3 Completeness of the selection method

The spectral energy distribution of QSOs in the optical wavelength regime is dominated by an ultraviolet excess and broad emission lines. Depending on redshift, one or the other feature is more prominent, and therefore the reliability to select QSOs with a given selection criterion varies with redshift. Quasars are not selected if the parameters of their density spectra are too similar to those of stars, unless the parameter space accepted for selection is made rather broad. This may lead to a contamination of the QSO candidate sample with stars, decreasing the effectiveness of the selection process to an unacceptable low level. Thus, completeness is traded off for efficiency and surveys have to emphasize one of the aspects, depending on their primary aims.

In the present stage the selection and the priorities for follow-up spectroscopy of the HQS emphasize effectiveness, motivated by the aim to find new bright high-redshift quasars. However, due to the classification strategy to exclude as quasar candidates only those objects, which can be classified positively as stars or as non-AGN-galaxies, the possibility to determine the survey selection function is preserved. The survey selection function determines the reliabilitity of a selection procedure as a function of brightness, redshift and spectral energy distribution of quasars (Hewett & Foltz 1994). While follow-up spectroscopy is made currently mostly of objects classified as prime QSO candidates, the determination of the selection function would require spectroscopy of the secondary candidates as well. Their number is a factor of $\approx$3 greater than the number of QSO candidates, making such an undertaking feasible only on a restricted part of the sky covered by the HQS.

Our selection process of quasar candidates is semi-automated. In the first step an automated selection is done by using the spectral slope as discriminating parameter. In the second step a subjective selection is made based on the visual classification of the high-resolution density spectra. For both steps the reliability of the selection has to be evaluated separately. For the search of bright high-redshift QSOs the first step is the critical one, because mostly the broad emission Ly-$\alpha$ line makes the density spectra so outstanding that they will not be missed visually, except that the spectra are distorted by overlaps.

To check the reliability of our candidate selection our present digitized database of 418 processed fields was correlated with the quasar catalogue of Véron-Cetty & Véron (1996). We compiled all Veron catalogue entries that have magnitudes less than 17 and a redshift from 0.1 to 3.2. The smaller redshifts were left out because bright extended objects often show crippled digitized LRS spectra allowing no reliable classification. We found 370 entries which we searched for among our digitized LRS spectra up to a maximum distance from their catalogue position. 5% could not be found due to overlapping spectra and another 5% could not be found on both the direct and the prism plate, possibly due to incorrect brightnesses or positions in the catalogue. Discarding all objects with a B magnitude of greater value than 17 on our Schmidt plates resulted in the final sample of 189 QSOs. In the first automatical slope dependent step of the selection process 1 QSO was not selected due to overlapping spectra. From the automatically selected 188 QSOs further 9 had overlapping spectra, and 8 were misclassified during the subsequently visual classification. Altogether, approximately 10% were lost due to overlaps on the Schmidt plates, and further 5% were misclassified during the interactive classification.

On the other hand the use of a compilation of QSOs drawn from many sources includes unknown biasing effects. For example, the parameter cube spanned by brightness, redshift and spectral slope is certainly not covered homogeneously. The number of objects is still too small for dividing the parameter cube into a large number of cells, inside which averaging over the properties of the plates (position on the characteristic curve, seeing effects etc.) would then be possible. Thus, at this stage it is not possible to determine the selection function for the full survey.

The use of the Véron-Cetty & Véron catalogue introduces possible biases of earlier surveys into the completeness test, as, e.g., the controversially discussed possibility that QSOs are hidden by dust will prevent selection by optical surveys because of the redness of their continuum (Webster et al. 1995; Boyle & di Matteo 1995). Summarizing, we consider the automatic selection using the continuum slope as insensible to losing bright quasars unless they have spectral slopes which cannot be distinguished from stars on objective-prism plates.