts, where galaxy evolution probably occurs (van Dokkum et al. 1998) since i) the low galaxy density of these regions is affected by even a few contaminants, and ii) the large observing area makes more probable the presence of a contaminating group. Recently, Huang et al. (1997) found an expression for estimating the error introduced by a non zero correlation function. This expression however, inflates errors as a consequence of the fact that the statistics is not simply Poissonian, and does not try to correct field counts to the value expected once the contribution due to other prospectically near overdensities is taken into account.

From an observational point of view, a proper determination of the LF with small field of view imagers and in presence of a non-zero correlation function is very time consuming since several fields all around the cluster need to be observed to estimate the field counts along the clusters line of sight. Therefore, in order to save precious telescope time, very often the field counts are taken from the literature (and usually concern a specific region of the sky which is often completely unrelated to the cluster line of sight) or only a few (usually one, except Bernstein et al. 1995) comparison fields at fairly different right ascensions are adopted. The alternative route is to recognize cluster membership individually, for instance on morphological grounds as Binggeli et al. (1985) did for the Virgo cluster, or by means of galaxy colors, as in Garilli et al. (1999, hereafter GMA99).

Wide-field imagers, such as Schmidt plates or large CCD mosaics, allow one instead to sample lines of sight all around the cluster, and accurately determine the field properties along the cluster line of sight (cf. Valotto et al. 1997).

Our group is currently exploiting the Digitized Palomar Sky Survey (DPOSS) and the resulting Palomar-Norris Sky Catalog (PNSC) in the context of the CRoNaRio collaboration (Caltech-Roma-Napoli-Rio) (Djorgovski et al. 1999). Due to the good photometric quality of the data and the wide sky coverage of DPOSS data, the survey is particularly tailored to explore the actual background contribution to the determination of the cluster LF.

This paper is organised as follow: in Sect. 2 we briefly describe the main characteristics of the data and we present the cluster sample. Section 3 deals with most technical problems related to the determination of the individual LF of clusters. Section 4 presents the results of this work and a comparison with literature results. Conclusions are summarised in Sect. 5. We adopt H₀=50 km s^-1 Mpc^-1 and q₀=0.5.

Figure 1: Comparison between aperture instrumental magnitudes measured on the photographic plate and CCD aperture magnitudes. The continuous line represents the median difference $\delta m={\rm mag_{ccd}-mag_{plate}}$ for galaxies (filled dots). Stars (empty triangles) are excluded from the fit because they are often saturated on POSS II plates. This diagram has been used for calibrating the plate F449