source: trunk/MagicSoft/GRB-Proposal/Timing.tex@ 6197

\section{Timing considerations}

The EGRET~\cite{EGRET} instrument on the CGRO has detected GeV emission of GRB940217 promptly and 90 min. after the burst onset.\\

%\subsection{Determine reasonable upper limit for observation duration }
According to the some calculation~\cite{DERISHEV}, GRB produces VHE emission consisting of three components, which have different spectral and time profile. Prompt emission of $\sim$ 100GeV photons should be observed prior to or during the GRB main pulse. During the GRB main pulse, the highest luminosity should be observed. The reprocessed photons from 10\% of GRB can be observed by ground-based experiments with sub-TeV energy range. Third component lasts longer than the GRB main pulse. The duration time of this component is from minutes to hours.\\
\par
For reprocessing of VHE Photons, the definition of minimal value B$_min$ is following. 
\begin{equation}
B_{min} \sim \frac{5\times10^{-2}}{\Gamma^{3}}\,
             \frac{\epsilon_{2ph}}{1TeV}\,
             \frac{t_{GRB}}{10s}\, G
\label{eq:minimal}
\end{equation}
And the duration time of delay of reprocessed VHE emission may by calculated via the following function:
\begin{equation}
t_{d} \simeq \frac{2^{4/3}}{3} \biggl(\frac{B_{\perp}}{B_{min}}\biggl)^{2/3}
\label{eq:duration}
\end{equation}
When absorption threshold$\epsilon_{2ph}$ is 1TeV, duration time of GRB main pulse is 10$^{2}$s, Lorentz factor of the GRB shell $\Gamma$ is 10$^{2}$, the duration of delayed VHE emission is about 0.8 hours for component of magnetic field perpendicular to electron's trajectory B$_{\perp}$ of 0.1 [Gauss], 3.6 hours for 1.0 [Gauss] and 17.3 hours for 10 [Gauss].\\
\par 
In~\cite{DERMER}, two peaks in the GeV light curve are calculated. An early maximum coincident with the MeV peak is some seconds after the burst onset. The second maximum peaking at $\approx$ 1.5 hours is up to 10$^5$ sec. ($\approx$ 25 hours) after the burst.\\
\par
Li, Dai and Lu~\cite{LI} suggest GeV emission after pion production and some thermalization of the UHE component with radiation maxima of up to one day or even one week (accompanied by long-term neutrino emission).\\
\par
It is not so easy to say a reasonable observation time after GRBs, because GRB has its own characteristic and time profile. But, if it is possible to point to the GRB sources before finishing a GRB main pulse and continue to observe for 5 hours, we can put some constraints on parameters of GRB sources.