0.1.
The analytic results provide at best order-of-magnitude accuracy
in the self-absorbed radio/infrared regime, and give poor fits
to the self-Compton spectra due to complications from Klein-Nishina
effects and photon-photon opacity.
C. D. Dermer, M. Böttcher, and J. Chiang
Astrophysical Journal, 537, 255 (2000)
Sari, Piran and Narayan have derived analytical formulae to model
the spectra from gamma-ray burst blast waves that are energized by
sweeping up material from the surrounding medium. We extend these
expressions to apply to general radiative regimes and to include the
effects of synchrotron self-absorption. Electron energy losses due
to synchrotron self-Compton processes are also treated in a very
approximate way. The calculated spectra are compared with detailed
numerical simulation results. We find that the spectral and temporal
breaks from the detailed numerical simulation are much smoother
than the analytic formulae imply, and that the discrepancies between
the analytic and numerical results are greatest near the breaks and
endpoints of the synchrotron spectra. The expressions are most
accurate (within a factor of ~ 3) in the optical/X-ray regime
during the afterglow phase, and are more accurate when the fraction
of swept-up particle energy that is transferred to electrons is
0.1.
The analytic results provide at best order-of-magnitude accuracy
in the self-absorbed radio/infrared regime, and give poor fits
to the self-Compton spectra due to complications from Klein-Nishina
effects and photon-photon opacity.