![]() | Annu. Rev. Astron. Astrophys. 1997. 35:
445-502 Copyright © 1997 by Annual Reviews. All rights reserved |
8.3. High-Frequency Synchrotron Emission: Energy Stratification?
At high frequencies (optical-UV for LBL, X-ray for HBL), the synchrotron
spectrum steepens
considerably and the largest spectral variability is observed. It is
natural to associate the steepening
with increasing radiative energy losses. Particle acceleration must also
occur or the high-energy
emission would vanish in a short time. Therefore the average spectrum
probably represents an
equilibrium among energy gains, losses, and escape. If the "injected"
particle spectrum is a power law, its equilibrium spectrum (in a
homogeneous region) is steeper by
= 1 above the energy
b at
which the radiative lifetime equals the escape time
(Kardashev 1962).
The peak in the synchrotron power would occur at
b
b2, and the associated
change in spectral slope would be
= 0.5.
Spectral variability above
b (flattening with
increasing intensity) could be due to fluctuations
in the acceleration process on time scales shorter than those over which
equilibrium can be
established; the flatter injected spectrum would be visible briefly
before energy losses set in. Another
possibility is that increased power dissipation causes the injection of
particles of higher energy. The
second hypothesis is favored in model fits (assuming the simple
homogeneous case) to the spectral
variability of Mrk 421
(Mastichiadis & Kirk
1997).
In both cases, the variations at the highest synchrotron and inverse
Compton frequencies are
quasisimultaneous, whereas at lower frequencies the time scales are
longer and the peaks are delayed.
Acceleration and loss processes can depend on position in the jet,
causing different electron energy
distributions as a function of location (inhomogeneous model). The
steeper spectrum above the peak
can be reproduced (even
> 0.5) if higher energy
electrons occupy progressively
smaller volumes
(Ghisellini et al
1985).
This occurs naturally behind a shock where the acceleration process is
localized at the shock front
(Marscher 1996).
Thus, a disturbance propagating along an
inhomogeneous jet or across a shock front would cause spectral
variability, usually with shorter time
scales and larger amplitudes at higher energies
(Celotti et al 1991,
Marscher & Travis
1991).
Indeed, the soft photons do lag the hard photons in both Mrk 421 and
PKS 2155-304 (the two
brightest HBL). In X rays, the frequency dependence of the measured lags
is consistent with a
-1/2 law, as expected
from a radiative lifetime; the EUV and UV could also be consistent
within the large uncertainties. At each frequency the decay times are
longer than the lags, which is
not easy to understand in a pure radiative case. A realistic model
likely involves both radiative and travel time effects.
In any case, the data require a fast acceleration process injecting high-energy particles. This is not easy to reconcile with diffusive shock acceleration, whereby high energies build up through a cumulative process (see spectral evolution computed for time-dependent shock acceleration, Fritz & Webb 1990). A viable alternative could be particle acceleration through a large scale electric field (Kirk & Bednarek 1996). Note that the achromatic variability found in the first epoch of multiwavelength monitoring of PKS 2155-304 is not expected from a synchrotron flare in a jet and may be caused by a different physical process such as rotation or microlensing.