A&A 453, 47-56 (2006)

DOI: 10.1051/0004-6361:20054176

## Stochastic particle acceleration and synchrotron self-Compton radiation in TeV blazars

**K. Katarzynski**

^{1, 2}, G. Ghisellini^{1}, A. Mastichiadis^{3}, F. Tavecchio^{1}and L. Maraschi^{1}^{1}Osservatorio Astronomico di Brera, via Bianchi 46, Merate and via Brera 28, Milano, Italy

^{2}Torun Centre for Astronomy, Nicolaus Copernicus University, ul. Gagarina 11, 87100 Torun, Poland

e-mail: kat@astro.uni.torun.pl

^{3}Dept. of Physics, Univ. of Athens, Panepistimiopolis, 15784 Zografos, Athens, Greece

(Received 8 September 2005 / Accepted 22 February 2006)

** Abstract ***Aims.*We analyse the influence of the stochastic particle acceleration for the evolution of the electron spectrum.
We assume that all investigated spectra are generated inside a spherical,
homogeneous source and also analyse the synchrotron and inverse Compton emission generated by such an object.
*Methods.*The stochastic acceleration is treated as the diffusion of the particle
momentum and is described by the momentum-diffusion equation. We investigate the stationary and time dependent solutions of
the equation for several different evolutionary scenarios. The scenarios are divided into two general classes.
First, we analyse a few cases
without injection or escape of the particles during the evolution. Then we investigate
the scenarios where we assume continuous injection and simultaneous escape of the
particles.
*Results.*In the case of no injection and escape the acceleration process, competing with the
radiative cooling, only modifies the initial particle spectrum. The competition leads
to a thermal or quasi-thermal distribution of the particle energy. In the case of
the injection and simultaneous escape the resulting spectra depend mostly on the energy
distribution of the injected particles. In the simplest case, where the particles are
injected at the lowest possible energies, the competition between the acceleration and the
escape forms a power-law energy distribution. We apply our modeling to the high energy
activity of the blazar Mrk 501 observed in April 1997. Calculating the evolution of
the electron spectrum self-consistently we can reproduce the observed spectra well
with a number of free parameters that is comparable to or less than in the "classic
stationary" one-zone synchrotron self-Compton scenario.

**Key words:**radiation mechanisms: non-thermal

**--**galaxies: active

**--**galaxies: BL Lacertae objects: individual: Mrk 501

**©**

*ESO 2006*