\section{Proposed Observation Strategies}

First, we make an estimate of how many observations we will perform.\\

A rough estimate of the needed observation time for GRBs derives 
from the claimed GRB observation frequency  of about 150-200 GRBs/year by the SWIFT
collaboration~\cite{SWIFT} and the results of the studies on the MAGIC duty-cycle 
made by Nicola Galante~\cite{NICOLA} and Satoko Mizobuchi~\cite{SATOKO}.
Considering a MAGIC duty-cycle of about 10\% and a tolerance of 5 hours
to point the GRB, we should be able to point about 1-2 GRB/month. 


Such duty-cycle studies, made before MAGIC started its observations,
are reliable as long as the considered weather constraints
(~maximum wind speed of 10 m/s, maximum humidity of 80\% and
darkness at astronomical horizon~) remain similar to the real ones in 2005.
In these duty-cycle studies also full-moon nights were considered (requiring
a minimum angular distance of the GRB from the moon of 30$^\circ$~),
while we propose here to skip the 3-4 full moon nights per month which are not 
yet under observational control. 

This reduction of the real duty-cycle w.r.t. the studies~\cite{NICOLA,SATOKO} 
gets compensated by the tolerance of 5 hours for considering the alert observable 
(5 hours more before the beginning of the night 
are equivalent to an increase of the duty-cycle of about 6 days per month). 
Observation interruptions due to technical shifts are not considered here. \\

To conclude, we ask here for about 1-2 nights per month for GRB observations, half-moon nights
included. 
Moreover, as the chances go linear with the time that the telescope is able to follow 
alerts, we ask do an effort as much as possible to maintain the telescope in alarm position 
EVERY time that a GRB follow-up can be considered possible.

\subsection{What to do with the AMC ? }

\ldots {\bf MARKUS G. } \ldots

\subsection{GRB observations in case of moon shine}

{\it gspot} allows only GRBs with an angular distance of $> 30^\circ$ from the moon.
The telescope's slewing in case of a GRB alert will be done
without closing the camera lids, so that the camera could be
flashed by the moon during such a movement. In principle
a fast moon-flash shouldn't damage the PMTs, but the behaviour
of the camera and the Camera Control {\it La Guagua} must
be tested. On the other hand,, if such test conclude that it is not safe
to get even a short flash from the moon, the possibility
to implement a new feature into the Steering System must be considered 
which follow a path around the moon while slewing.
\par
There was a shift observing the Crab-Nebula with half-moon at La Palma in December 2004. 
The experience was that the nominal High-Voltages could be maintained and gave no 
currents higher than 2\,$\mu$A. This means that moon-periods can be used for GRB-observations 
without fundamental modifications except for full-moon periods. We want to stress that 
these periods increase the chances to catch GRBs by 80\%, even if full-moon observations are excluded~\cite{NICOLA}. 
It is therefore mandatory that the shifters keep the camera in fully operational conditions with high-voltages 
switched on from the beginning of a half-moon night until the end. This includes periods where no other half-moon 
observations are scheduled.
\par
Because the background is higher with moon-light, we want to decrease then the maximun zenith angle from 
$\theta^{max} = 70^\circ$ to $\theta^{max} = 65^\circ$. 

\subsection{Calibration}

For ordinary source observation, the calibration is currently performed in the following way: 
\begin{itemize}
\item At the beginning of the source observation, a dedicated pedestal run followed by a calibration run is 
taken.
\item During the data runs, interlaced calibration events are taken at a rate of 50\,Hz.
\end{itemize}

We would like to continue taking the interlaced calibration events when a GRB
alert is launched, but leave out the pedestal and calibration run in order not to loose valueable time.

\subsection{Determine the maximum zenith angle}

We determine the maximum zenith angle for GRB observations by requiring that the overwhelming majority of 
possible GRBs will have an in principle observable spectrum. Figure~\ref{fig:grh} 
shows the gamma-ray horizon (GRH) as computed in~\cite{KNEISKE}. The GRH is defined as the 
gamma-ray energy at which a part of $1/e$ of a hypothiszed mono-energetic flux gets absorbed after 
travelling a distance of $d$, expressed in redshift $z$ from the earth. One can see that at typical 
GRB distances of $z=1$, all gamma-rays above 100\,GeV get absorbed before they reach the earth. 
\par
Even the closest GRB with known redshift ever observed, GRB030329~\cite{GRB030329}, lies at a redshift 
of $z=0.1685$. In this case, gamma-rays above 200\,GeV get entirely absorbed.

\begin{figure}[htp]
\centering
\includegraphics[width=0.85\linewidth]{f4.eps}
\caption{Gamma Ray Horizon, as derived in~\cite{KNEISKE}}
\label{fig:grh}
\end{figure}

\par
We assume now a current energy threshold of 50\,GeV for MAGIC at a zenith angle of $\theta = 0$\footnote{As 
this proposal is going to be reviewed in a couple of months, improvements of the energy threshold will be taken 
into account, then.}. According 
to~\cite{eckart}, the energy threshold of a Cherenkov telescope scales with zenith angle like:

\begin{equation}
E^{thr}(\theta) = E^{thr}(0) \cdot \cos(\theta)^{-2.7}
\label{eq:ethrvszenith}
\end{equation}

Eq.~\ref{eq:ethrvszenith} leads to an energy threshold of about 5.6\,TeV at $\theta = 80^\circ$, 
900\,GeV at $\theta = 70^\circ$ and 500\,GeV at $\theta = 65^\circ$. 
Inserting these results into the GRH (figure~\ref{fig:grh}), one gets 
a maximal observable GRB distance of $z = 0.1$ at $\theta = 70^\circ$ and $z = 0.2$ at $\theta = 65^\circ$. 
We think that the probability for 
GRBs to occur at these distances is sufficiently small in order to neglect the very difficult observations 
beyond these limits.

\subsection{In case of follow-up: Next steps}

We propose to analyse the GRB data at the following day in order to tell whether a follow-up observation during 
the next night is useful. We think that a limit of 3\,$\sigma$ significance should be enough to start such a 
follow-up observation of the same place. This follow-up observation can then be used in two ways:

\begin{itemize}
\item In case of a repeated outbursts for a longer time period of direct observation
\item In the other case for having Off-data at exactly the same location.
\end{itemize}