Astron. Astrophys. 324, 461-470 (1997)

5. Summary and discussion

In this contribution we introduced the idea that magnetic field-aligned electric fields may contribute significantly to the high number density of relativistic particles required in the AGN context. We proposed that macroscopic resistive instability processes or more generally magnetic reconnection may result in the preacceleration of leptons up to . Our approach was twofold: On the one hand, we made use of a kinematic description introduced by Schindler et al. (1991) without specifying for any microscopic dissipation mechanism. We showed that in the framework of kinematic reconnection the formation of acceleration regions with reasonable dimensions length scales ( and ) can be described even for relatively long time scales involved in the activity process (intraday variability). On the other hand, we performed numerical simulations in order to study the dynamics in more detail for concrete physical specifications. We showed that for relatively strong magnetic fields leptons can be accelerated along the main component of the magnetic field up to the required energies on a length scale of , if we assume the ion-cyclotron microturbulence as a plausible candidate for anomaleous dissipation which implies the existence of current sheets of the width of . However, it is a necessary condition for the acceleration mechanism to opperate effectively that the acceleration length is shorter than the loss lengths due to either synchrotron radiation or inverse Compton scattering (which one of the loss process is more important mainly depends on the actual strength of the magnetic field). The relevant length scales for the physical parameters , (i.e , ), , , , and are illustrated in Fig. 6. It shows the loss lengths due to synchrotron radiation as well as inverse Compton scattering, the acceleration lengths both according to the numerical simulations and the kinematic approach and the critical acceleration length which is defined by assuming that the field-aligned electric field () has the maximum strength obtained by the simulations under the assumption of ion-cyclotron microturbulence all along the acceleration region. One recognizes that for the chosen magnetic field strengths synchrotron losses dominate losses due to inverse Compton scattering. Both the critical and the dynamical acceleration length are well below the synchrotron loss length, i.e. the particles can be accelerated up to the maximum energies supported by the potential structures. Within the kinematic description the width of the current sheet has to be enlarged by two orders of magnitude in order to receive effective acceleration as long as one deals with the entire time scale of intraday variability.

Fig. 6. The relevant loss and acceleration length scales as functions of the distance of the central acceleration region to the central object for . In this plot , , , and denote the acceleration lengths according to the numerical dynamical simulations and the kinematic approach, the critical acceleration length and the loss lengths due to synchrotron radiation and inverse Compton scattering, respectively.

We note that the synchrotron loss length is overestimated, since it is assumed that the particles are isotropic in pitch angle . The isotropization time is proportional to the inverse of the ion gyrofrequency, which is much larger then the acceleration time of about . Thus, we cannot expect to have an isotropic energy distribution. For anisotropic distributions it was shown by Epstein (1973) that the loss length is larger then the isotropic loss length by a factor . In the case of an anisotropic distribution the length scale for synchrotron radiation is times larger then the synchrotron loss length for an isotropic distribution.

How does the situation change if the magnetic field is considerably weaker? Fig. 7 shows the relevant length scales for which implies , ), and a magnetic Reynoldsnumbers of for the case of lower-hybrid-drift turbulence and for the case of ion-cyclotron turbulence. Obviously, in this case inverse Compton scattering is the dominant loss process and dissipation caused by the lower-hybrid-drift turbulence results in a shorter acceleration length than dissipation caused by the ion-cyclotron turbulence. What is more, the critical acceleration lengths as well as the dynamical one for the ion-cyclotron instability (the one for the lower-hybrid-drift instability is even shorter) are shorter than the relevant loss lengths.

Fig. 7. The relevant loss and acceleration length scales as functions of the distance of the central acceleration region to the central object for . In this plot , , , and denote the acceleration length according to the numerical simulations, the critical acceleration length assuming ion-cyclotron or lower-hybrid-drift turbulence and the loss lengths due to synchrotron radiation and inverse Compton scattering, respectively.

We conclude that for a fairly large parameter regime in the AGN context resistive instabilities that can be regarded as generic magnetic reconnection processes may play an important role in the preacceleration of charge particles up to energies of 1 GeV, i.e. . The central result of our calculations is that field-aligned potential drops driven by sheared magnetic fields can act as extremely fast accelerators for leptons even in the presence of strong magnetic fields and/or intense radiation field. Future work on relativistic particle simulations for the obtained macroscopic electric and magnetic field configurations is under way in order to corroborate our model.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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