## Retardation of non-thermal photon light curves from flaring blazars

### I. Synchrotron radiation

^{1}
Institut für Theoretische Physik, Lehrstuhl IV:
Weltraum- und Astrophysik, Ruhr-Universität Bochum, 44780 Bochum, Germany e-mail: rsch@tp4.ruhr-uni-bochum.de

^{2}
Experimentelle Physik V, Technische Universität Dortmund, 44221 Dortmund, Germany

Received:
23
July
2009

Accepted:
28
November
2009

An analytical model is presented which describes the intrinsic synchrotron intensity emitted by
a spherical plasmoid volume of radius *R* in the jet of an active galactic nucleus (AGN). Analytical results
for the emergent synchrotron intensity could be achieved by using a monochromatic approximation
for the synchrotron power. The synchrotron intensity is given by an infinite
sum, reflecting the spatial eigenfunction distribution of the radiating electrons over the
emission knot. The radiative transport of the generated synchrotron photons is simplified
by the use of the escape probability concept which approximates the spatial
photon diffusion caused by multiple Compton scatterings off thermal electrons in the knot.
With these assumptions conclusions on the total duration of the synchrotron flare, its starting time and the cause for
even shorter time variabilities are derived. The total flare duration at all photon energies equals the
light travel time *2R/c*. Shorter photon energy-dependent synchrotron intensity time variations are possible,
which reflect the influence of the photon retardation and escape as well as the temporal and spatial dependences
of the relativistic electron density distribution. The starting time of the synchrotron flare
is delayed with respect to the injection time of ultrarelativistic electrons *t*_{0} by a photon energy
dependent time scale , reflecting the necessary cooling time
which relativistic electrons need in order to radiate at photon energies below the initial characteristic
synchrotron photon energy *E*_{0}.

Key words: radiation mechanisms: non-thermal / galaxies: active / gamma rays: galaxies

*© ESO, 2010*