The Variability of QSOs in the Optical Band

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Constraints on the emission mechanism of AGNs can be provided by the variability of their spectral energy distribution (SED). Recently Di Clemente et al. (1996) have shown that the positive correlation of QSO variability with redshift can be due to a hardening of the spectrum in bright phases, coupled with the increase of the rest-frame frequency of the (fixed) observing band, for increasing redshift. Direct evidences of slope changes in the SEDs of a limited number of individual AGNs have been provided by Cutri et al. (1985), Edelson et al. (1990), and Kinney et al. (1991). In the following we present some preliminary results of a direct measure of variations of the SED slope in the complete, magnitude limited, sample of QSOs of the Selected Area 57 (Koo, Kron & Cudworth 1986; Trèvese et al. 1989 (T89)). The data are derived from two sets of prime focus plates of the SA 57, in the U, B_J, F and N bands, obtained with the 4-m telescope at the Kitt Peak National Observatory at two epochs separated by one year. Photometric methods and signal-to-noise optimization are described in T89 and Trèvese et al. (1994). The quasar sample, of < z > ⋍ 1.4, consists of 33 objects from T89, plus the brightest 3 members of the the Bershady, Trèvese and Kron (1998) sample of extended objects selected on the basis of variability. In Figure 1a Δα is reported versus the changes Δlog f_v in the B_J band and shows positive correlation, indicating a hardening of the spectrum in the bright phase. A special care is needed to avoid spurious Δα – Δlog f_v correlations (see Massaro & Trèvese 1996). The correlation coefficient is r=0.46 with a probability P(>r)=0.995, after the exclusion of one deviant point, whose inclusion would produce a higher correlation. The slope of the linear regression of ΔαΔlogv is b=1.9. Assuming that the spectra are, dominated by the big blue bump (BBB) in the sampled spectral region, around λ ≍ 2000 Å, we can use the simple approximation of a single black-body spectrum. To check the hypothesis that both the slope and brightness changes are caused by a temperature variations only, we derive the black-body temperatures from the SED slope as deduced from a linear fit of the log f_v v.s. logv relation, based on the U, B_J and F data. The average slope (excluding the two highest and lowest z objects) is 〈α〉=-0.4±0.6 and the average temperature is T ≍ 25000 K. For a black-body of fixed emitting surface and varying temperature T, the changes of the local SED slope and the relevant luminosity variations are related by (dα/dT)/(dlogB_v/dT) ≡ f(x), where x ≡ hv/kT. The slope b of the linear regression of Δα v.s. log f_v of Figure la is compared with the function f(x) values of the sample determined by the dispersion of α. We can conclude that dα/dlogB_v and α are consistent for x ≍ 3. For an average sampling wavelength < λ > ≍ 2000 Å of the sample, this corresponds to an average temperature T ≍ 2.5 × 10⁴ of a black-body of fluctuating temperature.