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5 Discussion

The results found in this research could imply that strong perturbations (like propagating shock waves) are a common phenomenon in the initial section of the jets of RL objects whereas localized disturbances in the accretion disks are more rare occurrencies, at least at very short timescales. Roughly speaking, 1 out of 10 disks would display this latter kind of activity (to the extent it is strong enough to be visible above noise in measurement of the steady flux), according to the microvariability data for RQQSOs. Contrariwise, the relativistic jets of RL sources seem to be very prone to undergo strong perturbations. If the flux microvariations are associated, as proposed by several authors, to the interactions of thin shocks with small features (e.g. eddies or inhomogeneities in the particle density) in the otherwise steady jet flows, then rapid variability studies can be used to explore the fine-scale structure of the inner jets.

Let us consider, as an example, the microvariations displayed by the BL Lac object 0537-441 during our observations. The variability timescale associated to a flux change $\Delta F$ can be estimated as $t_{\rm v}=\Delta F/ ({\rm d}F/{\rm d}t)$, which in the case of 0537-441 gives $t_{\rm v}\approx 16.9$ hours. This timescale can be related to the size l of the feature in the jet by (e.g. Romero et al. 1995b):
l\sim t_{\rm v} c \gamma^2 (1+z)^{-1},\end{displaymath} (3)
where $\gamma=(1-\beta^2)^{-1/2}$ is the Lorentz factor of the shock and we have assumed a small viewing angle ($\cos \theta \sim \beta$) as suggested by VLBI observations of 0537-441 (e.g. Shen et al. 1998). This assumption allows us to replace the Doppler factor $\delta=[\gamma(1-\beta\cos\theta)]^{-1}$ by $\gamma$in the calculations. Adopting $\gamma\sim\!10$ we get a feature size of $l\sim\linebreak
0.2$ pc. Notice that the thickness of the shocked region behind the shock front must be considerably smaller than this length if the lightcurve displays a well-defined outburst as it is the case in 0537-441. We can reasonably assume, consequently, a thickness $\Delta
x\sim\!0.02$ pc for the post-shock region where the excess of radiation is produced. This means that the shock-feature interaction must be occurring very close to the jet's apex (at, let's say, 0.1-5 pc) because $\Delta x$ increases with the distance traveled by the shock along the jet (Blandford & McKee 1976). Features like density inhomogeneities, bends, or even turbulent eddies can be produced at such distances from the nucleus by Kelvin-Helmholtz instabilities in the interface between the jet and the external medium if the magnetic field is not very strong (Romero 1995).

It is an interesting point that XBL objects seem to have higher magnetic fields and/or electron energies than radio-selected blazars (Sambruna et al. 1996). This is consistent, in the shock-in-jet scenario, with the fact that the former objects present lower duty cycles and smaller variability amplitudes. Romero (1995) has shown that axial magnetic fields prevent the development of Kelvin-Helmholtz instabilities in sub-parsec to parsec-scale jets if their values exceed the critical value $B_{\rm c}$ given by:
B_{\rm c}=[4\pi n m_{\rm e} c^2 (\gamma^2-1)]^{1/2}\gamma^{-1},\end{displaymath} (4)
where n is the local electron density, $m_{\rm e}$ is the electron rest mass, and $\gamma$ is the flow's bulk Lorentz factor. In XBLs $B\gt B_{\rm
c}$ fields would inhibit the formation of small-scale structures reducing the incidence of microvariability in the optical lightcurves. Duty cycles for longer variations (timescales from months to years), originated in the shock own evolution (e.g. Marscher 1990), should instead be similar in both kind of objects unless there were differences in the shock-formation mechanism.

As we mentioned in the Introduction, superluminal gravitational microlensing has been also suggested as a possible explanation of microvariability in some objects (e.g. Rabbette et al. 1996). In the case of 0537-441 this alternative explanation cannot be ruled out. There is a report of a foreground galaxy (Stickel et al. 1988) at a possible redshift of z=0.186. Compact objects (planets, stars) in the galaxy can produce a rapidly variable lightcurve by gravitational magnification of a superluminal component in the background blazar. This scenario for the rapid variability of 0537-441 has been developed in detail by Romero et al. (1995a), including the constraints introduced in the mass density distribution of the interposed galaxy by the fact that just one macroimage of the blazar is observed (Narayan & Schneider 1990). Using this model, we have estimated that the observed optical microvariations require a superluminal shock with a radius $r_{\rm s}\sim\!1.8~10^{-3}$ pc, which should be propagating at a distance of $\sim\!0.018$ pc from the jet's apex (we assume, once again, $\gamma\sim\!10$ and $\cos \theta \sim \beta$). From the requirement that the angular radius of the source must be smaller than the Einstein angular radius of the lenses in the intervening galaxy we obtain that the masses must be $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle ... $M_{\hbox{$\odot$}}$ (i.e. they can be any kind of stars).

Whether microlensing is the main cause of microvariability in 0537-441 or not will be decided by simultaneous multifrequency observations in the near future (Romero et al., in progress). Beyond the final result for this particular object, it is clear that microlensing alone cannot account for the very high duty cycle of RL sources. The main candidate for producing very rapid variability in these AGNs is the interaction of shocks with features in the relativistic jets of these objects. New microvariability studies at different wavelengths of individual sources where shock velocities are well-constrained by frequent VLBI observations can be used to determine the microstructure of the innermost part of the jets.


The authors acknowledge use of the CCD and data acquisition system supported under U.S. National Science Foundation grant AST-90-15827 to R.M. Rich. They are also very grateful to the CASLEO staff for their kind and very professional assitance during the observations. Insightful comments by the referee, Dr. Paul Wiita, helped to improve the original version of this paper. Authors' work has been partially supported by the Brazilian agency FAPESP and the Argentinian agencies ANPCT and CONICET. G.E.R. also thanks Antorchas Foundation.

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