We discuss details of the mirror model proposed by Ghisellini & Madau. This model seems to be favourite by the multiwavelength observations of the -ray flare in 1996 from 3C 279 (Wehrle et al. 1997). Based on the analysis of the kinematics of the emission region (a blob moving relativistically along the jet) we come to the conclusion that only relatively small part of the mirror is able to re-emit soft photons which serve as a target for production of -rays. For the parameters of the -ray flare observed in 1996 from 3C 279, the radius of this part of the mirror should be comparable to the longitudinal extent of the blob. It has to be of the order of cm in order to be consistent with the rising time of the flare. This part of the mirror should lay inside the jet cone provided that its opening angle is of the order of . As mentioned in Ghisellini & Madau (GM), the physical processes in the jet may prevent the presence of the well localized mirror inside the jet.
The calculations of density of photons re-emitted by the mirror are done by Ghisellini & Madau (see Fig. 2 in GM) in a time independent picture which do not take into account the dynamics of the blob. As a consequence they integrate over the parts of the mirror at distances from the jet axis which are much larger than the maximum distance (Eq. (19)), found in our dynamical (time dependent) analysis. The photon densities seen by the blob cannot be directly compared with those obtained by us in a time dependent version of the mirror model. Ghisellini & Madau results are only correct for the continuous (time independent) flow of relativistic plasma along the jet axis but overestimates the density of soft photons seen by the relativistic electrons in the blob with limited longitudinal extent. The relativistic blobs in blazars has to be confined to the part of the jet in order to produce the -ray flares with the observed rising time scale.
We computed the -ray light curves expected in the dynamical version of the mirror model for different distribution of relativistic electrons inside the blob and assuming that the density of electrons in the blob changes during propagation along the jet. Slowly rising -ray flux with sudden cut-off towards the end of the flare, as observed in 3C 279, is obtained in the case of inhomogeneous blob with electron densities exponentially rising towards the end of the blob. Such electron distribution is difficult to understand in the popular scenario for -ray production in which relativistic shock moves along the jet. It seems that such shock should rather inject relativistic electrons with high efficiencies close to the front of the blob, with the trail of electrons on its downstream side (Kirk, Rieger & Mastichiadis 1998). However the -ray light curve expected in this case is different from that observed during the flares in the blazar 3C 279.
Since -rays are produced in a region which is close to the mirror, therefore the shape of the -ray light curve is not very sensitive on the variations of the density of electrons during the time of propagation of the blob between the base of the jet and the mirror. Of course the absolute -ray fluxes produced by the blobs with different evolutions of electron densities in time may differ significantly.
The -ray light curves presented in Figs. 2a and b show very sharp cut-offs towards the end of the flare due to our assumption on the negligible thickness of the mirror. In fact, the observed width of the peak in the -ray light curve of 3C 279, of the order of day (see Fig. 1 in Wehrle et al. 1997), may be related to the time in which relativistic blob is moving though the mirror with the finite thickness. If this interpretation is correct then the thickness of the mirror has to be limited to cm which is comparable to the distance of the mirror from the base of the jet.
In this analysis we do not consider production of -rays in terms of the SSC and EC models simultaneously with the mirror model since there is no clear evidence of their importance in the -ray light curve and the multiwavelength spectrum observed in 1996 from 3C 279 (Wehrle et al. 1997). The -ray light curves reported in Figs. 2 show only relative change of the -ray flux with time. They are not straightforwardly dependent on the parameters of the blob (the magnetic field, electron density, blob perpendicular extent, disk radiation) which are not uniquely constrained by the observations. The SSC and EC models will require to fix these parameters in order to guarantee reliable comparisons.
© European Southern Observatory (ESO) 1998
Online publication: July 7, 1998