The cyclo-synchrotron process and particle heating through the absorption of photons

Free access article

Issue		A&A Volume 451, Number 3, June I 2006


Page(s)		739 - 746
Section		Astrophysical processes
DOI		http://dx.doi.org/10.1051/0004-6361:20054346

A&A 451, 739-746 (2006)
DOI: 10.1051/0004-6361:20054346

The cyclo-synchrotron process and particle heating through the absorption of photons

K. Katarzynski^{1, 2}, G. Ghisellini¹, R. Svensson and J. Gracia³

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 IASA, Dept. of Physics, Univ. of Athens, Panepistimiopolis, 15784 Zografos, Athens

(Received 12 October 2005 / Accepted 11 January 2006 )

Abstract
Aims.We propose a new approximation for the cyclo-synchrotron emissivity of a single electron. In the second part of this work, we discuss a simple application for our approximation, and investigate the heating of electrons through the self-absorption process. Finally, we investigate the self-absorbed part of the spectrum produced by a power-law population of electrons.
Methods.In comparison to earlier approximations, our formula provides a few significant advantages. Integration of the emissivity over the whole frequency range, starting from the proper minimal emitting frequency, gives the correct cooling rate for any energy particle. Further, the spectrum of the emission is well-approximated over the whole frequency range, even for relatively low particle energies ( $\beta \ll 0.1$ ), where most of the power is emitted in the first harmonic. In order to test our continuous approximation, we compare it with a recently derived approximation of the first ten harmonics. Finally, our formula connects relatively smooth to the synchrotron emission at $\beta=0.9$ .
Results.We show that the self-absorption is a very efficient heating mechanism for low energy particles, independent of the shape of the particle distribution responsible for the self-absorbed synchrotron emission. We find that the energy gains for low energy particles are always higher than energy losses by cyclo-synchrotron emission. We show also that the spectral index of the self-absorbed part of the spectrum at very low frequencies differs significantly from the well-known standard relation $I(\nu) \sim \nu^{5/2}$ .

Key words: radiation mechanisms: non-thermal -- radiation mechanisms: thermal -- radiative transfer

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