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Astron. Astrophys. 358, 451-461 (2000)

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7. Discussion

The analysis of the total flux density light curves at mm and cm wavelengths, together with multi-epoch, multi-wavelength VLBI data, allows us to suggest that the 4-year cycle of the total flux density variations is connected with the regular ejection of components with apparent superluminal motion. The VLBI data reveal the existence of a superluminal component (B) during cycle C3, with a zero-separation time (from 43 GHz images) close to the beginning of the cycle. Comparison of total flux density variations with variations of the core and the most compact jet component (B) allow us to connect the first of the two most prominent outbursts of the aforementioned 4-year cycle (I in cycle C2 and 1 in cycle C3) with the core of the source and the second (II in cycle C2 and 2 in cycle C3) with the jet. According to the total flux density curves (Fig. 1 and also Fig. 16) the outbursts connected with the core show at 8 GHz a time delay (0.7[FORMULA]0.1) yr relative to 37 GHz during both cycles C2 and C3. If we assume that cycles of variability C2 and C3 are distinguished from each other mainly in amplitude and are otherwise similar in physical nature, then we can estimate their physical characteristics by combining the spectral parameters with the estimations of angular sizes and apparent superluminal velocities.

According to Kellermann & Pauliny-Toth (1969) and Marscher (1987) the magnetic field [FORMULA][Gauss] can be estimated from the turnover frequency [FORMULA][GHz], corresponding flux density [FORMULA][Jy], and angular diameter of the emitting component (approximated as a uniform sphere) at the turnover frequency [FORMULA][mas]:


The spherical angular diameter of a component [FORMULA] can be found from the elliptical gaussian FWHM of the VLBI model fit [FORMULA] by the relation [FORMULA] (Marscher 1987). From [FORMULA]=8.1 we determine the minimum possible Lorentz factor [FORMULA]8.2; the viewing angle for [FORMULA] can be estimated by the formula [FORMULA], and the Doppler boosting factor in this case is close to the value of the Lorentz factor [FORMULA] 8.2, but it can be much smaller for larger angles (up to [FORMULA] and much larger for smaller angles. For the core outburst (see Fig. 5), the turnover frequency [FORMULA]37 GHz and the corresponding flux density [FORMULA]=1.5 Jy. The mean elliptical gaussian size of the core from our 43 GHz VLBA data [FORMULA]=(0.085[FORMULA]0.035) mas (Table 3) and the corresponding spherical diameter [FORMULA] mas. We then obtain for the magnetic field of the core observed at [FORMULA]40 GHz a value [FORMULA] G. The corresponding time scale in the observer's frame for synchrotron losses of electrons at 37 GHz is [FORMULA] yr. The shortest timescale of variability observed (from the data shown in Fig. 1) is [FORMULA]0.6 yr (calculated from the formula [FORMULA]; Burbidge et al. 1974). Therefore, either the observed timescale corresponds to one of the following: (a) changes in the acceleration rate of relativistic electrons, (b) changes in strength of the magnetic field, or (c) value of the light-travel time across the emitting region, or the magnetic field is lower than the value derived above. This latter possibility would occur if there is substructure within the core: the core is only slightly resolved by our observations and could contain two or more smaller subcomponents. If this is the case, the magnetic field could be as low as [FORMULA] G, which is estimated from the condition [FORMULA].

Fig. 14 shows that outburst 2 (and probably II) coincides with the moment when jet component B goes through the point where the jet changes direction. Therefore, the observed ouburst can possibly be explained by a change of viewing angle [FORMULA]. As has been shown by Marscher et al. (1991) for 4C39.25, even a modest decrease of the viewing angle from the value that gives maximum apparent velocity can result in a flare that is essentially simultaneous at all radio frequencies, while the shock-in-jet model predicts significant delays at low frequencies (Gómez et al. 1997). The flux of component B during outburst 2 (see Fig. 16, Table 2) increased by a factor 3. Taking into account that the flux density varies as [FORMULA], we find that this corresponds to an increase of [FORMULA] by factor [FORMULA]1.4, namely from 8.2 to 11, and a decrease in the viewing angle from [FORMULA] to [FORMULA]. The apparent velocity [FORMULA] in this case should decrease from 8.1 to 7.3 c. Unfortunately, we have no proper motion data for this outburst to check this prediction. If a change in the direction of motion is indeed the cause of the outburst, then future VLBI monitoring should see a change in apparent velocity of superluminal components.

The appearance of a 1.3-yr periodicity, which is especially prominent in the high frequency light curves (see Fig. 7 and Table 1) is interesting. This could be caused, for example, by components passing through periodic compressions and rarefactions in the jet, generated by pressure imbalance with the external medium (e.g., Gómez et al. 1997).

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© European Southern Observatory (ESO) 2000

Online publication: June 8, 2000