4 Results

   
4.1 Quasar candidates

From the original sample of 1539 objects, morphologically classified as point sources (see Sect. 2) within the 0.25 square degrees covered in five optical passbands, 1494, detected in at least three filters, were considered. In total there are 204 objects classified as quasars in the magnitude range . This number is in excellent agreement with that predicted by quasar models (202 ⁺¹³¹_-78, e.g. Hatziminaoglou et al. 2002) at the limiting magnitude of B=25.0, which roughly corresponds to the completeness limit of the colour catalogue considered. It is also in good agreement with estimates based on observed number counts (e.g. Hartwick & Schade 1990; Glazebrook et al. 1995).

Figure 1: (U-B)/(B-V) (panel a)) and (B-R)/(R-I) (panel b)) two-colour diagrams showing the quasar candidates selected on the basis of the $\chi ^2$-technique. Open circles, plus signs and crosses denote candidates classified at 95%, 95-99% and outside 99% confidence level, respectively.

To help evaluate the results of the $\chi ^2$-method it is important to compare them with those obtained from a simple colour-colour selection. This is illustrated in Fig. 1 which shows the two colour-colour diagrams normally used to identify low to intermediate ( (U-B)/(B-V)) and high-redshift quasars ( (B-R)/(R-I)), respectively. In the plot the identified quasars are displayed with different symbols to indicate their associated confidence level as follows: robust (open circles); good (plus signs); and poor (crosses). The same notation applies to all colour-colour plots presented hereafter, unless noted otherwise.

From the careful inspection of these colour-colour diagrams several points can be made regarding the performance of the $\chi ^2$-analysis. Note, for instance, that nearly all robust candidates are located in the region predicted by the models for low- to intermediate-redshift ( ) quasars, i.e. and , with a few cases extending into the region where higher redshift quasars are expected to lie. One important short-coming of the standard colour selection is its inability to discriminate between objects with similar colours, leading inevitably to contamination problems. In the particular case of quasars, the main contaminants are white dwarves and early spectral type main-sequence stars. The results of $\chi ^2$-analysis suggest that this technique is capable of distinguishing among these different classes, as can been seen from quasar candidates lying very close to and sometimes overlapping objects of other types. Poor candidates are, in general, located at the outskirts of the region delineated by the robust candidates, except for a few cases where the two populations overlap. Similar conclusions can be drawn from the (B-R)/(R-I) diagram shown in panel b. In particular, given the B filter used, high-redshift quasars ( ) lie very close to the main sequence, making a colour selection problematic and susceptible to contamination by main-sequence stars. It is worth mentioning the object with $B-V~\sim1.8$ (see panel a) located in a region unlikely to be occupied by quasars. However, on other colour diagrams this object lies close to quasar tracks. A more detailed discussion about its nature will be presented in Sect. 5.

In order to evaluate the results obtained applying the $\chi ^2$-method, they can be compared with those based on the more traditional UVX and BRX selection. Adopting criteria similar to those used by Hall et al. (1996) one finds 298 UVX and 49 BRX independent quasar candidates. Out of these, 166 are in common with those classified using the $\chi ^2$-method. Considering the $\chi ^2$-classification as reference one estimates a contamination of $\sim$40% in a colour-colour quasar selection, demonstrating the potentiality of the technique for minimising the number of contaminants. Moreover, since it uses the colour information in a combined way, it should also lead to a higher completeness than those based on distances from the stellar locus (e.g. Gaidos et al. 1993; Newberg & Yanny 1997). For example, colour based selections will tend to miss quasars with redshifts in the range . This is a serious drawback because currently it is believed that the space density of optically-selected quasars starts decreasing in this redshift range. The possible benefits of the $\chi ^2$-classification over a simple colour selection remains to be evaluated, when spectroscopic data become available.

Figure 2: Optical-infrared colour-colour diagram used in the selection of KX candidates, showing the quasar candidates selected on the basis of the $\chi ^2$-technique. The symbols correspond to those defined in Fig. 1.

The CDF-S field has also been observed in the near-infrared $JK_{\rm s}$passbands over an area of $\sim$0.1 square degrees. For this seven passband sub-sample, the number of morphologically classified point sources is 623, out of which 605 are detected in at least three filters. In total there are 92 objects classified as quasar candidates, out of which 62 are in common with those found using only the optical data. The infrared information yields 30 new candidates. Five cases originally classified as quasars are now assigned different classifications: three as white dwarves, one as an G8I and one as a K3I stars.

For the case of optical/infrared all $\chi ^2$-selected quasar candidates are shown on the $(V-J)/(J-K_{\rm s})$ diagram, introduced by Croom et al. (2001), presented in Fig. 2. This diagram is suitable for identifying quasar candidates, due to the following reasons. First, it could partially solve the degeneracy between low to intermediate quasars and white dwarves, occuring when the UVX criterion is applied. Quasars should exhibit a K-excess due to the broad bump created by dust, present in their spectra at the wavelengths around $\sim$1 $\mu$m (in the rest frame). White dwarves do not have such near-infrared spectral features and should be separated from quasars when the infrared information is added. Second, as pointed out by Croom et al. (2001), KX-selection could identify reddened quasars possibly missed by the UVX selection. Choosing similar regions of colour space as these authors, one finds 65 quasar candidates, 52 of which in common with those UVX selected. Of the KX-selected candidates 34 belong to the quasar candidate list defined using the $\chi ^2$-technique. From Fig. 2 one sees that in order to ensure completeness of $\chi ^2$-selected robust quasar candidates, one is forced to consider all objects with V-J<3.0, which in turn leads to a contamination comparable ($\sim$50%) to the one introduced by the UVX selection. Another point worth mentioning is the fact that in Fig. 2 one finds red objects not predicted by models of the spectral properties of point-sources. As discussed below, this is probably due to the contamination of the sample by unresolved galaxies (see Sect. 5). This population is seen in all optical/infrared colour-diagrams presented below.

Another important feature of the the $\chi ^2$-method is that it can be used not only to classify the objects but also, in the case of extragalactic candidates, to estimate their redshifts. The photometric redshift distribution estimated for the quasar candidate sample selected from the five optical passbands by the $\chi ^2$-technique is shown in Fig. 3, where the three rankings are plotted separately. The distribution covers a broad range of estimated redshifts extending all the way to $z \sim 4.5$. The present sample includes 16 candidates with estimated redshifts , among which 10 are robust classifications. Due to the degeneracy in the assignment of quasar redshifts based solely on broad-band optical filters (HMP00) objects with have a considerable dispersion in their estimated photometric redshifts. This accounts for the excess seen at and the dearth at . At $z\sim1$there is also the increased probability of misclassifying Compact Emission Line Galaxies (CELGs) as quasar candidates, as shown by HMP00 using the DMS spectroscopic sample. The dearth of objects with redshifts in the interval is due to the colours of AGN at these redshifts, which are much like the colours of the main sequence stars, and can be very easily mis-classified as such. Note that in the present sample there are seven U-dropouts and a B-dropout robust candidates with photometric redshifts .

Figure 3: Photometric redshift distribution of quasar candidates selected by the minimum $\chi ^2$-method for the UBVRI data set. The solid histogram denotes the distribution for candidates selected when no constraint is applied on the values of the $\chi ^2$. The dotted histogram corresponds to objects selected at 99%; and the dashed histogram correspond to those selected at 95%, as described in the text. Finally, the thick solid histogram is that predicted according the model adopted for the evolution of the quasar LF.

The redshift distribution of the 92 quasar candidates selected from their optical/infrared photometry is presented in Fig. 4. A comparison between Figs. 4 and 3 shows that by including the infrared data one can significantly improve the redshift estimates. As can be seen, the excess of low-redshift quasars is considerably smaller and the distribution resembles more closely the model prediction in the redshift interval . For the objects in common, Fig. 5 shows the comparison of photometric redshifts based on five and seven passband data. The final redshift distribution for all quasar candidates identified in the present work, including those with poor classification, is shown in Fig. 6, using the optical and, whenever possible, the optical/infrared data.

Figure 4: Photometric redshift distribution of quasar candidates $\chi ^2$-selected in the area covered by the optical and infrared data. The figure shows the model predicted redshift distribution (thick solid line) and the one measured for objects with no $\chi ^2$ selection (solid line), at 99% (dotted line) and at 95% (dashed line).

Figure 5: Comparison of the photometric redshift distribution of the 63 common quasar candidates using the five and seven passbands.

Using the above redshift distribution one finds a surface density of $\sim$55 quasar candidates with redshifts in the range per square degree, within the area covered by the optical observations. By contrast, using the optical/infrared data one finds a surface density of $\sim$100 per square degree, thereby improving the completeness of the sample.

Figure 6: Final photometric redshift distribution for all 234 quasar candidates. The thick solid line shows the model predictions.

Table 1 lists the first 40 entries of the final quasar candidate sample comprising 234 objects,

  

Table 1: First 40 entries of the CDF-S quasar candidate list. R-magnitudes are given in the Vega system.

extracted from the CDF-S. The table gives the following information: in Col. 1 the EIS identification number; in Cols. 2 and 3 the J2000 coordinates; in Col. 4 the R-band magnitude (Vega system); in Cols. 5-10 the optical/infrared colours; in Col. 11 the estimated photometric redshift; in Col. 12 the ranking (1-3) of the candidate based on the $\chi ^2$ confidence level, with the most robust classifications denoted by rank equal to one; and in Col. 13 notes as described in Sect. 5. The complete table can be retrieved from the URL http://www.eso.org/eis/eis_rel/dps/dps_rel.html Note that in the complete table the four candidates identified in optical but rejected when using the infrared data have been included.

4.2 Galactic objects

The $\chi ^2$-technique primarily used for classification of quasar, galaxies and stars has been extended to consider stellar sub-classes such as white dwarves, low mass stars and brown dwarves. Even though confirmation of these classifications will depend on spectroscopic data this method is applied here as a first attempt to define a robust procedure to select different sub-classes of galactic objects.

4.2.1 White dwarves

In order to search for white dwarf candidates, 66 theoretical spectra were provided from D. Köster, as well as three observed spectra of very cool white dwarves ( $T_{\rm eff} < 4000$ K) from Ibata (2000; F351-50, F821-07) and Oppenheimer (2001; WD0346). The template spectra were again compared to the broad-band photometry. A total of 97 objects were classified as white dwarf candidates in the magnitude range , out of which 86 are robust classifications. The number of 97 candidates is a factor of 1.5 higher that the 65 white dwarves with $\log g > 7$, brighter than B=25, expected to be found within the area of 0.25 square degrees, as predicted by current estimates of the white dwarf luminosity function (Girardi et al. 2001). From the total number of candidates, 89 have estimated temperatures in the range from 6000 K to 16000 K according to the theoretical spectra. The remaining nine were better matched by the observed very cool white dwarf spectra, with seven being robust classifications. The distribution of all candidates in the (U-B)/(B-V) plane is shown in Fig. 7. Two of the cool white dwarves are located at $(B-V)\sim0.7$ and in the interval 1.0<(U-B)<1.5, superposing the main-sequence locus. The location of these candidates are by and large consistent with the white dwarf cooling curve kindly provided by P. Bergeron. It is interesting to point out that one of the tracks, representing the cooling curve of hydrogen white dwarves curves towards the main-sequence. Note that five of the cool candidates are U-dropouts and do not appear in this colour diagram.

Comparison of Fig. 7 with Fig. 1 shows that for the characteristics of the present survey a simple UVX selection would lead to a large contamination of this sample by quasar candidates, since these populations have a significant overlap in this diagram. In fact, choosing typical values for the colours to delineate the region occupied by white dwarves in this diagram, the fraction of white dwarf candidates would correspond to about 30% of the total number of objects within this region. This is in contrast with the high success rate (72% spectroscopically confirmed) obtained by Christlieb et al. (2001) in their analysis of the Hamburg/ESO Survey (HES). These results illustrate the strong dependence of the efficiency of colour selection with the characteristics of the survey. A bright survey like HES would yield a low quasar and a high white dwarf surface density while exactly the opposite is true for the deep observations considered here.

Figure 7: (U-B)/(B-V) colour-colour diagram showing the $\chi ^2$-selected white dwarf candidates within the area covered by the optical data.

Figure 8: (V-J)/(J-K) colour-colour diagram showing the $\chi ^2$-selected white dwarf candidates within the area covered by the optical/infrared data.

The results obtained from the $\chi ^2$-analysis of the optical/infrared data are as follow: a total of 21 candidates are selected with 18 being robust detections. Figure 8 shows the distribution of the candidates in the same colour-colour diagram as Fig. 2. The locus of the white dwarves in this diagram is shifted redwards relative to that computed by P. Bergeron. The candidates have estimated effective temperatures in the range 6000 to 14000 K. The overlap between the sub-samples extracted from the five and seven passbands comprises 18 objects. The remaining three objects were originally classified as quasar candidates. Another 17 objects selected as white dwarf candidates based on the optical only, are now classified as quasar candidates. These results show how difficult it is to distinguish between quasars and white dwarves, and how useful the infrared data can be for that purpose.

It is worth pointing out that none of the cool white dwarf candidates identified using the optical colours are confirmed when the infrared colours are included in the analysis. This may be due to inadequacies in the near-infrared part of the model spectra, which could also explain the shift of the locus of white dwarf candidates mentioned above. This point will be further investigated when more infrared spectra become available.

Table 2 lists the first 40 entries of the white dwarf candidate sample,

  

Table 2: First 40 entries of the CDF-S white dwarf candidate list.

comprising 100 objects. The format is the same as in Table 1, with the effective temperature for the best-fit model presented in Col. 11.

   
4.2.2 Low mass stars and brown dwarfs

The low mass and brown dwarf spectral library was provided by Chabrier and Baraffe and consists of 105 theoretical spectra. They correspond to three sets of models which attempt to account for differences in the formation and settling of dust in the atmospheres (Chabrier et al. 2000). In this paper 53 of these models are used, corresponding to objects with masses 0.1 $~M_{\odot}$ (  K), to select low-mass stars and/or brown dwarf candidates. These template spectra were compared to our broad-band SED and over the 0.25 square degree area covered in five passbands a total of 18 candidates were identified with (all fainter than $B \sim 24$), with 13 being robust detections. All of the candidates are matched to spectra with effective temperatures between 1700 K and 2800 K, corresponding to masses roughly between 0.05 and 0.1 $M_{\odot}$, close to the hydrogen-burning limit. Their position on a (V-R)/(R-I) diagram is shown in Fig. 9. The objects with (R-I) > 2.5 seen on this figure that have not been selected as low mass or brown dwarf candidates were identified as M6V stars. Note that this class marks the transition between main sequence stars and low mass stars. Comparing the results of the $\chi ^2$-analysis with those obtained selecting objects redder than (R-I)>2.3, roughly corresponding to the (V-I)>3.5criterion adopted by Zaggia et al. (1999), one finds a significant contamination ($\sim$75%) by other types of objects.

Applying the $\chi ^2$-test on the optical/infrared data one finds a total of 35 candidates out of which 14 are robust classifications. All five low-mass star candidates that have both optical and near-infrared data are confirmed when the J and $K_{\rm s}$ information is included in the analysis. Furthermore, 11 stars originally classified as M5V and M6V stars using the UBVRI catalogues, are classified as low-mass stars when the infrared data are used. All candidates lie in the range and have estimated effective temperatures in the range between 1700 K and 2800 K. The candidates identified are shown in Fig. 10. The figure shows two main concentrations of low mass star candidates. One at ${(J-K_{\rm s})}\sim 0.8$ and ${(I-J)}\sim 1.5$, with 19 candidates, roughly corresponding to the transition between main sequence and very low mass stars. The other covers the region defined by and (13 objects), consistent with the location of the L-dwarves (L3) as reported in the literature (e.g. Reid et al. 2001; Leggett et al. 2001; Schweitzer et al. 2001). In this optical/infrared colour diagram, as mentioned in the previous sections, one sees again a population of objects with colours which are not predicted by any model describing the spectral properties of point-sources. As discussed below, most of these objects are associated with unresolved galaxies which contaminate the point-source catalogue.

Figure 9: Optical colour-colour diagram showing the brown dwarf candidates selected from the $\chi ^2$-technique.

Figure 10: Optical/infrared colour-colour diagram showing the brown dwarf candidates selected using the $\chi ^2$-technique.

Based on the results of the $\chi ^2$-selection one finds a surface density of very low mass stars of about 72 candidates per square degree using optical colours. When the near-infrared data is added, this value increases by a factor of 3, yielding a surface density of 350 per square degree. These estimates for the surface density are a factor of 3 higher than the expected value of 116 low-mass stars per square degree with  K and brighter than B=25, predicted by models (e.g. Girardi et al. 2001).

The final list of individual low-mass star candidates in the CDF-S field is given in Table 3.

  

Table 3: First 40 entries of the CDF-S low-mass star candidates.

The table format is the same as that of Table 2.

   
4.3 Very red objects

In the previous sections only objects detected in at least three passbands have been considered. There are, however, objects detected in one or two passbands, that may be of interest as well and for which neither the $\chi ^2$-method nor colour-colour selection can be of use. Of particular interest are those detected in the red-most passbands available, e.g. R and/or I over 0.25 square degrees and J and/or $K_{\rm s}$ for 0.1 square degrees. While impossible to classify them having a single colour and, in some cases, just a lower limit, these very red objects are natural candidates for follow-up spectroscopy. However, they could also be associated with possible features in the colour catalogue production, as discussed in Sect. 5. Table 4 lists the identification, coordinates, colour (whenever available) and red-most magnitude of the objects detected in R and I (16 objects), in Ionly (4 objects), in J and $K_{\rm s}$ (5 objects), and in $K_{\rm s}$ only (4 objects).

   

Table 4: Very red objects detected in the red-most filters available.

Name	$\alpha ({\rm J}2000)$	$\delta ({\rm J}2000)$	I	R-I	Notes
EIS$\;$J033112.31-275640.1	03:31:12.31	-27:56:40.1	21.86	2.53
EIS$\;$J033119.40-274834.9	03:31:19.40	-27:48:34.9	21.73	3.75
EIS$\;$J033140.38-275942.9	03:31:40.38	-27:59:42.9	20.50	1.79	d
EIS$\;$J033141.54-273505.2	03:31:41.54	-27:35:05.2	21.64	2.94
EIS$\;$J033143.33-274707.3	03:31:43.33	-27:47:07.3	21.71	2.79
EIS$\;$J033155.88-280344.7	03:31:55.88	-28:03:44.7	21.22	2.58
EIS$\;$J033221.01-273659.1	03:32:21.01	-27:36:59.1	20.89	2.12	d
EIS$\;$J033226.53-273721.2	03:32:26.53	-27:37:21.2	21.60	3.38
EIS$\;$J033226.64-280248.9	03:32:26.64	-28:02:48.9	20.71	3.76
EIS$\;$J033249.39-273405.8	03:32:49.39	-27:34:05.8	21.45	3.75
EIS$\;$J033254.87-280224.1	03:32:54.87	-28:02:24.1	21.47	3.99
EIS$\;$J033257.33-280310.1	03:32:57.33	-28:03:10.1	22.00	2.68
EIS$\;$J033302.20-275914.4	03:33:02.20	-27:59:14.4	21.80	3.29
EIS$\;$J033317.64-274040.0	03:33:17.64	-27:40:40.0	21.94	1.58	d
EIS$\;$J033327.41-280253.5	03:33:27.41	-28:02:53.5	20.95	4.07
EIS$\;$J033342.70-274618.1	03:33:42.70	-27:46:18.1	21.87	1.91
EIS$\;$J033132.87-274111.4	03:31:32.87	-27:41:11.4	21.11	>4.9	d
EIS$\;$J033211.00-275904.7	03:32:11.00	-27:59:04.7	21.86	>4.1	d
EIS$\;$J033230.20-273337.6	03:32:30.20	-27:33:37.6	21.12	>4.8	d
EIS$\;$J033251.60-275917.5	03:32:51.60	-27:59:17.5	21.57	>4.4	d
Name	$\alpha ({\rm J}2000)$	$\delta ({\rm J}2000)$	$K_{\rm s}$	$J-K_{\rm s}$	Name
EIS$\;$J033229.58-274812.5	03:32:29.58	-27:48:12.5	19.86	2.24
EIS$\;$J033238.14-274750.1	03:32:38.14	-27:47:50.1	20.33	1.37
EIS$\;$J033241.92-274512.5	03:32:41.92	-27:45:12.5	20.32	1.29
EIS$\;$J033245.80-274211.4	03:32:45.80	-27:42:11.4	19.98	1.13	d
EIS$\;$J033304.21-275137.3	03:33:04.21	-27:51:37.3	19.25	1.00	d
EIS$\;$J033225.12-274219.7	03:32:25.12	-27:42:19.7	19.09	>4.3	d
EIS$\;$J033226.12-274327.0	03:32:26.12	-27:43:27.0	20.42	>3.0
EIS$\;$J033242.43-274236.7	03:32:42.43	-27:42:36.7	19.71	>3.7	d
EIS$\;$J033307.51-274435.6	03:33:07.51	-27:44:35.6	20.18	>3.2	d

Figure 11 shows the $(R-I) \times I$ colour-magnitude diagram for all point-sources within the area of 0.25 square degrees (left panel) and the $(J-K_{\rm s}) \times K_{\rm s}$ diagram for the central area of the CDF-S covered by infrared data (right panel). The symbols are described in the figure caption. The extreme colour lower limits of the R- and J-dropouts shown in the figure make them likely to be brown dwarves (but see Sect. 5).

Figure 11: Colour - magnitude diagrams for the very red objects: I versus R-I (left panel) and $K_{\rm s}$ versus $J-K_{\rm s}$ (right panel). The filled circles show objects detected in two bands. Arrows indicate lower limits in the colour of objects detected only in the red-most passband.

4.4 Outliers

As discussed in Sect. 3.2 there are several reasons why one would like to search for outliers. From a pure technical point of view, objects with odd colours have to be identified and visually inspected as they may reveal problems in the construction of the colour catalogue, contamination by close neighbours, cosmic rays or other image artifacts. Alternatively, they may represent potentially interesting rare cases, either of known objects such as quasars at very high-redshifts or previously unknown populations. Therefore, classifying objects as outliers is an important step towards verifying the integrity of the colour catalogue and avoiding overlooking new discoveries.

Figure 12: Illustration of the selection of outliers applied on the five passband sub-sample for m=2. For definitions of $d_{\rm S_1}$ and $d_{\rm S_2}$ see Sect. 3.

As described in Sect. 3.2, outliers are identified in colour space based on their distances $d_{\rm S_1}$ and $d_{\rm S_2}$ from their nearest neighbour. An isolation criterion is then chosen, depending on the position of the objects on the $d_{\rm S_1}$ versus $d_{\rm S_2}$ diagram, as schematically shown in Fig. 12. This criterion divides the $d_{\rm S_1}$ versus $d_{\rm S_2}$ space in two regions, a densely populated one towards low values of the parameters and a much less dense region, where outliers lie. The parameters describing the separation line are chosen by fine-tuning them to include the most obvious cases of isolated objects in different colour-colour projections, separately for m=2 and m=3. Note, however, that objects isolated in one of the colour-colour projections are not necessarily isolated in all of them.

 

 

Table 5: Number of objects identified as outliers for different samples.

Sub-sample	N	m=2	m=3
UBVRI	1164	19	26
BVRI	300	13	17
${\it UBVRIJK}_{\rm s}$	385	19	18
${\it BVRIJK}_{\rm s}$	119	13	19

The results from the outlier analysis are summarised in Table 5, which lists the sub-samples, the number of objects in them and the number of outliers for m=2 and m=3, respectively. Note that in general the number of outliers increases with m. From the table one finds that the fraction of outliers is small being typically $\sim$10% of the whole sample. For both m=2and m=3, about 60% of the outliers are indeed poorly classified by the $\chi ^2$-method, while 30% are robust candidates. These results indicate, as expected, that the outliers consist of a mix population including known rare objects, objects possibly not well described by the available spectral library, or undesirable features on the images or the derived catalogues. The total number of outliers is 64 (80) for the sub-samples analysed using m=2 (m=3), out of which about 60% deserve a closer investigation as presented in the next section.

Figure 13 illustrates the location of outliers identified by applying the methodology described above to the five (seven) passband sub-sample. The figure shows two projections of the colour space, one for each of the sub-samples considered. The different symbols represent outliers selected using different values of m. Since nearly all of the outliers identified using m=2 are also identified when m=3 is used, in these plots only the additional objects identified with m=3 are represented by a different symbol. While a single projection is not sufficient to determine whether an object is truly an outlier in the multi-dimensional colour space, most objects far from the main concentration of points are successfully identified. In particular, in the left panel one finds the object with very particular colours, mentioned in Sect. 4.1, originally classified as a quasar. This case as well as others will be discussed in the next section.

Generally speaking, among the 30% of outliers which are also robust $\chi ^2$ classifications about half are identified as quasar candidates and half are identified as galactic object candidates from the $\chi ^2$-technique. In both cases, the candidates found to be outliers are associated with sparse populations with nearly all quasars having and most of the stars being early spectral types (O-A) which are rare, especially at high-galactic latitudes. These results apply equally well to all the sub-samples and isolation criteria adopted.

Note that the selection of the mth neighbour as well as the separation line must be empirically determined. Even thought there is a correspondence between the outlier selection and the values of the $\chi ^2$, the exact relation is not easy to establish.

Figure 13: (U-B)/(B-V) (left panel) and $(B-V)/(V-K_{\rm s})$ (right panel) showing objects classified as outliers by the criteria given in Sect. 3 adopting m=2 (circles) and m=3(rectangles). Open (filled) symbols denote objects with good (poor) classifications.