In this paper we studied correlations between the optical light curve and the 37 and 22 GHz radio light curves. The sample was 20 active galaxies, of which 11 are BL Lac objects and 9 are quasars. The analysis was done using the discrete correlation function (DCF). The seven sources that showed a clear correlation were S2 0109+22, 3C 66A, AO 0235+16, OI 090.4, 3C 345, BL Lac and 3C 454.3. A possible correlation between optical and radio events was found in six more sources: PKS 0420-01, PKS 0422+00, OJ 287, 4C 29.45, 3C 273 and 3C 446. No correlation was found in sources PKS 0735+17, PKS 0736+01, ON 231, 3C 279, 4C 38.41, 4C 09.57 and 3C 371. Of these sources PKS 0736+01, 4C 09.57 and 3C 371 had a very limited amount of optical data.
There are no clear rules for defining which correlations given by the DCF are significant and which are not. Some good instructions were given by Hufnagel & Bregman (1992). A rule of thumb used here is that the correlation is real if it can be confirmed by another method. It is also good to notice that due to sampling or gaps in the light curves the DCF analysis may miss some real correlations that are seen in the visual inspection of the light curves. Using visual inspection, for twelve sources at least one simultaneous event in optical and radio was seen (3C 66A, AO 0235+16, PKS 0420-01, PKS 0735+17, OJ 287, 3C 279, 4C 38.41, 3C 345, 3C 371, BL Lac, 3C 446 and 3C 454.3).
A new qualitative method to study correlations was introduced. The radio light curves were replaced by model fit light curves that consist of flares that have exponential rise and decay. At each optical observation epoch the phase and the brightness of the individual outbursts and the brightness of the model light curve were calculated. The optical flux level was then compared with the phase and the flux level of the coincident individual outbursts, as well as with the flux level of the composite model light curve.
In practice, our method is similar to interpolation of radio data in order to determine the radio flux at the time of each optical observation. However, the advantage of our method in comparison with, e.g., spline interpolation, is that we use an exponential interpolation function which appears to provide a realistic description of radio flare evolution (Valtaoja et al. 1999). Our model fitting not only provides an estimate of the total radio flux at any given epoch, but also parameters (phase and flux) of the individual radio flares at the time of each optical observation. We can therefore also search for overall statistical connections, such as whether optical flaring tends to occur during the rise or the decay of radio flares.
We agree with T94 that radio-optical connections would be found in many sources, were there more frequent observations in both optical and radio bands. However, even with fully sampled optical and radio flux curves statistically significant correlations might not be found by using the whole data. Individual flaring events in a single source can have variable time delays, and some events may even be clearly simultaneous in both radio and optical regimes. Examples of such behaviour can be seen in e.g., BL Lac (this paper, T94 and Tornikoski et al. 1994a). In addition, at least some sources appear to have both thermal and non-thermal optical events, e.g. OJ 287 (Valtaoja et al. 2000).
With these caveats, we summarize the results of our new method as follows.
For 11 sources the optical flux levels were high at the peak of the radio outburst at least for one of the radio frequencies: S2 0109+224, PKS 0422+00, PKS 0735+17, PKS 0736+017, OI 090.4, ON 231, 3C 273, 3C 279, 3C 345, 4C 09.57, 3C 454.3). For ON 231 this was the only evidence of correlation found. Also the flux levels of the model outbursts were high when the optical flux level was highest for 16 sources at least for one of the radio frequencies: S2 0109+224, 3C 66A, AO 0235+16, PKS 0420-01, PKS 0422+00, PKS 0735+17, PKS 0736+01, OI 090.4, OJ 287, 4C 29.45, 3C 279, 4C 38.41, 3C 345, 4C 09.57, 3C 371, 3C 454.3.
Acknowledgements
This work has been supported by Finnish Academy of Sciences projects number 875067 and 863510.
Copyright ESO 2002