A&A 477, 701-715 (2008)

DOI: 10.1051/0004-6361:20078651

## Synchrotron self-Compton flaring of TeV blazars

##### I. Linear electron cooling

**R. Schlickeiser and C. Röken**

Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, 44780 Bochum, Germany

e-mail: rsch@tp4.ruhr-uni-bochum.de

(Received 11 September 2007 / Accepted 4 November 2007 )

** Abstract **

The vast improvement of the sensitivity of modern ground-based air Cherenkov telescopes,
together with the sensitive flux measurements at lower frequencies, requires accurate elaborations
of the theoretical radiation models for flaring blazars. Here the flaring of TeV blazars
due to the synchrotron-self Compton (SSC) process is considered.
We assume that, at the moment *t*=*t*_{0}, a flare in the emission knot
occurs due to the instantaneous injection of monoenergetic (*E*_{0}) ultrarelativistic electrons.
The ultrarelativistic electrons are injected uniformly over the knot volume and at later times are subject to linear
synchrotron radiation cooling in a magnetic field whose strength remains constant during the
time evolution of the relativistic electrons.
The generated synchrotron photons are subject to multiple Thomson-scattering
off the cold electrons in the source giving rise to spatial photon
diffusion. Optically thick and thin synchrotron radiation intensities and photon density distributions in the emission
knot as functions of frequency and time are analytically determined. The synchrotron photons serve as
target photons for the SSC process, which is calculated in the optically thin frequency range using the
Thomson approximation of the inverse Compton cross section. It is shown that the optically thick part of the
synchrotron radiation process provides a negligible contribution to
the resulting SSC intensity at all frequencies and times.
Because the high-energy TeV photons undergo no elastic multiple Compton scatterings, we neglect
the influence of photon diffusion in the calculation of the SSC intensity and fluence distribution with energy.
The SSC fluence exhibits a break at
*E*_{f}=15.8*b*^{-1/3} GeV from a
*E*_{s}^{-1/4}-power law spectrum at lower
photon energies
to a
*E*_{s}^{-2}[1-(*E*_{s}/*E*_{0})^{7/3}]-distribution at high energies
. The application to the observed TeV fluence spectrum
of the flare of PKS 2155-304 on July 28, 2006 yields
.
The emergent SSC light curve is independent of spatial photon diffusion and determined by the temporal
variations on the relativistic electron density distribution and the synchrotron photon density.
The comparison of the observed with the theoretical monochromatic synchrotron light curve
determines the photon escape distribution.

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

**--**galaxies: active

**--**gamma rays: theory

**©**

*ESO 2008*