The Optical Variability of QSO's

The long-term variability of a sample of 486 optically selected QSOs in the fields of the SA94, SA57 and SGP has been studied. The relations of variability with luminosity and redshift have been investigated by means of statistical estimators that are ``robust'' and allow at the same time to eliminate the influence of the measurement errors. The analysis in the QSOs rest frame of both the ensemble structure function ($SF$) and individual variability indices show: 1) a negative correlation between variability and luminosity; 2) a significant positive correlation between variability and $z$; 3) such correlations may be equally well parameterized either with a model in which the timescale of the variability is fixed for all the QSOs ($\tau \sim 2.4$ yr), while the amplitude linearly increases with the absolute magnitude and $z$, or with a model in which the timescale of the variability linearly depends on the absolute magnitude and the amplitude is only a function of $z$. The same analysis carried out in the observer's frame shows: 1) a negative correlation between variability and luminosity; 2) the timescale of variability does not depend significantly either on the absolute magnitude or on $z$; 3) the ensemble structure function is well represented by a parameterization in which, with a fixed timescale of about 5.5 yr, the amplitude linearly increases with the absolute magnitude; 4) although the general behaviour of the $SF$ does not show a systematic variation of the timescale and/or amplitude with $z$, if we examine the average variability index for objects with $-25>M_B>-27$, we find that below $z=1$ QSOs are significantly less variable than at higher redshift. Implications in terms of the black-hole, starburst and microlensing models are briefly discussed.