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A&A 452, 743-749 (2006)
DOI: 10.1051/0004-6361:20035604
Channelled relativistic outflows in active galactic nuclei: analytic solutions for the evolution of particle spectra
C. Schuster1, I. Lerche1, 2, R. Schlickeiser1 and M. Pohl31 Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, Germany
e-mail: rsch@tp4.rub.de
2 Institut für Geophysik und Geologie, Universität Leipzig, Germany
3 Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011
(Received 31 October 2003 / Accepted 4 November 2005)
Abstract
Context.Calculations of highly energetic neutrino and TeV
-ray emission
from relativistic jets of Active Galactic Nuclei (AGN) are often based
on a model that involves a collimated relativistic blast wave,
in which the spectral evolution of energetic particles is determined by
the interplay between the particle injection by sweep up of the
interstellar medium, energy losses by radiation and diffusive escape.
Aims.To date such models only have been solved numerically because of the highly
non-linear nature of the time-dependent equations describing particle
spectra and bulk energy loss. However it is difficult to see how
parameters and groupings of parameters influence the resulting numerical
solutions, except through intensive investigations of many
numerical simulations. Therefore analytic solutions are particularly
helpful.
Methods.We provide exact mathematical solutions to a very broad class
of AGN type models. By selecting different functional behaviors of
parameter values,
we cover a large compendium of possible situations. The comparison of the exact
solutions with observational information can help to improve our understanding of
the evolution of individual AGN. Exact solutions can also be used to
provide controls on the appropropriateness and accuracy of numerical programs used
to solve the equations.
Results.We provide an analytical description of the evolution of proton spectra
according to the pick-up model. We analyze
the behavior of the particle spectra in the plasma frame. The solutions are
determined by two competing processes: the deceleration of the jet plasmoid
and particle cooling via radiation.
Key words: methods: analytical -- radiation mechanisms: non-thermal -- galaxies: jets -- galaxies: active -- plasmas -- gamma rays: theory
© ESO 2006
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