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Astron. Astrophys. 353, 473-478 (2000)

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5. Discussion

We have considered the acceleration of charged test particles via rotating magnetospheres based on a model topology which is motivated by the standard model for AGN (cf. Begelman 1994; Camenzind 1995; Fendt 1997). Accordingly, the jet magnetosphere originates very close to the central black hole from an accretion disk, with initially spherical profile until the relativistic jet is collimated to a cylindrical shape outside the light cylinder.

The centrifugal particle acceleration model described in this paper extends the calculations by Machabeli & Rogava (1994) and Gangadhara & Lesch (1997). We find that the maximum Lorentz factor attainable for an electron moving along a rotating magnetic field line is substantially limited not only by radiation losses (e.g. inverse-Compton) but also by the breakdown of the bead-on-the-wire approximation which occurs in the vicinity of the light cylinder. Due to these limiting effects, the acceleration of particles by rotating magnetospheres seems to be rather less important in the case of AGN. Our current calculations indicate, that for sub-Eddington accreting black holes, such as black holes with advection-dominated accretion flows (e.g. Narayan & Yi 1994; Narayan 1997), efficient pre-acceleration of electrons to Lorentz factors of the order of a few hundred might be possible, at least under the highly idealized conditions of our analytical toy model. It seems interesting that the highest energy gamma rays have been discovered from AGN of the BL Lac type which very likely accrete in a sub-Eddington mode (e.g. Celotti et al. 1998). Under such conditions, inverse-Compton scattering of accretions disk photons with energy [FORMULA] keV produces gamma rays with a maximum energy of [FORMULA] MeV, which is in general too low to explain the observed high-energy gamma rays in blazars (e.g. Kanbach 1996; Catanese 1999).

We wish to mention that the results in this paper essentially depend on the assumed intrinsic magnetic field and the angular frequency [FORMULA], i.e. on the size of the light cylinder radius ([FORMULA]). Therefore, one could find a way out of the problem above, for example, by assuming a light cylinder radius in BL Lac type objects which is much greater than [FORMULA] for a black hole mass of [FORMULA]. However, in view of magnetohydrodynamic models already existing, this seems to be rather improbable. In any case, the acceleration of supra-thermal test particles by rotating magnetospheres might possibly provide an interesting explanation for the pre-acceleration which is required for efficient Fermi-type particle acceleration at larger scales in radio jets.

There are several restrictions on our approach, e.g. we have assumed a projected, two-dimensional geometry and rigid rotation of magnetic field lines almost up to the light cylinder, hence, concerning the last point, neglected a kind of toroidal twist (Begelman 1994), when the inertial forces overcome the tension in the field line so that the field line is swept back opposite to the sense of rotation. However, one would not expect that these restrictions alter our conclusions essentially since they should lower the upper limit for the maximum Lorentz factor by making the acceleration mechanism ineffective somewhat earlier. Another restriction is the use of special relativity in our analysis, which is only justified far away from the black hole. A detailed general relativistic model is needed to assess whether this might affect the results very strongly or not.

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© European Southern Observatory (ESO) 2000

Online publication: December 17, 1999