2 Quasar samples

2.1 Observational material

The parent sample of quasars for the analysis of variability amplitude comes from a large scale survey and monitoring programme being undertaken in the ESO/SERC field 287, at 21h 28m, $-45^{\circ}$. Quasars have been selected according to a number of criteria, including colour, variability, radio emission and objective prism spectra, or a combination of these techniques. Redshifts for over 600 quasars have so far been obtained, and several complete samples defined within specific limits of magnitude, redshift and position on the sky (Hawkins & Véron [1995]). A detailed description of the survey is given by Hawkins & Véron ([1995]) and Hawkins ([1996]). Briefly, a large set of UK 1.2 Schmidt plates spanning 20 years was scanned with the COSMOS and SuperCOSMOS measuring machines to provide a catologue of some 200 000 objects in the central 19 square degrees of the plate. These were calibrated with CCD frames to provide light curves in $B_{{\rm J}}$ and R, and colours in UBVRI. Photometric errors have been discussed in detail in earlier papers (Hawkins 1996 and references therein) and are $\sim 0.08$ magnitudes for any individual machine measurement, and only weakly dependent on magnitude. There are approximately four plates in each year which reduces the error to $\sim 0.04$ magnitudes per epoch. This is small compared with the amplitudes of interest in this paper, and no attempt has been made to deconvolve it.

2.2 Sample selection

For the analysis in this paper three samples will be defined. The first (UVX) is based only on position on the sky and ultraviolet excess. The area on the sky containing the sample is defined by a number of AAT AUTOFIB fields and a 2dF field (Folkes et al. [1999] and references therein), covering a total area of 7.0 square degrees. Within this area all objects with U-B < -0.2 and $B_{{\rm J}} < 21.0$ were observed. This was extended to $B_{{\rm J}} < 21.5$ in the 2dF field. The ultra-violet excess (UVX) cut although necessary to give a relatively clean sample of quasar candidates, has the well known limitation of only being effective for redshifts z < 2.2. Beyond this redshift quasars become red in U-B as the Lyman forest enters the U band. For samples at higher redshift, variability has been found to provide a very useful criterion for quasar selection (Hawkins [1996]). The second sample for consideration here (VAR), was selected on this basis, with the requirement that the object should lie in the same area of sky as for the first sample with a magnitude limit $B_{\rm J} < 21$, or anywhere in the measured area of the plate with a magnitude limit $B_{\rm J} < 19.5$, and should have an amplitude $\delta m > 0.35$. The defining epoch for the magnitudes was the year 1977. This sample was selected without any reference to colour and so can be used to measure trends over a large range of redshift (z < 3.5). The third sample (AMP) was selected in a similar manner, but over the whole measured area of the plate (19 square degrees), and with an amplitude cut $\delta m > 1.1$. There is some evidence that these large amplitude objects form a distinct group, which is discussed below. The development of fibre fed spectrographs has meant that every object included within a given set of search criteria can be observed to give a high completeness level. In the case of fields observed with AUTOFIB, the existence of forbidden regions in the 40 arcmin field, and the very variable throughput for different fibres aligned at different positions on the spectrograph slit meant that up to 20% of spectra did not have sufficient signal to provide an unambiguous redshift. These objects where re-observed later with the faint object spectrograph EFOSC on the ESO 3.6 m telescope at La Silla. The 2dF observations where of very uniform quality, and the redshift measures or other classification were almost 100% successful from the fibre-feed spectra.

Details of all three samples, containing a total of 384 quasars, are given in the Appendix. B magnitudes are in the $B_{{\rm J}}$ system defined by the IIIa-J emulsion and the GG395 filter, and refer to the year 1977. The amplitude $\delta m$ is the difference between maximum and minmum magnitude achieved over the 20 year run of data. The samples which each quasar belongs to are indicated by 1, 2 and 3 corresponding to VAR, UVX and AMP respectively, as defined above. Data for many of the quasars have already been published by Hawkins & Véron ([1995]), but are given again here for completeness. Any small differences in the parameters are the result of further refinement of the calibration, and more extended monitoring of the light curves.

UVX selected samples have been used many times in the past for quasar surveys, and the constraints are quite well known. Variability selection has been less often used, and some additional comments are appropriate. In particular, there is the important question of completeness. Hawkins & Véron ([1995]) use a small sample of quasars in field 287 from Morris et al. ([1991]) selected by objective prism to test completeness. In 1993, 79% of the objective prism quasars would have also been detected according to the variability criterion $\delta m > 0.35$; by 1997 this figure had risen to 93%, with two quasars remaining below the variability threshold. In fact both of these quasars are clearly variable, with amplitudes 0.32 and 0.29 magnitudes. Strangely, they lie at either extreme of the redshift and luminosity range of the sample, with redshifts 3.23, 0.29 and luminosities -27.55, -22.33 respectively. Figure 1a shows the distribution of epoch at which quasars first satisfy the detection criterion given by Hawkins ([1996]). This is generally speaking equivalent to attaining an amplitude of 0.35 magnitudes. The distribution peaks between 2 and 4 years, and most quasars have satisfied the criterion after 7 years. Figure 1b shows the cumulative distribution of detection epochs, illustrating the point that after 15 years nearly all quasars have varied sufficiently to put them in the variability selected sample.

Figure 1: The top panel shows a histogram of the epochs at which quasars could first have been detected on the basis of the variability criterion. The bottom panel shows the same plot in cumulative form

The distribution of amplitudes is best shown with the UVX sample, which was selected without any reference to variability. Figure 2a is a histogram of amplitudes over a 20 year baseline, and shows a median amplitude of around 0.7 magnitudes. As would be expected from Fig. 1, nearly all of the sample lies above the threshold amplitude of the variability selected sample of 0.35 mags. With this in mind it is worth investigating the possibility of using the variability selected sample to look for correlations at higher redshift. Figure 2b shows a histogram of amplitudes for the VAR sample, which from the way it was selected has a cut-off at an amplitude of 0.35 mags. More interestingly, the distribution as a whole peaks at an amplitude of about 0.7, similar to the UVX sample. This peak is well clear of the cut-off, and implies that only a small fraction of quasars are missed from the VAR sample. There may however be a problem detecting the most luminous quasars, ( M_B < -27) for which there is evidence for relatively small variations (Cristiani et al. [1996]). Nonetheless, the sample can be used with caution to extend quasar correlations to high redshift.

Figure 2: The top panel shows a histogram of amplitudes for the complete UVX detected sample. The bottom panel shows a similar histogram for the variability detected sample (VAR). Quasars are constrained to have an amplitude greater than 0.35 mags