4 Properties of the QSO sample

  
4.1 General

Table 3 lists redshifts, absolute magnitudes, colours, proper motion indices, and the two variability indices of the 77 QSOs, Sey1s, and NELGs from our follow-up spectroscopy. In a similar style, Table 4 summarises the data for the 104 QSOs, Sey1s, and NELGs identified in the NED. The distribution of these types over the three priority classes from the VPM survey is given in Table 4. In the high priority subsample, 94% of the candidates were found to be QSOs/Sey1s, while the contamination by foreground stars is as low as 4%. For the combined sample of high-and-medium-priority objects the success rate (i.e., the fraction of established QSOs/Sey1s among all candidates) is still as high as 63%.

Figure 6: Cumulative QSO surface density $N (\le B)$, i.e. number of QSOs brighter than a given magnitude B per square degree where B has been corrected for an interstellar extinction of AB=0.05mag. Solid polygon: all QSOs outside the cluster region ( $d_{\rm c} > 24'$). Bullets with error bars: integral surface densities from Hartwick & Schade (1990). The long-dashed curve corresponds to an analytical approximation given by Wisotzki (1998) that was derived from a composite optical QSO sample.

Figure 7: Spectra (normalized flux $f_{\lambda }$ versus wavelength $\lambda$) of the QSOs, Sey1s, and NELGs from Table 3, sorted by increasing redshift. The running number from Table 3 and the redshift are given for each spectrum. Note that the spectra were not corrected for the atmospheric absorption bands at 6880 and 7620 Å.

Figure 2 illustrates that a high fraction of all QSOs in the field are strongly variable. The B standard deviation due to variability is about 0.2 mag for QSOs with B<19.7. In this magnitude range, more than 60% of the QSOs/Sey1s show the strong variability of high-priority VPM candidates. (A detailed analysis of the variability properties will be deferred to a separate study.) For 90% of QSOs/Sey1s, both variability indices are above the selection thresholds. We find that 50 out of the 53 NED QSOs/Sey1s with B<19.7 match the selection criteria of our survey, corresponding to a completeness of 94% for the VPM survey. Only for two objects both variability indices fall below the selection thresholds; another one has a proper motion index slightly above the threshold. The subsample of the 114 QSOs with B<19.7 is considered nearly complete. These QSOs are homogeneously distributed over the search field (Fig. 3). In particular, the QSO surface density in the northern half of the field, which is not covered by the CFHT blue grens survey, is comparable to that in the southern part where almost all known QSOs are in the CFHT survey. An additional three QSOs were detected by the VPM search in the CFHT field. Two of them (No. 5, 15) have "normal'' spectra and were obviously ignored by chance in the CFHT survey; the other one (No. 7) shows very strong broad absorption line (BAL) features. The subsample is of course flux-limited, and $M_{\rm B}$ is therefore strongly correlated with z (Fig. 4). Only for $z\le0.55$, the subsample is complete with regard to luminosities (since B<19.7 for QSOs of such z). Note that most of the objects with z<0.55 shown in Fig. 4 are Sey1s.

  
4.2 Redshift distribution

The redshift distribution is shown in Fig. 5 both for (a) the subsample from Table 3 and (b) the sample of all identified QSOs with $B\le 19.7$. The shape of the z distribution is roughly comparable with that from the SDSS Quasar Catalogue I. Early Data Release (Schneider et al. 2002), corroborating the result from VPM survey in the M 92 field (Brunzendorf & Meusinger 2002). This impression is confirmed by the two-tailed KS two-sample test. According to this test on a significance level $\alpha=0.05$, we have not to reject the null hypothesis that our subsamples (a) and (b) and the SDSS sample were drawn from the same population.

  
4.3 Surface density

Figure 8: Colour-colour diagram for the M3 field. QSOs/Sey1s are shown as $\bullet$ (present study) or $\blacklozenge$ (CFHT survey), respectively. Quasars with z>2.2 are framed with a $\Box$. The arrows on the right and at the top, respectively, indicate QSOs with unknown B-V and U-B colours, respectively. The # symbols indicate narrow emission line galaxies. Open circles are VPM-QSO candidates that were spectroscopically identified as foreground stars; medium-priority candidates without spectroscopic follow-up observations are shown as plus signs. Other star-like objects with 14<B<20 are shown as small dots. Selection criteria from colour surveys are indicated by horizontal dotted line: UVX search, diagonal dotted line: two-colour search as discussed in Paper I, dashed curve: two-colour selection according to LaFranca et al. (1992).

Figure 9: Colour-redshift relations for the the QSOs/Sey1s in the M3 field. Panels  a), b) show the objects from Table3 ($\bullet$). Panels  c), d) show the QSOs/Sey1s from the NED identified with objects from our list ( $\blacklozenge$). For comparison, the mean relations for the QSOs from Véron-Cetty & Véron (2001) are plotted.

The "completeness'', or absolute efficiency, of the survey can be estimated by comparing the QSO surface densities, i.e. number counts per solid angle, to the densities predicted by other surveys. Figure 6 shows the surface density of all QSOs (i.e., $z>0,\ M_{\rm B}<-23$) with B<19.7 in our search field, compared with mean relations from various data samples. The cumulative density N(<B) is simply computed by dividing the number of QSOs brighter than a given magnitude by the effective search area where the B magnitudes were corrected for an interstellar extinction of $A_{\rm B} = 0.05$ mag. The size of the Schmidt field is $3\hbox{$.\!\!^\circ$ }3\times3\hbox{$.\!\!^\circ$ }$3. After subtracting the areas of the plate margins (not shown in Fig. 3), the calibration wedge, the crowded inner part of M 3, and the area covered by the images of the objects in the remaining field, the effective search area amounts to 7.8 deg².

The resulting number-magnitude relation is roughly described by $\log~N(<B) \propto xB$ with $x\approx0.6$ for 17.5<B<18.5and $x\approx0.75$ for 18.5<B<19.5, in agreement with the result from the M 92 field (Brunzendorf & Meusinger 2002). The surface densities for our total QSO sample are higher than those derived by Hartwick & Schade (1990), especially at brighter magnitudes. There are 9 QSOs with B<18 in our search field, corresponding to 1.15 QSOs deg^-2 mag^-1, i.e. a factor of 1.8 more than in the Hartwick & Schade data. More recently, La Franca & Cristiani (1997) derived surface densities of 0.76 QSOs deg^-2 0.5 mag^-1for $17.9<B<18.4,\ 0.3<z<2.2,$ and $M_{\rm B}<-23$, to be compared with 1.28 QSOs deg^-2 0.5 mag^-1 for our sample. The surface densities based on single-epoch observations are affected by variability and cannot be compared directly to those based on time-averaged magnitudes. It should be noticed however that Hartwick & Schade corrected their data for such a variability-induced over-completeness. Note also that the different assumptions for q₀ (both Hartwick & Schade and La Franca & Cristiani adopted q₀=0.5 while we used q₀=0) make no significant difference for the number counts. We cannot exclude that the relative overabundance of apparently bright QSOs is due to the limitations of small-number statistics, but note that a similar result was found for the VPM survey in the M 92 field (Meusinger & Brunzendorf 2001).

  
4.4 Spectra

The low-resolution spectra of the objects from Table 3 are shown in Fig. 7. The spectra are dominated by the typical AGN-emission lines: Ly$\alpha$+N V $\lambda1240$, Si IV+O IV] $\lambda1400$, C IV $\lambda1549$, C III] $\lambda1909$, Mg II $\lambda2798$, [O III] $\lambda\lambda4959,5007$, and the Balmer series. A few objects (Nos. 10, 19, 64, 50, 11, 69, 7) apparently have relatively weak lines. Unfortunately, many of these spectra were taken at relatively bad atmospheric transparency, and poorly removed telluric lines may effect the equivalent widths of the QSO emission lines. Therefore we do not quantitatively discuss the distribution of the equivalent widths in this paper. The analysis of the QSOs from the VPM survey in the M 92 field (where most of the spectra were taken under better weather conditions) has shown that the sample-averaged line equivalent widths for the VPM QSOs are in good agreement with those from other samples of radio-quiet QSOs (Meusinger & Brunzendorf 2001).

Broad absorption troughs are indicated in the spectra of the QSOs Nos. 3, 49, 37, 57, 7, 44, 75, 33, 65, and 70. For some other QSOs absorption features may be hidden due to the low signal-to-noise. The fraction of BAL QSOs is about 10%, in good agreement with the BAL percentage in the SDSS Early Data Release (Schneider et al. 2002). There is only one object with an unusual spectrum: the BAL QSO No. 7 where the emission lines are almost completely masked by extremely broad absortion lines. The best guess for the emission redshift is $z_{\rm em} \approx 1.7$, compared to $z_{\rm abs} \approx 1.5$ for the strongest absorption lines (C IV $\lambda1549$, Al III $\lambda1860$, and the Fe II-multiplet at $\lambda2500$). This object is a high-priority VPM QSO candidate with quite red colours (see below). There is no entry in the NED at this position. Objects like No. 7 are not very likely to be recognized by most other optical QSO surveys. For a few other QSOs/Sey1s, the spectra in Fig. 7 have unusually red continua (Nos. 42, 64, 48, 3). However, the U-B indices (Table 3) of these objects closely follow the mean colour-redshift relation (Fig. 9) and thus the missing blue light in the spectra is interpreted by the slit-loss effect due to atmospheric dispersion (Sect. 1). We conclude that, up to the limit of the survey, the fraction of QSOs with unusual spectra is at maximum a few percent. This conclusion is again in agreement with the statistics from the (still incomplete) SDSS data (Hall et al. 2002).

  
4.5 Colour indices

In Paper I, a colour-colour diagram of the QSO candidates was presented showing a broad scatter of their colour indices and a large fraction of red QSO candidates. The distribution of the spectroscopically classified objects on the U-B versus B-V plane is shown in Fig. 8. The most important result is the fact that all candidates with extremely red colours proved to be foreground stars, in agreement with what we found from the VPM survey in the M 92 field. Obviously, the QSOs from Table 3 populate essentially the same area as the QSOs from the CFHT grens survey. For z<2.2 this area is well defined by the selection criteria of classical colour surveys. There are only 7 low-redshift (z<2.2) QSOs located beyond the demarcation line for colour selection discussed in Paper I. A typical fluctuation of about 0.35 mag per colour index is expected due to photometric errors and variability (as the time-lines for the three colour bands are not identical). In addition, a scatter may be produced by intrinsic differences in the continuum slope and/or the strength of emision lines and/or absorption troughs. Remarkably, the strongest deviation from the colour selection line is measured for the two absorption line QSOs Nos. 7 and 75.

The same conclusion is reached from the colour-redshift relations (Fig. 9). Apart from the scatter due to variability and photometric errors, the QSOs from our sample closely follow the mean relation of QSOs from the Véron-Cetty & Véron (2001) catalogue. Among the QSOs from Table 3, the strongest deviation is measured again for Nos. 7 and 75. The QSO No. 28, which is the faintest object in Table 3, shows a strong deviation in B-V. Fainter QSOs tend to have larger colour indices B-V (Fig. 9d).

Data from the 2 Micron All Sky Survey (2MASS; Skrutskie et al. 1997), March 2000 data release are available for  25% of the field. With an identification radius of 10 arcsec we identified six QSOs from our whole sample with catalogued 2MASS sources. For all six objects the $B-K_{\rm s}$ colour index is smaller than 4, i.e. smaller than for the red QSOs found by Webster et al. (1995) among the flat-spectrum radio-loud QSOs.

For the M 92 field we have estimated that the fraction of QSOs with unusually red B-V colour indices must be less than 3% up to B=19.8 (Brunzendorf & Meusinger 2002). From the data in the M 3 field we estimate a similar fraction of about 2% up to B=19.7. Although a survey in the B-band is obviously not an ideal approach to derive strong conclusions about the underlying population of possibly highly reddened QSOs, the unbiased VPM QSO sample provides a constraint of its properties. Let us assume for simplicity that there are two QSO populations of comparable size: normal QSOs and reddened QSOs with an intrinsic dust reddening equivalent to  E_B-V = 0.5 - a not unreasonable level in a dusty system - implying an extinction of about 2 mag in the B-band (assuming a galactic extinction curve). Using the number-magnitude relation from Fig. 6, we would expect to detect about 5-7 strongly reddened QSOs up to $B_{\rm lim} = 19.7$ in each search field. This is clearly more than what we found, indicating that the red QSOs are either redder on average or less frequent. A more detailed discussion of this question has to be deferred to a separate study.

  
4.6 QSO pairs

The search for pairs with an angular separation of up to 2 arcmin yields 8 combinations, but the redshift differences are very large for 7 of them. The closest pair in the three-dimensional space consists of Nos. 38 and 40 from Table 4 with z=1.310 and 1.325 and an angular distance of 96 arcsec. For objects with small separations (e.g., <10 arcsec), the measurements of variability and proper motion are attended with additional uncertainties. Such objects are, in principle, rejected from the VPM candidate list. This does not significantly reduce the general efficiency of the search method but the efficiency of the detection of close pairs.