2 The data and the sample

The data used in this paper were extracted from the DPOSS frames taken in the photographic J, F and N bands (Reid et al. 1991). Weir et al. (1995c) describe the characteristics of the SKICAT package, which performs the plate linearization and the object detection and classification (based on a classification tree, see Weir et al. 1995a).

SKICAT measures four different magnitudes for each object detected on the plates, among which the FOCAS (Jarvis & Tyson 1981) total magnitude, obtained by dilatation of the detection isophote in all directions until the object area is doubled. These magnitudes approximate true asymptotic magnitudes.

The plates are individually calibrated to the Gunn system (Thuan & Gunn 1976; Wade 1979) by means of CCD frames of clusters of galaxies. We used the data set presented in Garilli et al. (1996), which has been used in GMA99 to compute the cluster LF. As they point out, their Gunn g photometry does not perfectly match the standard Thuan-Gunn system (for historical reasons): $g_{\rm Garilli}=g-0.20\pm 0.14$. However, the error is systematic, so that we recover the true Gunn g magnitude by adding this offset. We note that this is different from the general CCD calibration of DPOSS/PNSC, which is mainly based on the extensive CCD data sets obtained at Palomar for this purpose (Gal et al. 2000).

Plates are photometrically calibrated by comparing plate and CCD aperture (within 5 arcsec radius) photometry of common galaxies, and magnitudes are corrected for Galactic absorption. A typical calibration diagram is shown in Fig. 1. The adopted zero point is the median of the differences ${\rm mag_{ccd}-mag_{plate}}$, after excluding bright stars (empty triangles) that are usually saturated on photographic plates. No color term has been adopted as required by the POSS-II photometric system (Weir et al. 1995b). The mean error on the zero-point determination is 0.02 mag in g and 0.04 mag in r and i, while the typical photometric error on individual magnitudes (including Poissonian errors, residuals of density to intensity conversion, etc.) is 0.2 mag in g and 0.16 in r and i. K-corrections were taken from Fukugita et al. (1995). Our data do not have enough resolution to distinguish between different morphological types, nor this selection can be done using galaxy colors due to the errors on individual magnitudes. Anyway the difference in k-corrections between E and Scd is $\leq$0.25 mag in the r and i bands for the most distant cluster in our sample ($\leq$0.3 mag at our median redshift in all bands) so that we could adopt the k-correction of the dominant E-S0 population.

We estimated the photometric completeness limit of our data for each cluster and in each band independently, in order to take into account the depth variations of our catalogs from plate to plate and as a function of the projected cluster location on the plate. We adopt as our completeness limit the magnitude at which nearby field counts systematically deviate from linearity (in logarithmic units). The use of homogeneous data, reduced in one single way, both for the control field and the cluster galaxy counts, helps to partially compensate for systematic errors due to selection effects which cancel out (at least in part) in the statistical subtraction of the counts.

The studied sample is extracted from the Abell catalogue (Abell 1958; Abell et al. 1989), among those clusters with known redshift, which are imaged in a fully reduced plate triplet (i.e. J, F and N) and with photometric zero points already available to us, in all three bands, at the start of this work. At that time, 39 Abell clusters satisfied the above conditions, the bottleneck being due to the low number of calibration frames and the requirement of having at least one reliable spectroscopic redshift for the cluster.

A few more clusters satisfying the above condition were also rejected from the sample on the following grounds:
Abell 154 - There are two density peaks at two different redshifts, along the line of sight, respectively at z=0.0640 (A154) and z=0.0428 (A154a).
Abell 156 - There are two discordant redshift measurements in the literature. Since there is no galaxy overdensity at the cluster position we can safely assume that it is a spurious object.
Abell 295 - Two density peaks in the cluster direction: A295 at z=0.0424 and A295b at z=0.1020.
Abell 1667 - Two density peaks in the cluster direction: A1667 at z=0.1648 and A1667b at z=0.1816.
Abell 2067 - Two density peaks in the cluster direction: A2067 at z=0.0756 and A2067b at z=0.1130.
Two more clusters, Abell 158 and Abell 259, show a double structure with two adjacent but distinct density peaks. In these cases we included only the galaxies belonging to the peaks with measured redshift, without assuming that the secondary peak lies at the same redshift as the first one. The final sample is listed in Table 1.

 

 

Table 1: The cluster sample

Cluster	Redshift	Plate	Richness class	B-M type
A1	0.1249	607	1	III
A16	0.0838	752	2	III
A28	0.1845	680	2	III
A41	0.2750	752	3	II-III
A44	0.0599	680	1	II
A104	0.0822	474	1	II-III
A115	0.1971	474	3	III
A125	0.188	610	1	III
A150	0.0596	610	1	I-II
A152	0.0581	610	0	...
A158	0.0645	610	0	...
A180	0.1350	755	0	I
A192	0.1215	755	2	I
A202	0.1500	755	2	II-III
A267	0.2300	829	0	...
A279	0.0797	829	1	I-II
A286	0.1603	829	2	II
A293	0.1650	757	2	II
A294	0.0783	757	1	I-II
A1632	0.1962	443	2	II-III
A1661	0.1671	443	2	III
A1677	0.1845	443	2	III
A1679	0.1699	443	2	III
A1809	0.0788	793	1	II
A1835	0.2523	793	0	...
A2049	0.1170	449	1	III
A2059	0.1305	449	1	III
A2061	0.0782	449	1	III
A2062	0.1122	449	1	III
A2065	0.0721	449	2	III
A2069	0.116	449	2	II-III
A2073	0.1717	449	1	III
A2083	0.1143	449	1	III
A2089	0.0743	449	1	II
A2092	0.066	449	1	II-III
A2177	0.1610	517	0	...
A2178	0.0928	517	1	II
A2223	0.1027	517	0	III
A2703	0.1144	607	0	...