2 QSO candidate selection

Figure 1: Proper motion index $I_{\rm pm}$ as a function of the mean B magnitude for about 7000 star-like objects with 17 < B < 20 (small grey dots). The 154 QSOs, Sey1s, and NELGs in this magnitude range are marked as bullets. The horizontal line indicates the proper motion selection threshold.

The VPM search is based on indices for star-like image structure, positional stationarity, overall variability, and long-term variability measured on 57 B plates taken with the Tautenburg Schmidt plates between 1964 and 1994, i.e. with a time-baseline of three decades. The B magnitudes given in the present paper are mean magnitudes from this database. The strategy for the QSO candidate selection of the VPM search in the M 3 field and the definitions of the indices are outlined at length in Paper I. Here we review only the basic ideas and describe the modifications in the selection procedures.

The proper motion index, $I_{\rm pm}$, is expressed simply by the measured proper motion in units of the proper motion error. The overall variability index, $I_{\rm var}$, is assessed by the deviation of the individual magnitudes about the mean magnitude, and is normalised by the average magnitude scatter for star-like objects in the same magnitude range. Finally, an index for long-term variability, $I_{\rm lt var}$, is defined by means of structure function analysis and is computed for all star-like objects with $I_{\rm pm} < 4$ (see below) and B<20. The selection thresholds for the indices were derived from the statistics of the previously known QSOs in the field. There are 90 such QSOs identified with star-like objects measured on at least 7 of our B plates. We found that a good compromise between the success rate (i.e., the fraction of candidates that turn out to be QSOs) and the completeness (i.e., the fraction of all QSOs found by the survey) is achieved for the following set of constraints: $I_{\rm pm}<4,~ I_{\rm var}>1.3$, and $I_{\rm ltvar}>1.4$. (In Paper I, the long-term variability index was denoted RS₁₀₀.) The pre-estimated values for the success rate and the completeness are 90% and 40%, respectively, for a limiting magnitude  $B_{\rm lim} = 19.7$. (Note that the limiting magnitudes of the individual B plates vary from 19.5 to 21.3.)

For stationary objects, the probability  $p_{\rm pm}$ to measure a non-zero proper motion follows a Weibull-distribution and depends only on the proper motion index (Brunzendorf & Meusinger 2001). An object with $I_{\rm pm} \ge 4$ has a probability of $p\ge 0.9997$ for non-zero proper motion. As illustrated by Fig. 1, the proper motion selection is in particular efficient for brighter magnitudes where the proper motion errors are smaller. For B < 18.5, the typical proper motion error is about 1 mas yr^-1, and 83% of the star-like objects have $I_{\rm pm} > 4$. For 19<B<20, on the other hand, the typical proper motion error is about 3 mas yr^-1, and only about 21% of the star-like objects have $I_{\rm pm} > 4$. In a flux-limited sample, most of the objects have magnitudes close by the limit. Hence, the proper motion selection appears not very efficient for the whole survey with a limit at $B \approx 19.7$. However, at brighter magnitudes, the number-magnitude relation for QSOs is much steeper than for the foreground stars. This means that the contamination of the variability-selected QSO candidate sample by foreground stars is stronger at brighter magnitudes where the proper motion selection works more efficiently. At fainter magnitudes, the zero proper motion constraint is important in particular for the efficient rejection of nearby variable late-type main sequence stars (see Paper I).

The selection starts with 32 700 objects detected on a deep master plate. About 24 600 objects were identified on at least two further plates, among them are about 21 500 objects with star-like images. A basic object sample for the variability selection is defined by the 12 800 star-like objects measured on at least 7 B plates. After excluding the objects in the crowded cluster region (distance to the centre of M 3 less than 24'), this sample is reduced to 8582 objects in total and to 4614 objects in the magnitude range $16.5\le B \le 19.7$, respectively. About 65% of the objects from this reduced sample are rejected due to the zero proper motion constraint $I_{\rm pm} < 4$. Finally, the variability constraints strongly reduce the candidate sample to a manageable size.

 

 

Table 1: Object numbers for the subsamples of QSO candidates with high, medium, or low priority.

priority class	high	medium	low
number of candidates	80	95	607
already catalogued	26	17	15
newly observed	54	68	27
QSOs/Sey1s	75	36	20
NELGs	2	-	1
stars	3	49	21

For practical reasons, the candidate sample is devided into three subsamples of different priority. A similar approach was used for the VPM search in the M 92 field (cf. Brunzendorf & Meusinger 2001). However, the variability indices defined there are slightly different from those used in the present study, and the priority classification in the two VPM fields are not completely identical. Here, the priority depends mainly on the variability indices. In addition, the B magnitudes and the crowding of the field (expressed by the distance $d_{\rm c}$ from the centre of M 3) are taken into account. For all priority classes, star-like objects are considered with $I_{\rm pm} < 4,~ B=15-19.7$, and $d_{\rm c}>24$ arcmin. The high-priority subsample consists of the strongly variable objects with $I_{\rm var} > 1.8,~ I_{\rm ltvar} > 1.8$. The medium-priority subsample contains the objects with smaller variability indices $I_{\rm var} = 1.3{-}1.8$ and $I_{\rm ltvar} > 1.4{-}1.8$. In addition, we included the few objects with somewhat higher variabiliy indices ( $I_{\rm var} = 1.6{-}1.8$ and $I_{\rm ltvar} = 1.6{-}1.8$) in the stronger crowded region $d_{\rm c}= 12{-}24$ arcmin. Finally, the low-priority subsample comprises the objects having only one of the two variability indices above the threshold (i.e., $I_{\rm var} > 1.3$ or $I_{\rm ltvar}>1.4$). In addition, we consider also objects with $19.7\le B\le19.8$ and $d_{\rm c} > 12$ arcmin as low-priority candidates if at least one of the two variability indices exceeds the threshold. The variability selection is illustrated by Fig. 2.

As discussed in Paper I, the U band variability index may serve as an additional selection criterion. In practice, however, the fainter objects are measured on only a small number of U plates. Therefore, the U variability index was invoked only in one case: the QSO No. 51 from Table 3 has insignificant B variability indices but shows significant variability in the U band.

The numbers of selected candidates are 80, 95, and 607, respectively, for the subsamples of high, medium, or low priority (Table 1). It is expected that the fraction of QSOs/Sey1s strongly decreases with decreasing priority. In particular, the low-priority subsample is expected to be strongly contaminated by galactic stars with relatively enhanced photometric errors.

A cross-check of the candidate list against the NED (2002, February) yields the identification (identification radius 10 arcsec) of 57 QSOs/Sey1s and one narrow emission line galaxie (NELG) with catalogued redshifts. Over the whole magnitude range, 104 objects with catalogued redshifts z>0 were identified (100 QSOs/Sey1s, 4 NELGs). The overwhelming fraction of the QSOs/Sey1s are from the CFHT blue grens survey (e.g., Crampton et al. 1990) which covers approximately half of our survey field.

Figure 2: Long term variability index $I_{\rm lt var}$ versus overall variability index $I_{\rm var}$ for the 4 379 star-like objects from the reduced basic object sample with 14 < B < 20 (small grey dots). The previously known QSOs, Sey1s, and NELGs in the field are shown as $\blacklozenge$ in the first two panels a) for $B\le 19.7$ and b) for $19.7 < B \le 20$). In panel c), the objects from Table 3 are indicated by $\bullet$. The symbols for QSOs with z>2.2 are framed. Panel d) shows the QSO candidates from the present study that were proved to be foreground stars ($\circ$) as well as the 10 medium-priority candidates without follow-up spectra (+). The lines indicate the variability selection criteria (see text).