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%Novel Technology: 
\title{Proposal: Observations of the Galactic Center \\
Key Programs: Galactic Center / Dark Matter
}
\author{H. Bartko, A. Biland, E. Bisesi, S. Commichau, P. Flix,\\
 S. Stark, W. Wittek}
\date{March 21, 2005\\}
\TDAScode{}%MAGIC 05-xx\\ 04mmdd/HBartko
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\begin{abstract}  
Due to the wealth of sources, the region around
the Galactic Center (GC) is very interesting. Recently, gamma radiation above 
a few hundred GeV has been detected by the Whipple, Cangaroo and HESS 
collaborations. The reconstructed spectra from Cangaroo and HESS show 
significant differences. The reasons for this discrepancy and the acceleration mechanisms have still to be identified.

Various possibilities for the production of very-high-energy (VHE)
gamma rays near the GC are discussed in the literature, like accretion flow onto the 
central black 
hole, supernova shocks in Sgr A East, proton acceleration near the event 
horizon of the black hole, or WIMP dark matter annihilation. Although the 
observed VHE gamma radiation from the GC is most probably not due to 
the annihilation of SUSY-neutralino dark matter (DM) particles, other models 
like Kaluza-Klein dark matter are not ruled out. Moreover, assuming a 
universal DM density profile, the GC is expected to yield the largest gamma flux from particle DM annihilation 
amongst the favored candidates, due to its proximity.

At La Palma, the GC culminates at about 58 deg zenith angle (ZA). It can be 
observed with MAGIC at up to 60 deg ZA, between 
April and late August, yielding a total of 150 hours without moon per year. 
The expected integral flux above 700 GeV derived from 
the HESS data is $(3.2 \pm 1.0)\cdot 10^{-12}\mathrm{cm}^{-2}\mathrm{s}^{-1}$. 
Comparing this to the expected MAGIC sensitivity from MC simulations, this 
could result in a 5 $\sigma$ detection in about $1.8\pm0.5$ hours. 

The observations have to be conducted as early as possible in order to 
participate in the ongoing discussion about gamma radiation from the GC. 
The main motivations for the observation of the GC are:

\begin{itemize}
\item to measure the gamma-ray flux and its energy dependence (due to the high
zenith angles higher energies up to about 20 TeV are accessible),
\item to inter-calibrate MAGIC and HESS,
\item to help resolving the flux discrepancies between HESS and 
Cangaroo,
\item to gain information about the nature and acceleration mechanism of the 
source, 
\item to set constraints on models for dark-matter-particle annihilation.
\end{itemize}

In order to collect a data sample comparable in size to those of the other 
experiments and to be able to measure the energy spectrum, 40 hours of
observation time are requested. This 40 hours will be split into 20 hours ON
and 20 hours dedicated OFF data or they will be devoted to observations in
the wobble mode. In addition, 60 hours of observation during moonshine are 
applied for.
\end{abstract}

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\section{Introduction}


The Galactic Center (GC) region contains many unusual objects which may be 
responsible for the high-energy processes generating gamma rays 
\cite{Aharonian2005,Atoyan2004,Horns2004}. The GC is rich in massive stellar 
clusters with up to 100 OB stars \cite{GC_environment}, immersed in a dense 
gas. There are young supernova remnants e.g. G0.570-0.018 or Sgr A East, and nonthermal radio arcs. The dynamical center of the Milky Way is associated with the compact radio source Sgr A$^*$, which is believed to be a massive black hole \cite{GC_black_hole,Melia2001}. Within a radius of 300 pc around the Galactic Center there is a mass of $2.7 \cdot 10^7 M_{\odot}$. An overview of the sources in the GC region is given in Figure \ref{fig:GC_sources}. Some data about the GC are summarized in Table \ref{table:GC_properties}.


\begin{table}[h]{\normalsize\center
\begin{tabular}{lc}
 \hline
 (RA, dec), epoch J2000.0 & $(17^h45^m12^s,-29.01$ deg)
\\ heliocentric distance  & $8\pm0.4$ kpc \cite{Eisenhauer2003} 
(1 deg = 140 pc)
\\ mass of the black hole & $2\pm0.5 \cdot 10^6 M_{\odot}$ 
\\ 
\hline
\end{tabular}
\caption{Properties of the Galactic Center.}\label{table:GC_properties}}
\end{table}



\begin{figure}[h!]
\begin{center}
\includegraphics[totalheight=9cm]{GC_sources_1.eps}
\end{center}
\caption[Sources near the Galactic Center.]{Overview about the sources near the Galactic Center \cite{GC_overview}.} \label{fig:GC_sources}
\end{figure}


In fact, EGRET has detected a strong source in direction of the GC, 
3 EG J1745-2852 \cite{GC_egret}, which has a broken power law spectrum 
extending up to at least 10 GeV, with a spectral index of 1.3 below the break at a few 
GeV. Assuming a distance of 8.5 kpc, the gamma ray luminosity of this source 
is very large, $~2.2 \cdot 10^{37} \mathrm{erg}/\mathrm{s}$, which is 
equivalent to about 10 times the gamma flux from the Crab nebula. An independent analysis of the EGRET data 
\cite{Hooper2002} indicates a point source whose position is different from the GC at a confidence level beyond 99.9 \%. %\cite{Hooper2002, A&A 335 (1998) 161} 

At energies above 200 GeV, the GC has been observed by Veritas, Cangaroo and HESS, \cite{GC_whipple,
GC_cangaroo,GC_hess}. The spectra as measured by these experiments are displayed in Figure \ref{fig:GC_gamma_flux} while Figure \ref{fig:GC_source_location} shows the 
different reconstructed positions of the GC source. Recently a second TeV 
gamma source only about 1 degree away from the GC has been 
discovered \cite{SNR_G09+01}. Its integral flux above 200 GeV represents about 
2\% of the gamma flux from the Crab nebula with a spectral index of about 2.4.

\begin{figure}[h!]
\begin{center}
\includegraphics[totalheight=6cm]{sgr_figure4.eps}
\end{center}
\caption[Gamma flux from GC.]{The VHE gamma flux from the Galactic Center as observed by Whipple, Cangaroo, HESS and by the EGRET experiment \cite{GC_hess}.} \label{fig:GC_gamma_flux}
\end{figure}


\begin{figure}[h!]
\begin{center}
\includegraphics[totalheight=8cm]{gc_legend.eps}
\end{center}
\caption[Gamma flux from GC.]{The source locations as measured by the other IACTs Whipple, Cangaroo and HESS \cite{Horns2004}.} \label{fig:GC_source_location}
\end{figure}

The discrepancies between the measured flux spectra could indicate
inter-calibration problems between the IACTs. But it could also indicate an
apparent source variability at a timescale of about of one year or it could be due to the different regions in which the signal is integrated.


%An apparent source variability of the order of one year could be due to the different regions in which the signal is integrated.



\section{Investigators and Affiliations}

The investigators of the proposed observations of the GC are stated in Table \ref{table:GC_investigators} together with their assigned analysis tasks. All members of the MAGIC collaboration are invited to join these efforts.


\begin{table}[h]{
\scriptsize{
\centering{
\begin{tabular}{llll}
 \hline
 Investigator & Institution& E-mail & Assigned task\\ \hline
   Hendrik Bartko      & MPI Munich    & hbartko@mppmu.mpg.de & data analysis, spectra, wobble mode
\\ Adrian Biland       & ETH Zurich    & biland@particle.phys.ethz.ch & MC generation, Moon observations
\\ Erica Bisesi        & Univ. Udine   & bisesi@fisica.uniud.it & dark matter halo modelling, clumpness
\\ Sebastian Commichau & ETH Zurich    & commichau@particle.phys.ethz.ch &
 data analysis, spectra, geomagnetic effects
\\ Pepe Flix           & IFAE Barcelona& jflix@ifae.es & data analysis, disp, spectra, dark matter
\\ Sabrina Stark       & ETH Zurich    & lstark@particle.phys.ethz.ch  & data analysis, spectra
\\ Wolfgang Wittek     & MPI Munich    & wittek@mppmu.mpg.de & padding, unfolding
\\ 
\hline
\end{tabular}
}
\caption{The investigators and the assigned tasks.}\label{table:GC_investigators}}}
\end{table}

S. Commichau and H. Bartko are nominated to be principle investigators in order to allow for a continous contact person till the final publication of the results.

%The principal investigator is shared between S. Commichau and H. Bartko to allow for 


\section{Scientific Case} 


In the GC region high-energy gamma rays can be produced in different sources:

\begin{itemize}
\item{interaction between cosmic rays and the dense ambient gas within the innermost 10 pc region}
\item{in non-thermal radio filaments  \cite{Pohl1997}}
\item{in the young SNR Sgr A East \cite{Fatuzzo2003,Yusef-Zadeh1999}}
\item{in the compact radio source Sgr A*}
\item{in the central part of the dark matter halo.}
\end{itemize}

It is quite possible that some of these potential gamma-ray production sites contribute comparably to the observed TeV flux. For example, the young SNR Sgr A East is only located about 7 pc (about 0.05 deg) away from the Galactic Center \cite{Yusef-Zadeh1999}.


% in the non-thermal radio filaments by high-energy leptons which scatter background infrared photons from the nearby ionized clouds \cite{Pohl1997,Aharonian2005}, or by hadrons colliding with dense matter. These high-energy hadrons can be accelerated by the massive black hole \cite{GC_black_hole}, associated with the Sgr A$^*$, by supernovae or by energetic pulsars. Alternative mechanisms invoke the hypothetical annihilation of super-symmetric dark matter particles (for a review see \cite{jung96}) or curvature radiation of protons in the vicinity of the central super-massive black hole \cite{GC_black_hole,Melia2001}.


In order to shed new light on the high-energy phenomena in the GC region, and to constrain the emission mechanisms and sources, new observations with high sensitivity, good energy and angular resolution are necessary. For the interpretation of the observed gamma flux the following observables are important:

\begin{itemize}
\item{source location, source extension}
\item{energy spectrum}
\item{time variability of the gamma flux.}
\end{itemize} 



\begin{figure}[h!]
\begin{center}
\includegraphics[totalheight=8cm]{total_spectrum.eps}
\end{center}
\caption[Total spectrum of the GC.]{Total spectrum of the gamma radiation from the Galactic Center, compiled by \cite{Aharonian2005}.} \label{fig:GC_source_location}
\end{figure}



\subsection{Models for the gamma-ray emission from Sgr A$^*$}

Production of high-energy gamma rays within 10 Schwarzschild radii of a black hole (of any mass) could be copious because of effective acceleration of particles by the rotation-induced electric fields close to the event horizon or by strong shocks in the inner parts of the accretion disk. However, these energetic gamma rays generally cannot escape the source because of severe absorption due to interactions with the dense, low-frequency radiation through photon-photon pair production. Fortunately the supermassive black hole in our Galaxy is an exception because of its unusually low bolometric luminosity. The propagation effects related to the possible cascading in the photon field may extend the high-energy limit to 10 TeV or even beyond \cite{Aharonian2005}.



\subsubsection{Leptonic Models}

Many proposed acceleration mechanisms of VHE gamma radiation in the Galactic Center are based on so called advection dominated accretion flow (ADAF) models \cite{Atoyan2004}.

%Also advection dominated accretion flow (ADAF) models can describe the production of high-energy gamma radiation in the Galactic Center \cite{Atoyan2004}.

A viable site of acceleration of highly energetic electrons could be the compact region within a few gravitational radii of the black hole. In this case the electrons produce not only curvature radiation, which peaks around 1 GeV, but also inverse Compton gamma rays (produced in the Klein-Nishina regime) with the peak emission around 100 TeV. As these high-energy gammas cannot escape the source the observed gamma rays would be due to an electromagnetic cascade.

\subsubsection{Hadronic Models}

Another scenario is related to protons accelerated to about $10^{18}$ eV \cite{Aharonian2005}. These protons produce gamma rays via photo-meson processes. This scenario also predicts detectable fluxes of  $10^{18}$ eV neutrons and perhaps gamma rays and neutrinos. A hint of an excess of highest energy neutrons from the GC has been reported in \cite{Hayashida1999}.

TeV gamma rays can also be produced by significantly  lower energy protons, accelerated by the electric filed close to the gravitational radius of the black hole or by strong shocks in the accretion disk \cite{Aharonian2005}. In this case the gamma-ray production is dominated by interactions of $10^{13}$ eV protons with the accretion plasma. This scenario predicts a neutrino flux which should be observable with northern neutrino telescopes like NEMO and Antares. It also predicts strong TeV--X-ray--IR correlations.


\subsection{Dark Matter Annihilation}


The presence of a Dark Matter halo of the Galaxy is well established by stellar dynamics \cite{Klypin2002}. At present, the nature of Dark Matter is unknown, but a number of viable candidates have been advocated within different theoretical frameworks, mainly motivated by particle physics (for a review see \cite{jung96}) including the widely studied models of supersymmetric (SUSY) Dark Matter \cite{Ellis1984}. Also models involving extra dimensions are discussed like Kaluza-Klein Dark Matter \cite{Kaluza_Klein,Bergstrom2004}.

The supersymmetric particle dark matter candidates might self-annihilate into boson or fermion pairs yielding very high-energy gammas in subsequent decays and from hadronisation. The gamma flux above an energy threshold $E_{\mathrm{th}}$ per solid angle $\Omega$ is given by:

\begin{equation*}
\frac{\text{d} N_{\gamma}(E_{\gamma}>E_{\mathrm{th}})}{\text{d}t\  \text{d}A\  \text{d}\Omega }= N_{\gamma}(E_{\gamma}>E_{\mathrm{th}}) \cdot \frac{1}{2} \cdot \frac{\langle \sigma v \rangle}{4 \pi m_{\chi}^2} \cdot  \int_{\text{los}}\rho_{\chi}^2(\vec{r}(s,\Omega)) \text{d}s \ ,
\end{equation*}


where $\langle \sigma v \rangle$ is the thermally averaged annihilation cross section, $m_{\chi}$ the mass and $\rho_{\chi}$ the spatial density distribution of the hypothetical dark matter particles. $N_{\gamma}(E_{\gamma}>E_{\mathrm{th}})$ is the gamma yield above the threshold energy per annihilation. The predicted flux depends on the SUSY parameters and on the spatial distribution of the dark matter. The energy spectrum of the produced gamma radiation has a very characteristic feature: a sharp cut-off at the mass of the dark matter particle. Also the flux should be absolutely stable in time.

Numerical simulations of cold dark matter \cite{NFW1997,Stoehr2002,Hayashi2004,Moore1998} predict universal DM halo profiles with a density enhancement in the center of the dark halo. In the very center the dark matter density can be even more enhanced through an adiabatic compression due to the baryons \cite{Prada2004} present. Depending on the steepness of the density profile and on the instrument PSF some source extension might be observed. Nevertheless, the profiles which yield the largest flux \cite{Moore1998,Prada2004} predict nearly point-like sources.

%In principle, the radial density profile could be measured from the sourc
% All dark matter distributions that predict observable fluxes are cusped, yielding an approximately point-like source.

Using fits of these dark matter profiles to the rotation data of the Milky Way predictions for the density profile $\rho_{\chi}$ of the dark matter can be made \cite{Fornego2004,Evans2004}. On the other hand, for a given choice of SUSY parameters $m_{\chi},\;\langle \sigma v \rangle$ and $N_{\gamma}$ are determined. 
%Assuming parameters for the SUSY models determine the neutralino mass, the thermally averaged annihilation cross section and the gamma yield. Combining both models about the dark matter distribution and SUSY 
Combining the SUSY predictions with the predictions for the DM density profile
predictions for the gamma flux from SUSY particle dark matter annihilation are derived.


Figure \ref{fig:exclusion_lmits} shows exclusion limits for MAGIC (solid straight lines) for the four most promising sources,
in the plane $N_{\gamma}(E_{\gamma}>E_{\mathrm{th}})\langle \sigma v \rangle$ vs. $m_{\chi}$. The energy threshold $E_{\mathrm{th}}$ has been assumed to be 100 GeV. Due to its proximity the GC yields the largest expected flux from particle dark matter annihilation and thus the lowest exclusion limit. Nevertheless, this minimum measurable flux is more than one order of magnitude above the highest fluxes predicted by SUSY models (full circles). Also the flux measured by the HESS experiment is far above the theoretical expectation (dotted line).


\begin{figure}[h!]
\begin{center}
\includegraphics[totalheight=7cm]{mSugra_Scan2.eps}% {plot_DM_exclusion_1.eps}%{Dark_exclusion_limits.eps}
\end{center}
\caption[DM exclusion limits.]{Exclusion limits (solid straight lines) for the four most promising sources of dark matter annihilation radiation. The GC is expected to give the largest flux (lowest exclusion limits) amongst all sources. For energies above 700 GeV, the flux from the GC as observed by the HESS experiment (dotted line) is within the reach of MAGIC. The full circles represent flux predictions from some typical SUSY models.} \label{fig:exclusion_lmits}
\end{figure}



Detailed discussions of the observed gamma fluxes from the GC can be found in \cite{Hooper2004,Horns2004}. The observed spectrum extends to more than 18 TeV, well beyond the favored mass region of the lightest SUSY particle, and the observed flux is larger than the flux expected in most theoretical models. This leads to the conclusion that most likely the dominating part of the observed gamma flux from the GC is not due to SUSY particle Dark Matter annihilation. Other dark matter scenarios like Kaluza-Klein Dark Matter can not be excluded.


%\newpage

\section{Preparatory Work}

The Sgr A$^*$ data that has been taken in September 8, 9 and 10 2004, is
still being analyzed. Preliminary results were presented at the MAGIC
collaboration meeting in Berlin, 21-25th February 2005.\\
Up to now only 2.9 hours of ON data are available, at zenith angles between 60.3 and 67.8 degrees. Some details of the data set are shown in Table \ref{table:GC_dataset}.\\

\begin{table}[!ht]{
\centering{
\begin{tabular}{l|l|l|l}
 \hline
   Date       & Time          & Az $[^\circ]$ & ZA $[^\circ]$\\ \hline
   09/08/2004 & 21:00 - 22:16 & 198.3 - 214.7 & 60.3 - 67.8
\\ 09/09/2004 & 21:17 - 22:12 & 203.4 - 214.7 & 62.0 - 67.7
\\ 09/10/2004 & 21:06 - 22:03 & 202.2 - 213.7 & 61.6 - 67.1
\\
\hline
\end{tabular}
\caption{The Sgr A$^*$ data set from September 2004.}\label{table:GC_dataset}}}
\end{table}

In our preliminary analysis we used the Random Forest method \cite{RF} for the gamma
hadron separation. For this purpose high
ZA (65$^\circ$ ZA and 205$^\circ$ Az) Monte Carlo gammas showers were generated, 
99500 events in all, with energies between 200
and 30,000 GeV. The differential spectral index of the generated spectrum is $-2.6$, conforming with the energy spectrum of the Crab nebula.

The MC sample was divided into a training
and a test sample and its slope was normalized to $-2.21$. Since no dedicated OFF data were available, we used a
subsample of Sgr A$^*$ ON data to represent the hadronic background in the Random Forest training. As training
parameters we used SIZE, DIST, WIDTH, LENGTH, CONC, and M3Long. The training
was done for SIZE $>100$ p.e..

\begin{figure}[!h]
\centering
\subfigure[SIZE $> 300$ p.e.]{
\includegraphics[scale= .3]{alpha_tmpl_s100_h006}}
\subfigure[SIZE $> 500$ p.e.]{
\includegraphics[scale= .3]{alpha_tmpl_s800_h02}}
\caption{Preliminary ALPHA distributions for lower SIZE cuts of 100 and 800 p.e..}\label{fig:prelresults}
\end{figure}

The results of the preliminary analysis can be summarized as follows. After
the gamma/hadron separation, the ALPHA distributions of the ON data show
excess signals of 60 and 12 events, with significances of 3.5 and 2.5
$\sigma$, for SIZE values above 100 p.e. and 800 p.e., respectively (figure \ref{fig:prelresults}). If the
SIZE cut at 100 p.e. corresponds to an energy threshold of 900 GeV and if the
effective collection area is assumed to be $10^5$ m$^2$ the observed excess is
by a factor of 5 higher than that expected on the basis of the HESS flux.

Studies are going on concerning appropriate OFF data, the false-source plot 
and better estimates of the energy threshold and the effective collection area.



\section{Feasibility} 
\label{section:feasibility}

\subsection{Expected gamma-ray fluxes}
The HESS collaboration has observed the GC for 16.5 hours, at zenith angles around 20 degrees, with energy thresholds between 165 and 255 GeV. The total number of excess events amounts to $\sim$300. The differential gamma flux as determined in the energy region from 200 GeV to 10 TeV is \cite{GC_hess}:

\begin{equation}
\frac{\mathrm{d}N_{\gamma}}{\mathrm{d}A\;\mathrm{d}t\;\mathrm{d}E} = (2.50 \pm 0.21 \pm 0.6) \cdot 10^{-12} \frac{1}{\mathrm{cm}^2\;\mathrm{s\;TeV}} \left(\frac{E}{\mathrm{TeV}}\right)^{-2.21\pm 0.09 \pm 0.15}
\end{equation}

A fit to the flux data points from Cangaroo \cite{GC_cangaroo} yields:

\begin{equation}
\frac{\mathrm{d}N_{\gamma}}{\mathrm{d}A\;\mathrm{d}t\;\mathrm{d}E} = (3.4 \pm 3.8) \cdot 10^{-12} \frac{1}{\mathrm{cm}^2\;\mathrm{s\;TeV}} \left(\frac{E}{\mathrm{TeV}}\right)^{-4.4\pm 1.1}
\end{equation}

The flux integrated above 700 GeV is determined as

\begin{equation}
\frac{\mathrm{d}N_{\gamma}(E>700 \mathrm{GeV})}{\mathrm{d}A\;\mathrm{d}t}=(3.2 \pm 1.0)\cdot 10^{-12}\frac{1}{\mathrm{cm}^2\;\mathrm{s}}
\end{equation}

for HESS and $(3 \pm 5)\cdot 10^{-12}\frac{1}{\mathrm{cm}^2\mathrm{s}}$
for Cangaroo, respectively.

The energy thresholds and flux sensitivities estimated for MAGIC on the basis of MC simulations (\cite{MC-Sensitivity, ECO-1000}) are given in Table \ref{table:MAGIC_sensitivity}.

\begin{table}[h]{\normalsize\center
\begin{tabular}{c|cccc}
 \hline
 ZA          &  $E_{\mathrm{th}}$      & sensitivity    & $\Phi(E>E_{\mathrm{th}})$            
                              & $T_{5\sigma}$       \\
             &                & above $E_{\mathrm{th}}$ &   &\\
$[^{\circ}]$ & $[{\rm GeV}]$  & $[{\rm cm}^{-2}\;{\rm s}^{-1}]$  
                              & $[{\rm cm}^{-2}\;{\rm s}^{-1}]$     
                              &  $ [{\rm hours}]$   \\
\hline
 60   &   700     & $6\cdot10^{-13}$ &  $3.20\cdot10^{-12}$ &  1.8        \\
 70   &  1900     & $4\cdot10^{-13}$ &  $0.95\cdot10^{-12}$ &  8.9        \\
\hline
\end{tabular}
\caption{Energy threshold $E_{\mathrm{th}}$ and sensitivity for MAGIC for two zenith angles ZA. The 4th and 5th column contain the expected integrated flux above $E_{\mathrm{th}}$ and the time needed for observing a 5$\sigma$ excess, respectively.}\label{table:MAGIC_sensitivity}}
\end{table}


Figure \ref{fig:MAGIC_flux_limits} shows the measured HESS and Cangaroo fluxes together with the minimum flux detectable by MAGIC in 20 hours observation time.




\begin{figure}[h!]
\begin{center}
\includegraphics[totalheight=8cm]{MAGIC_flux_limits.eps}
\end{center}
\caption[Flux limits.]{Observed gamma spectra of the HESS and Cangaroo experiments compared to the minimum flux detectable by the MAGIC telescope in 20 hours observation time.} \label{fig:MAGIC_flux_limits}
\end{figure}

It can be seen from Table \ref{table:MAGIC_sensitivity}
that in the ZA range from 60 to 70 degrees the energy threshold rises from 700 GeV to 1900 GeV. Correspondingly, the time necessary for observing a 5$\sigma$ excess (assuming an integrated gamma flux as measured by HESS) increases from 1.8 to 8.9 hours. This strongly suggests the MAGIC data to be taken at the smallest ZA possible. Only then the MAGIC observations will contribute to an understanding of the discrepancies between the HESS and Cangaroo results. Due to the observation under high zenith angles ($\sim$60 deg) MAGIC will be able to extend the measurements of the energy spectrum to higher energies ($\sim$20 TeV).

The HESS experiment has a PSF (in stereo mode) of about 0.6 deg while MAGIC has about 0.1 deg PSF.


???? We still have no good estimate of the expected number of excess event for the different conditions. ??? \\

???? How long do we have to observe to get a good spectrum above 7 TeV  ??? \\

\subsection{Verification of the MAGIC analysis at high zenith angles}
In order to verify the correct performance of the MAGIC analysis at high ZA it is proposed to take Crab data in the interesting ZA range from 58$^{\circ}$ to 70$^{\circ}$, to reconstruct the gamma energy spectrum and to compare it with existing measurements. Like for the GC, either dedicated OFF data should be taken or observations should be made in the wobble mode.

???? Propose suitable OFF regions ???


\section{Observational Constraints}


The GC culminates at about 58 deg ZA in La Palma. Below 60 deg ZA, it is visible between April and late August for about 150 hours. The GC region has a quite high and non-uniform level of background light from the night sky. This together with the large ZA requires to take either dedicated OFF data or to take data in the wobble mode (see Section \ref{section:skydirections}). 
%Since the LONS level is in any case very large moon observations are considered in addition to the normal observations.


\section{Suggested sky directions to be tracked}
\label{section:skydirections}

%The number of bright stars around the GC, up to a magnitude of 9, within a distance of 1.75 degrees is given in Table \ref{table:GC_brightstars}. Their total number is 42, of which 16 have a distance to the GC of less than 1 degree. The brightest star is Sgr 3  with a magnitude of 4.5 at a distance of 1.3 degrees. There is no star brighter than mag = 8.4 which is closer than 1 degree to the GC.


%\begin{table}[h]{\normalsize\center
%\begin{tabular}{c|cc|c}
% \hline
% mag range & distance$<1^{\circ}$ & 1$^{\circ}<$distance$<1.75^{\circ}$
%                                  & total number \\
%           &                      &                &           \\
%\hline
% 4 - 5     &          0           &        1       &     1     \\ 
% 5 - 6     &          0           &        0       &     0     \\ 
% 6 - 7     &          0           &        1       &     1     \\ 
% 7 - 8     &          0           &        5       &     5     \\ 
% 8 - 9     &         16           &       19       &    35     \\ 
%\hline
% 4 - 9     &         16           &       26       &    42     \\ 
%\end{tabular}
%\caption{Number of bright stars in the region around the Galactic center, including stars up to mag = 9.
%}\label{table:GC_brightstars}}
%\end{table}

The star field around the GC, including stars up to a magnitude of 14, is depicted in Figure \ref{fig:GC_starfield}. Within a distance of 1$^{\circ}$ from the GC there are no stars brighter than mag = 8.4, and there are 16 stars with $8<$ mag $<9$. At distances between 1$^{\circ}$ and 1.75$^{\circ}$ from the GC the total number of stars with  $4<$ mag $<9$ is 26. The brightest ones are Sgr 3 with mag = 4.5, GSC 6836-0644 with mag = 6.4 and GSC 6839-0196 with mag = 7.2.

\subsection{Wobble mode}

As can be seen from Figure \ref{fig:GC_starfield} the star field around the GC is roughly uniform except for the left lower part (RA$\;>\;$RA$_{GC}+4.7$ min), from the GC 1$^{\circ}$ to the left, where the field is significantly brighter. The sky directions (WGC1, WGC2) to be tracked in the wobble mode should be chosen such that in the camera the sky field relative to the source position (GC) is similar to the sky field relative to the mirror source position (anti-source position). For this reason the prefered directions for the wobble mode are WGC1 = (RA$_{GC}$, dec$_{GC}$+0.4$^{\circ}$) and WGC2 = (RA$_{GC}$, dec$_{GC}$-0.4$^{\circ}$. During one night, 50\% of the data should be taken at WGC1 and 50\% at WGC2, switching between the 2 directions every 30 minutes. 

A larger sky area than in Fig.\ref{fig:GC_starfield} is shown in Figs. \ref{fig:GC_starfield_largeW} and \ref{fig:GC_starfield_OFF1}. The circles in the center indicate the region around the GC. The positions of WGC1 and WGC2 are indicated as full circles.

\begin{figure}[h!]
\begin{center}
\includegraphics[totalheight=16cm]{GCregion14.eps}
\end{center}
\caption[Star field around the GC.]{Star field around the GC. Stars up to a magnitude of 14 are plotted. The 2 big circles correspond to distances of 1$^{\circ}$ and 1.75$^{\circ}$ from the GC, respectively. The $x$ axis is pointing into the direction of decreasing RA, the $y$ axis into the direction of increasing declination. The grid spacing in the declination is 20 arc minutes. The Galactic Plane is given by the dotted line.
} \label{fig:GC_starfield}
\end{figure}

\begin{figure}[h!]
\begin{center}
\includegraphics[totalheight=16cm]{GCregion14largeW.eps}
\end{center}
\caption[Star field around the GC.]{Star field around the GC. Stars up to a magnitude of 14 are plotted. The 2 big circles correspond to distances of 1$^{\circ}$ and 1.75$^{\circ}$ from the GC, respectively. The wobble positions WGC1 and WGC2 are given by the full circles. The $x$ axis is pointing into the direction of decreasing RA, the $y$ axis into the direction of increasing declination. The grid spacing in the declination is 1 degree.
} \label{fig:GC_starfield_largeW}
\end{figure}

\begin{figure}[h!]
\begin{center}
\includegraphics[totalheight=16cm]{GCregionOFF1.eps}
\end{center}
\caption[Star field around the GC.]{Star field around the GC. Stars up to a magnitude of 14 are plotted. The ON region is indicated by the bigger circle in the center. A possible OFF region is shown by the bigger circle in the left upper part of the figure. The $x$ axis is pointing into the direction of decreasing RA, the $y$ axis into the direction of increasing declination. The grid spacing in the declination is 1 degree.
} \label{fig:GC_starfield_OFF1}
\end{figure}

\subsection{ON/OFF mode}

The bigger circle in the center of Fig. \ref{fig:GC_starfield_OFF1}
indicates the ON region around the GC. 
An appropriate OFF region, with a sky field similar to that of the ON region,  would be the one marked by the bigger circle in the upper left part of Fig.\ref{fig:GC_starfield_OFF1} . Like the ON region, the OFF region is centered at the Galactic Plane and contains the bright star Sgr 3 (at (RA, dec) = $(17^h47^m34^s,\;-27^{\circ}49'51"$) ) in its outer part. The center of the OFF region has the coordinates GC$_{OFF}$ = (RA, dec) = $(17^h51^m12^s,\;-26^{\circ}52'00")$. The difference in RA between the GC and GC$_{OFF}$ corresponds is 6 minutes. Thus GC$_{OFF}$ culminates 6 minutes later than the GC.

%In order to have the most appropriate OFF data we propose to
%take OFF data each night directly before or after the ON observations under
%the same condition. 



\section{Requested Observation Time}

Based on the above estimates, a 5$\sigma$ excess is expected to be observed in about 2 hours, under optimal conditions. To acquire a data set which is comparable in size to those of the other experiments at least 40 hours of observation time are requested. These 40 hours may be either split into 20 hours ON and 20 hours OFF data taking or be devoted exclusively to data taking in the wobble mode. At present, the prefered mode is the wobble mode. However, a final decision has not yet been taken.

As pointed out in Section \ref{section:feasibility}, all data should be taken at the
smallest possible zenith angles between culmination at about 58 deg and 60
deg. This limits the data taking interval to about 1 hour per night between
April and August. 


To increase statistics at high energies we propose to take additional data during moonshine. Also in this case, the maximum ZA of 60 deg should not be exceeded.

In order to take part in exploring the exciting physics of the GC
we propose to start taking data as soon as possible, beginning in April. In this way first results may be available at the time of the summer conferences 2005.



\section{Outlook and Conclusions}

The GC is an interesting target in all wavelength bands. There is a great wealth of scientific publications, over 600 since 1999. First detections of the GC by the IACTs Whipple, Cangaroo and HESS were made. The measured fluxes exhibit significant differences. These may be explained by calibration problems, by time variations of the source or by different source regions due to different point spread functions. The nature of the source of the VHE gamma rays has not yet been identified. 

Conventional acceleration mechanisms for the VHE gamma radiation utilize the accretion onto the black hole and supernova remnants. The GC is expected to be the brightest source of VHE gammas from particle dark matter annihilation. Although the observed gamma radiation is most probably not due to dark matter annihilation, it is interesting to investigate and characterize the observed gamma radiation as a contribution due to dark matter annihilation is not excluded.

Data taken by MAGIC could help to determine the nature of the source and to understand the flux discrepancies. Due to the large zenith angles MAGIC will have a large energy threshold but also a large collection area and good statistics at the highest energies. The measurements may also be used to inter-calibrate the different IACTs.






%------------------------------------------------------------------------------

\appendix

\section{Acknowledgements}

The authors thank A. Moralejo for helpful discussions about the Monte Carlo simulations. 

%\newpage

\bibliography{bibbib}
\bibliographystyle{GC}


\end{document}



\appendix


\subsection{Dark Matter Halo Modeling}


The tidal radius $r_t$ is that distance from the center of Draco, beyond which tidal effects due to the gravitational field of the Milky Way are expected to become important.

\subsection{Star Distribution}

Stars are tracer particles in the combined potential from the stars and the DM halo. As the Draco dSph has a negligible ISM component the luminosity is due to stars. The star distributions are modeled in the literature. %The models fit the data well.


\subsection{DM Profiles}

We use DM halo profiles which are suggested or compatible with numerical simulations of cold dark matter halo simulations, see \cite{NFW1997,Stoehr2002,Hayashi2004}. The Moore et al. profile \cite{Moore1998} has not been considered because it is not compatible with the measured velocity profiles of low surface brightness galaxies \cite{Stoehr2004}.


Cusped spherical power law \cite{NFW1997,Evans2004} for the DM density:

\begin{equation} \label{eq:NFW_profile}
\rho_{\mathrm{cusp}}(r)=\frac{A}{r^{\gamma}(r+r_s)^{3-\gamma}}
\end{equation}


Cusped spherical power law with exponential cut-off \cite{Kazantzidis2004a,Kazantzidis2004b}:

\begin{equation} \label{eq:Kazantzidis_profile}
\rho_{\mathrm{cusp}}(r)=\frac{C}{r}\exp\left(-\frac{r}{r_b}\right)
\end{equation}



Intermediate profile \cite{Stoehr2002} of the circular velocity $V_c$ as a function of the distance $r$ from the center of Draco:

\begin{equation} \label{eq:Stoehr_profile}
\log\left(V_c/V_{max}\right) = - a\left[ \log(r/r_{max})\right]^2
\end{equation}


Intermediate profile \cite{Hayashi2004} of the dark matter density $\rho(r)$ as a function of the distance from the center of Draco:

\begin{equation} \label{eq:Hayashi_profile}
\ln(\rho_{\alpha}/\rho_{-2}) = (-2 / \alpha) \left[(r/r_{-2})^{\alpha} -1 \right] 
\end{equation} 


Cored spherical power law from \cite{Wilkinson2002} 

\begin{equation} \label{eq:Wilkinson_Profile}
\psi(r) = \frac{\psi_0}{[1+r^2]^{\alpha/2}} = \frac{G_N M(r)}{r} \quad \alpha \neq 0 ,
\end{equation}

where $G_N$ is Newtons gravitation constant.


Cored spherical power law from \cite{Evans1994} for the DM density:
 
\begin{equation} \label{eq:Evans_Profile}
\rho_{\mathrm{pow}}(r)=\frac{v_a^2 r_c^{\alpha}}{4 \pi G} \frac{3 r_c^2 + r^2(1-\alpha)}{(r_c^2 + r^2)^{2+\alpha/2}}
\end{equation}

