## 3. Statistical indices of the variability## 3.1. The structure functionTo study the ensemble variability properties of the SA94 sample we have used the structure function (Simonetti et al. 1985, Paper I), defined as: where mag are the magnitudes at the time
In Fig. 1 the R-band
It should be noted that points in Fig. 1 with are all derived from the comparison of the POSS plate with the remaining plates. Being 28 years apart from Plate R5413, Plate E1453 does not play any role in the estimates of the SF on the shorter timescales (5 yr or less). In Fig. 2 a comparison between the
In order avoid any possible bias deriving from different time samplings or time dilation effects, a direct comparison of the variability in the R and B band has been carried out. As shown in Fig. 3, for each object we have computed the quantities , as the difference between the magnitude at a given epoch and the average magnitude. Since the epochs of the R plates are in large part coincident with the epochs sampled with the B plates (epochs 2, 3, 4, 5, 6, 7 of the present paper correspond to epochs 2, 6, 8, 9, 10, 11+12 of Paper I, respectively) it has been possible to plot the versus the for all the objects with at least 5 epoch-magnitudes in common. Again, the POSS plate does not play any role in this comparison.
We have then fitted a straight-line relationship between and , with a least-squares technique that takes into account the errors of the data points on both axes (Fasano & Vio 1988). The result is . The dispersion of the points around this relation is fully compatible with the measurement errors, with no intrinsic scatter. If we make the additional assumption that the R flux varies in phase with the B flux, i.e. that for , then we obtain , again fully consistent with no intrinsic scatter. The coefficient between the R and the B variability obtained in this way is consistent within the errors with what has been estimated on the basis of the SF analysis. In Fig. 4 the distribution of QSOs in the redshift-magnitude
plane is illustrated. To further investigate and disentangle the
dependences of the variability on the luminosity and redshift we have
examined two subsamples. The first is defined within the redshift
limits (the area between the dashed lines in
Fig. 4). The second is defined within the absolute magnitude
limits (the area between the continuous lines
in Fig. 4). As in Paper I, the
## 3.2. The variability indexIn order to further verify the results obtained in the previous
section, we have evaluated the variability index (
The correlation coefficients indicate a correlation of the variability index with the absolute magnitude and an almost equal anticorrelation with redshift (correlation coefficients respectively of and -0.18, both with a significance greater than 99%). Due to the strong flux-redshift anticorrelation in the QSO sample it is not possible to disentangle if one of the two correlations is spurious. However, if, on the basis of the results of the previous subsections and of Paper I, we assume as fundamental the absolute magnitude - variability correlation, it is possible to subtract its influence from the variability-redshift anticorrelation via the method of partial correlation analysis (Spiegel 1991). Applying this recipe to the results of Table 3, the corrected correlation coefficient between variability index and redshift, turns out to be (65%), not significant, in agreement with the result shown in Fig. 6. © European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |