next previous
Up: The early afterglow


3 The reverse shock and the optical flash


There are many attempts to detect early optical emission and there is a good chance that this emission will be observed in the near future. A strong 5th magnitude optical flash would have been produced if the fluence of a moderately strong GRBs, 10-5 erg/s/cm2 would have been released on a time scale of 10 s in the optical band. Even a small fraction of this will be easily observed. It is important, therefore, to explore the expected optical emission from the GRB and the early afterglow.

During the GRB and the initial emission from the forward shock the emission peaks in $\gamma$-rays, and only extremely small fraction is emitted in the optical band. For example, the prompt optical flash from the GRB would be of 21st magnitude if the flux drops according to the synchrotron low energy tail of $F_\nu \sim \nu^{1/3}$.

A considerably stronger flux is obtained from the reverse shock. The reverse shock contains, at the time it crosses the shell, a comparable amount of energy to the forward shock. However, its effective temperature is significantly lower (typically by a factor of $\gamma
\sim 300$) than that of the forward shock. The resulting peak frequency is therefore lower by $\gamma^2 \sim 10^5$. A more detailed calculation shows that the reverse shock frequency is
\begin{displaymath}
\nu _{\rm m}=1.2\ 10^{14}\ {\rm Hz}\left( \frac{\epsilon _{\...
 ...) ^{1/2}\left(
\frac{\gamma _{0}}{300}
\right)^{2}n_{1}^{1/2} .\end{displaymath} (6)
The cooling frequency is similar to that of the forward shock, since both have the same magnetic field and the same Lorentz factor. Using the parameters obtained by Granot et al. (1998), from the afterglow of GRB 970508, and using $\gamma_0=300$ we get for the reverse shock $\nu_{\rm c}=3\ 10^{16}$ Hz and $\nu_{\rm m}=3\ 10^{14}$ Hz leading to an 8th magnitude flash. With higher initial Lorentz factor of $\gamma_0=10^4$ the flash drops to 13th magnitude. Inverse Compton cooling, if exists, can reduce the flux by $\sim 2$ magnitudes, while self absoption can influence only very short bursts with small surface area. Therefore, quite concervatively, the optical flash should be stronger than 15th magnitude and should be soon seen with modern experiments. The reverse shock signal is very short living. After the shock crosses the shell, no new electrons are injected and there is no emission above $\nu_{\rm c}$. Moreover, $\nu_{\rm c}$ drops fast with time as the shell's material cools adiabatically.



next previous
Up: The early afterglow

Copyright The European Southern Observatory (ESO)