Annu. Rev. Astron. Astrophys. 1997. 35: 445-502
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3. VARIABILITY OF THE OPTICAL CONTINUUM IN HIGH REDSHIFT AGN

3.1. Observed Characteristics of the Optical Variability

The high surface density of high-z AGN, ~ 100 per square degree at mB brighter than 22, is such that a significant number of radio-quiet AGN can be recorded on a single image taken with a Schmidt telescope or a large telescope with a wide field. The technique of choice to study the optical variability of high-z radio-quiet quasars is thus the definition of large optically selected samples and their repeated broadband imaging at regular intervals (a few months to a year) over many years. This results in a light curve for each quasar in the sample, with the advantage that all the light curves have the same number of data points.

The very large effort in monitoring high-z quasars has recently come to fruition. There are now enough data in various samples to separate the effects of luminosity and redshift on the variability, avoiding the inherent correlation that exists in magnitude-limited samples. The observation that optical-UV spectra of both low- and high-luminosity AGN vary more at short than at long wavelengths (as found for high-luminosity AGN by Cutri et al 1985) accounts completely for the observed increase of variability with redshift (Giallongo et al 1991, Trevese et al 1994, Di Clemente et al 1996, Cristiani et al 1996). It also explains the long-puzzling absence of a time-dilation effect (Deltatrest-frame = Deltatobserved(1 + z)-1), wherein quasars at higher redshift are sampled more frequently and for shorter time intervals in their rest frames, because this effect is compensated by the intrinsic increase of variability with decreasing rest-frame wavelength.

The recent developments come mostly from the four largest on-going programs (the first three based on Schmidt plates): (a) the South Galactic Pole sample of 300 radio-quiet quasars observed over 16 years (Hook et al 1994); (b) the monitoring program in field ESO/SERC 287 (Hawkins 1993, 1996), with more than 200 plates since 1975 (Hawkins & Véron 1993), which has produced the best quasar light curves to date; (c) the sample in SA 94 comprising 183 quasars observed in B over 10 years (Cristiani et al 1990); and (d) the sample in SA 57 based on prime focus plates at the Mayall 4-m telescope at Kitt Peak (Koo et al 1986, Trevese et al 1989).

The main result is that, in a given proper time interval and at a fixed rest-frame wavelength, more luminous AGN vary with a smaller fractional amplitude than less luminous AGN. Also, the maxima and minima of the light curves are symmetric, a result also suggested by the light curves of low-z AGN.

The analysis of the variability is normally done using the structure function, which is the curve of growth of variability with time. It is defined in slightly different ways in the literature but generally has the form S(Deltatj) = <|mik - miell|>, where Deltatj = |tk - tell|, mik is the magnitude of the quasar i at epoch k, and brackets signify the median of the ensemble (Hook et al 1994) or the average of the ensemble (Di Clemente et al 1996, Cristiani et al 1996).

Parametrizations of the structure function usually assume that the dependences on Deltat and luminosity are separable. In Hook et al (1994) for example (also in Trevese et al 1994 and references therein), the best-fit model has the form

Equation 1          (1)

with b about 0.022 and p = 0.18 ± 0.02. This value of p corresponds to a power spectrum of the light curve P (omega) = omega-(1+alpha), with alpha = 0.36 ± 0.04. For comparison, in this description, p = 0, 0.5, and 1 correspond to uncorrelated measurements, random walk variations, and linear variations, respectively.

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