Index: /trunk/MagicSoft/GC-Proposal/GC.tex
===================================================================
--- /trunk/MagicSoft/GC-Proposal/GC.tex	(revision 6824)
+++ /trunk/MagicSoft/GC-Proposal/GC.tex	(revision 6825)
@@ -46,9 +46,8 @@
 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 acceleration mechanisms have still to be 
-identified.
-
-Various possibilities for the acceleration of the very high energy (VHE)
-gamma rays are discussed in the literature, like accretion flow onto the 
+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 
@@ -61,6 +60,6 @@
 
 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 for about 150 hours per year, between 
-April and late August. The expected integral flux above 700 GeV derived from 
+observed with MAGIC at up to 60 deg ZA, between 
+April and late August, yielding a total of 150 hours 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 
@@ -72,5 +71,5 @@
 
 \begin{itemize}
-\item to measure the gamma flux and its energy dependence (due to the high
+\item to measure the gamma-ray flux and its energy dependence (due to the high
 zenith angles higher energies are accessible),
 \item to inter-calibrate MAGIC and HESS,
@@ -107,5 +106,5 @@
 
 The Galactic Center (GC) region contains many unusual objects which may be 
-responsible for the high energy processes generating gamma rays 
+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 
@@ -142,11 +141,9 @@
 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 Crab pulsars. An independent analysis of the EGRET data 
+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} 
 
-Up to now, the GC has been observed at 
-energies above 200 GeV by Veritas, Cangaroo and HESS, \cite{GC_whipple,
-GC_cangaroo,GC_hess}. Figure \ref{fig:GC_gamma_flux} shows the reconstructed 
-spectra by the other IACTs while Figure \ref{fig:GC_source_location} shows the 
+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 
@@ -158,5 +155,5 @@
 \includegraphics[totalheight=6cm]{sgr_figure4.eps}
 \end{center}
-\caption[Gamma flux from GC.]{The VHE gamma flux as observed by the other IACTs and by the EGRET satellite \cite{GC_hess}.} \label{fig:GC_gamma_flux}
+\caption[Gamma flux from GC.]{The VHE gamma flux as observed by Whipple, Cangaroo , HESS and by the EGRET experiment \cite{GC_hess}.} \label{fig:GC_gamma_flux}
 \end{figure}
 
@@ -169,5 +166,5 @@
 \end{figure}
 
-The discrepancies between the measured flux spectra could indicate inter-calibration problems between the IACTs, a source variability of the order of one year could be due to the different regions in which the signal is integrated.
+The discrepancies between the measured flux spectra could indicate inter-calibration problems between the IACTs. An apparent source variability of the order of one year could be due to the different regions in which the signal is integrated.
 
 
@@ -175,5 +172,5 @@
 \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 other interested members of the MAGIC collaboration are invited to join these efforts.
+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.
 
 
@@ -190,5 +187,5 @@
 \\ Pepe Flix           & IFAE Barcelona& jflix@ifae.es & data analysis, disp
 \\ Sabrina Stark       & ETH Zurich    & lstark@particle.phys.ethz.ch  & data analysis, spectra
-\\ Wolfgang Wittek     & MPI Munich    & wittek@mppmu.mpg.de & padding
+\\ Wolfgang Wittek     & MPI Munich    & wittek@mppmu.mpg.de & padding, unfolding
 \\ 
 \hline
@@ -198,25 +195,26 @@
 \end{table}
 
+The principal investigator is .......
 
 \section{Scientific Case} 
 
 
-In the GC region high energy gamma rays can be produced in different sources:
+In the GC region high-energy gamma rays can be produced in different sources:
 
 \begin{itemize}
-\item{entire innermost 10 pc region (interaction between cosmic rays and the dense ambient gas)}
-\item{non-thermal radio filaments  \cite{Pohl1997}}
-\item{young SNR Sgr A East \cite{Fatuzzo2003}}
+\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}}
 \item{in the compact radio source Sgr A*}
-\item{central part of the dark matter halo.}
+\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 the observed TeV flux.
-
-
-% 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:
+It is quite possible that some of these potential gamma-ray production sites contribute comparably to the observed TeV flux.
+
+
+% 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}
@@ -237,7 +235,7 @@
 
 
-\subsection{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. But 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 filed may extend the high-energy limit to 10 TeV or even beyond \cite{Aharonian2005}.
+\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 filed may extend the high-energy limit to 10 TeV or even beyond \cite{Aharonian2005}.
 
 
@@ -245,7 +243,7 @@
 \subsubsection{Leptonic Models}
 
-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.
+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}
@@ -261,5 +259,5 @@
 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 $E_{\mathrm{thresh}}$ per solid angle $\Omega$ is given by:
+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 $E_{\mathrm{thresh}}$ per solid angle $\Omega$ is given by:
 
 \begin{equation*}
@@ -279,5 +277,5 @@
 
 Figure \ref{fig:exclusion_lmits} shows exclusion limits for MAGIC (solid straight lines) for the four most promising sources,
-in the plane $N_{\gamma}(E_{\gamma}>E_{\mathrm{thresh}})\langle \sigma v \rangle$ vs. $m_{\chi}$. The energy threshold $E_th$ 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.
+in the plane $N_{\gamma}(E_{\gamma}>E_{\mathrm{thresh}})\langle \sigma v \rangle$ vs. $m_{\chi}$. The energy threshold $E_{th}$ 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).
 
 
@@ -286,5 +284,5 @@
 \includegraphics[totalheight=6cm]{plot_DM_exclusion.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 from 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.  -- Figure to be updated --} \label{fig:exclusion_lmits}
+\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.  -- Figure to be updated --} \label{fig:exclusion_lmits}
 \end{figure}
 
@@ -343,50 +341,55 @@
 %\end{figure}
 
+Preliminary conclusion : ??????????????????
+
 
 \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, and the differential gamma flux is measured as \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{sTeV}} \left(\frac{E}{\mathrm{TeV}}\right)^{-2.21\pm 0.09 \pm 0.15}
-\end{equation}
-
-A fit to the published Cangaroo flux data points \cite{GC_cangaroo} yields:
+\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{sTeV}} \left(\frac{E}{\mathrm{TeV}}\right)^{-4.4\pm 1.1}
-\end{equation}
-
-
-For a 60 deg ZA we conservatively estimate the analysis energy threshold to be about 700 GeV. The integrated flux of the HESS spectrum is:
+\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}
-
-
-while the integrated flux above 700 GeV obtained from the Cangaroo spectrum is given by:
-
-\begin{equation}
-\frac{\mathrm{d}N_{\gamma}(E>700 \mathrm{GeV})}{\mathrm{d}A\mathrm{d}t}=(3 \pm 5)\cdot 10^{-12}\frac{1}{\mathrm{cm}^2\mathrm{s}} \ .
-\end{equation}
-
-
-Thus the integral fluxes above 700 GeV based on the HESS and Cangaroo data agree within errors.
-
-Using MC simulations \cite{MC-Camera} for small zenith angles we conservatively estimate MAGICs sensitivity \cite{MC-Sensitivity} to the integral flux to be:
-
-\begin{equation}
-\frac{\mathrm{d}N_{\gamma}(E>700 \mathrm{GeV})}{\mathrm{d}A\mathrm{d}t}\vline_{\mathrm{min}} \approx 6\cdot 10^{-13}\frac{1}{\mathrm{cm}^2\mathrm{s}} \ .
-\end{equation}
-
-Assuming this sensitivity and using the integrated flux of $3.2\cdot 10^{-12} \mathrm{cm}^{-2}\mathrm{s}^{-1}$ MAGIC will obtain an excess at the 5
-$\sigma$ significance level in $1.8 \pm 0.5$ h observation time. 
-
-The observed Cangaroo and HESS spectra differ
-substantially in the spectral index. While the Cangaroo spectrum only extends
-to about 2 TeV, the recently published HESS spectrum goes up to about 9 TeV. Figure \ref{fig:MAGIC_flux_limits} shows the HESS and Cangaroo observed fluxes together with the minimum flux detectable by MAGIC in 20 hours observation time.
-
-MAGIC will be able to solve the obvious discrepancy between the observed fluxes. Due to the observation under high zenith angle of about 60 deg MAGIC will be able to extend the source spectrum to higher energies.
+\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          &  $E_{th}$      & sensitivity    & $\Phi(E>E_{th})$            
+                              & $T_{5\sigma}$       \\
+             &                & above $E_{th}$ &   &\\
+$[^{\circ}]$ & $[{\rm GeV}]$  & $[{\rm cm}^2\;{\rm s}]^{-1}$  
+                              & $[{\rm cm}^2\;{\rm s}]^{-1}$     
+                              &  $ [{\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 $E_{th}$ and sensitivity for MAGIC for 2 zenith angles ZA. The 4th and 5th column contain the expected integrated flux above $E_{th}$ 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 HESS and Cangaroo fluxes together with the minimum flux detectable by MAGIC in 20 hours observation time.
+
+
 
 
@@ -398,8 +401,14 @@
 \end{figure}
 
-
-
-%?? How long do we have to observe to get a good spectrum above 7 TeV??
-
+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$20 TeV).
+
+
+???? We still have no good estimate of the expected number of excess event for the different conditions. ??? \\
+
+???? How long do we have to observe to get a good spectrum above 7 TeV  ??? \\
+
+\subsection{Verification of the MAGIC analysis at high zenith angles}
+In order to verify the correct performance of the MAGIC analysis at high ZA it is proposed to take Crab data in the interesting ZA range from 58$^{\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.
 
 
@@ -407,21 +416,19 @@
 
 
-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 has a quite large LONS background. This together with the large ZA requires to take either dedicated OFF data or to take data in the wobble mode. Since the LONS level is in any case very large moon observations are considered in addition to the normal observations.
+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 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{Requested Observation Time}
 
-Based on the above estimates a 5 $\sigma$ excess is expected to be observed in about 2 hours. 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. It is still being investigated which of the observation modes is to be preferred.
-
-To get the lowest possible threshold all data shall be taken at the
+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. 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, i.e. ZA and azimuth. At such high zenith angles the effect
-of the earth's magnetic field can be non-negligible. This depends of course on
-ZA and azimuth under which the data is taken.
-
-To extend the available observation time we propose to take moon ON and OFF data in addition. Also in this case, the proposed maximum ZA of 60 deg should not be exceeded during moon observations.
+April and August. 
+
+
+To increase statistics we propose to take data during moonshine in addition. 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
@@ -429,11 +436,74 @@
 
 
+\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}
+
+\subsection{Wobble mode}
+The star field around the GC, including stars up to a magnitude of 14, is depicted in Figure \ref{fig:GC_starfield}. One can see that the star field is roughly uniform except for the left lower part (RA$\;>\;$RA$_{GC}+4.7$ min), 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.
+
+\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.
+} \label{fig:GC_starfield}
+\end{figure}
+
+\begin{figure}[h!]
+\begin{center}
+\includegraphics[totalheight=16cm]{GCregion14large.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 1 degree.
+} \label{fig:GC_starfield_large}
+\end{figure}
+
+\begin{figure}[h!]
+\begin{center}
+\includegraphics[totalheight=16cm]{GCregionOFF.eps}
+\end{center}
+\caption[Star field around the GC.]{Star field around the GC. Stars up to a magnitude of 12 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_OFF}
+\end{figure}
+
+\subsection{ON/OFF mode}
+
+A larger sky area than in Fig.\ref{fig:GC_starfield} is shown in Figs. \ref{fig:GC_starfield_large} and \ref{fig:GC_starfield_OFF}. The bigger circle in the center 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_OFF} . It is centered at the Galactic Plane, contains the bright star Sgr 3 (at (RA, dec) = $(17^h47^m34^s,\;-27^{\circ}49'51"$) ) in its outer part and has the coordinates GC$_{OFF}$ = (RA, dec) = $(17^h52^m00^s,\;-26^{\circ}39'06")$. The difference in RA between the GC and GC$_{OFF}$ corresponds to about 7 minutes.
+
+%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{Outlook and Conclusions}
 
-The GC is an interesting target in all wavelengths. A great wealth of scientific publications is available, over 600 since 1999. First detections of the GC by the other IACTs Whipple, Cangaroo and HESS are made. Nevertheless the reconstructed fluxes differ significantly. This can be explained by calibration problems, time variations of the source or different integrated sources due to different point spread functions. The nature of the source of the VHE gamma rays is not yet been agreed on. 
-
-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 it is not excluded that a part of the flux is due to dark matter annihilation.
-
-The MAGIC data could help to determine the nature of the source and to solve the flux discrepancies between the measurements by other experiments. Due to the large Zenith angle MAGIC will have a large energy threshold but also a large collection area and good statistics at the highest energies. The observation results can also be used to inter-calibrate the different IACTs.
+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.
 
 
@@ -450,15 +520,8 @@
 The authors thank A. Moralejo for helpful discussions about the Monte Carlo simulations. 
 
+\newpage
 
 \bibliography{bibbib}
 \bibliographystyle{GC}
-
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Index: /trunk/MagicSoft/GC-Proposal/GCregion14.eps
===================================================================
--- /trunk/MagicSoft/GC-Proposal/GCregion14.eps	(revision 6825)
+++ /trunk/MagicSoft/GC-Proposal/GCregion14.eps	(revision 6825)
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+/solid { [] 0 setdash } def
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+%%%%%%%%%%%%%%%%%%%%
+% Spline to Bezier curve
+%   [x0 y0 x1 y1 x2 y2 ... ] Spline
+% Chris Beecroft (chrisb@netcom.com)
+%%%%%%%%%%%%%%%%%%%%
+
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+
+SplineDict begin
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+
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+/recipSQR2 1 SQR2 div def
+
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+	   % return: xa ya xb yb
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+    /theta1 exch def
+
+    /theta theta1 theta2 add 2 div def
+
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+	/theta2 theta 90 sub def
+    } {
+	/s theta2 theta sub sin def
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+	/theta2 theta 90 add def
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+(RA:) 124 193 rstr (17:45:12.0) 134 193 lstr
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+(Largest Eyepiece: 3:49) 306 138 cstr
+
+% Boiler plate:
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+(Created by XEphem Version 3.5.2 8 Jan 2002) 306 105 cstr
+(Copyright (c) 1990-2002 by Elwood Charles Downey) 306 94 cstr
+(http://www.ClearSkyInstitute.com) 306 83 cstr
+(Generated Mon Mar 14 16:12:48 2005 UTC) 306 72 cstr
+
+% All finished
+showpage
Index: /trunk/MagicSoft/GC-Proposal/GCregion14large.eps
===================================================================
--- /trunk/MagicSoft/GC-Proposal/GCregion14large.eps	(revision 6825)
+++ /trunk/MagicSoft/GC-Proposal/GCregion14large.eps	(revision 6825)
@@ -0,0 +1,41577 @@
+%!PS-ADOBE
+%%BoundingBox: 0 0 492 733
+% Define solid and dashed
+/dashed { [4 6] 0 setdash } def
+/solid { [] 0 setdash } def
+
+%%%%%%%%%%%%%%%%%%%%
+% Spline to Bezier curve
+%   [x0 y0 x1 y1 x2 y2 ... ] Spline
+% Chris Beecroft (chrisb@netcom.com)
+%%%%%%%%%%%%%%%%%%%%
+
+/SplineDict 7 dict def
+
+SplineDict begin
+
+/CPointDict 8 dict def
+/ComputeCPDict 21 dict def
+
+% Some constants
+/Tension 0.65 def  % 0 (loose) to 1 (tight)
+/SQR2 2 sqrt def
+/recipSQR2 1 SQR2 div def
+
+/CPoint    % calculate control bezier points
+{          % stack:  x y len1 len2 angle1 angle2 
+	   % return: xa ya xb yb
+CPointDict begin
+    /theta2 exch def
+    /theta1 exch def
+
+    /theta theta1 theta2 add 2 div def
+
+    theta1 theta2 gt {
+	/s theta theta2 sub sin def
+	/theta1 theta 90 add def
+	/theta2 theta 90 sub def
+    } {
+	/s theta2 theta sub sin def
+	/theta1 theta 90 sub def
+	/theta2 theta 90 add def
+    } ifelse
+
+    s recipSQR2 gt {
+	/s SQR2 s sub def
+    } if
+
+    /s s 1 Tension sub mul def
+
+    % stack: x y len1 len2
+
+    /len2 exch s mul def  % len2 = len2 * s
+    /len1 exch s mul def  % len1 = len1 * s
+
+    /y exch def
+    /x exch def
+
+  x len1 theta1 cos mul add % x + len1 * cos(theta1)
+  y len1 theta1 sin mul sub % y - len1 * sin(theta1)
+  x len2 theta2 cos mul add % x + len2 * cos(theta2)
+  y len2 theta2 sin mul sub % y - len2 * sin(theta2)
+end
+} def
+
+
+/ComputeCP % spline through points
+{          % stack:  [ x0 y0 x1 y1 x2 y2 .... ]
+	   % return: nothing  % spline path added to current path
+ComputeCPDict begin
+    /SplinePoints exch def
+    /elems SplinePoints length def
+
+    /x1 SplinePoints 0 get def
+    /y1 SplinePoints 1 get def
+    /x2 SplinePoints 2 get def
+    /y2 SplinePoints 3 get def
+    /x3 SplinePoints 4 get def
+    /y3 SplinePoints 5 get def
+
+    /dx x1 x2 sub def
+    /dy y2 y1 sub def
+    /len1 dx dx mul dy dy mul add sqrt def
+    len1 0.0 eq {
+	/theta1 0.0 def
+    } {
+	/theta1 dy dx atan def
+	theta1 0 lt {
+	    /theta1 theta1 360 add def
+	} if
+    } ifelse
+
+    /dx x3 x2 sub def
+    /dy y2 y3 sub def
+    /len2 dx dx mul dy dy mul add sqrt def
+    len2 0.0 eq {
+	/theta2 0.0 def
+    } {
+	/theta2 dy dx atan def
+	theta2 0 lt {
+	    /theta2 theta2 360 add def
+	} if
+    } ifelse
+
+    % compute and store the left and right control points
+    x2 y2 len1 len2 theta1 theta2 CPoint
+    /yright exch def
+    /xright exch def
+    /yleft  exch def
+    /xleft  exch def
+
+    x1 y1 moveto
+
+    x1 3 xleft mul add 4 div
+    y1 3 yleft mul add 4 div
+    xleft 3 mul x2 add 4 div
+    yleft 3 mul y2 add 4 div
+    x2 y2 curveto
+
+    /xsave xright def
+    /ysave yright def
+    
+    6 2 elems 1 sub {
+	/index exch def
+
+	/x2 x3 def
+	/y2 y3 def
+	/len1 len2 def
+
+	theta2 180 ge {
+	    /theta1 theta2 180 sub def
+	} {
+	    /theta1 theta2 180 add def
+	} ifelse
+
+	/x3 SplinePoints index get def
+	/y3 SplinePoints index 1 add get def
+
+	/dx x3 x2 sub def
+	/dy y2 y3 sub def
+	/len2 dx dx mul dy dy mul add sqrt def
+	len2 0.0 eq {
+	    /theta2 0.0 def
+	} {
+	    /theta2 dy dx atan def
+	    theta2 0 lt {
+		/theta2 theta2 360 add def
+	    } if
+	} ifelse
+
+	x2 y2 len1 len2 theta1 theta2 CPoint
+	/yright exch def
+	/xright exch def
+	/yleft  exch def
+	/xleft  exch def
+
+	xsave ysave xleft yleft x2 y2 curveto
+	/xsave xright def
+	/ysave yright def
+    } for
+
+    xright 3 mul x2 add 4 div
+    yright 3 mul y2 add 4 div
+    xright 3 mul x3 add 4 div
+    yright 3 mul y3 add 4 div
+    x3 y3 curveto
+end
+} def
+
+end
+
+
+/Spline
+{
+    SplineDict begin ComputeCP end
+} def
+%%%%%%%%%%%%%%%%%%%%
+% General Rotated ellipses.
+%   x y a0 xrad yrad a1 a2 ellipse
+%   N.B. xrad and yrad must be != 0 
+% Chris Beecroft (chrisb@netcom.com)
+%%%%%%%%%%%%%%%%%%%%
+/ellipsedict 9 dict def
+ellipsedict /mtrx matrix put
+/ellipse
+    { ellipsedict begin
+      /endangle exch def
+      /startangle exch def
+      /yrad exch def
+      /xrad exch def
+      /rotation exch def
+      /y exch def
+      /x exch def
+
+      /savematrix mtrx currentmatrix def
+      x y translate
+      rotation rotate
+      xrad yrad scale
+
+      % convert angle/radius (radius=1) to x,y
+      % divide in x,y scaling and convert back to polar.
+      % subtract a bit off endangle to force 360 sin
+      % to be a small negative number to atan rseults in
+      % a degree of 360 rather than 0. If startangle is 0
+      % then a surprise appears and no ellipse is drawn.
+
+      /endangle endangle 0.001 sub sin yrad div endangle cos xrad div atan def
+      /startangle startangle sin yrad div  startangle cos xrad div  atan def
+
+      0 0 1 startangle endangle arc
+      savematrix setmatrix
+      end
+    } def
+% Define l-justified string: (..) x y lstr
+/lstr { newpath moveto show } def
+
+% Define r-justified string: (..) x y rstr
+/rstr { newpath moveto
+  dup         % make copies for stringwidth and show
+  stringwidth % yields X and Y size
+  pop         % don't need Y
+  neg 0 rmoveto % move back
+  show        % show the string
+} def
+
+% Define centered string: (..) x y cstr
+/cstr { newpath moveto
+  dup         % make copies for stringwidth and show
+  stringwidth % yields X and Y size
+  pop         % don't need Y
+  2 div neg 0 rmoveto % move back halfway
+  show        % show the string
+} def
+
+% Define string size: (..) strsz w h
+/strsz {
+  gsave
+    newpath 0 0 moveto true charpath pathbbox
+    4 2 roll pop pop
+  grestore
+} def
+
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+(RA:) 124 193 rstr (17:45:12.0) 134 193 lstr
+(Declination:) 124 182 rstr (-29:00:36) 134 182 lstr
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+
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+(Generated Tue Mar 15 09:51:58 2005 UTC) 306 72 cstr
+
+% All finished
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Index: /trunk/MagicSoft/GC-Proposal/GCregionOFF.eps
===================================================================
--- /trunk/MagicSoft/GC-Proposal/GCregionOFF.eps	(revision 6825)
+++ /trunk/MagicSoft/GC-Proposal/GCregionOFF.eps	(revision 6825)
@@ -0,0 +1,18343 @@
+%!PS-ADOBE
+%%BoundingBox: 0 0 493 734
+% Define solid and dashed
+/dashed { [4 6] 0 setdash } def
+/solid { [] 0 setdash } def
+
+%%%%%%%%%%%%%%%%%%%%
+% Spline to Bezier curve
+%   [x0 y0 x1 y1 x2 y2 ... ] Spline
+% Chris Beecroft (chrisb@netcom.com)
+%%%%%%%%%%%%%%%%%%%%
+
+/SplineDict 7 dict def
+
+SplineDict begin
+
+/CPointDict 8 dict def
+/ComputeCPDict 21 dict def
+
+% Some constants
+/Tension 0.65 def  % 0 (loose) to 1 (tight)
+/SQR2 2 sqrt def
+/recipSQR2 1 SQR2 div def
+
+/CPoint    % calculate control bezier points
+{          % stack:  x y len1 len2 angle1 angle2 
+	   % return: xa ya xb yb
+CPointDict begin
+    /theta2 exch def
+    /theta1 exch def
+
+    /theta theta1 theta2 add 2 div def
+
+    theta1 theta2 gt {
+	/s theta theta2 sub sin def
+	/theta1 theta 90 add def
+	/theta2 theta 90 sub def
+    } {
+	/s theta2 theta sub sin def
+	/theta1 theta 90 sub def
+	/theta2 theta 90 add def
+    } ifelse
+
+    s recipSQR2 gt {
+	/s SQR2 s sub def
+    } if
+
+    /s s 1 Tension sub mul def
+
+    % stack: x y len1 len2
+
+    /len2 exch s mul def  % len2 = len2 * s
+    /len1 exch s mul def  % len1 = len1 * s
+
+    /y exch def
+    /x exch def
+
+  x len1 theta1 cos mul add % x + len1 * cos(theta1)
+  y len1 theta1 sin mul sub % y - len1 * sin(theta1)
+  x len2 theta2 cos mul add % x + len2 * cos(theta2)
+  y len2 theta2 sin mul sub % y - len2 * sin(theta2)
+end
+} def
+
+
+/ComputeCP % spline through points
+{          % stack:  [ x0 y0 x1 y1 x2 y2 .... ]
+	   % return: nothing  % spline path added to current path
+ComputeCPDict begin
+    /SplinePoints exch def
+    /elems SplinePoints length def
+
+    /x1 SplinePoints 0 get def
+    /y1 SplinePoints 1 get def
+    /x2 SplinePoints 2 get def
+    /y2 SplinePoints 3 get def
+    /x3 SplinePoints 4 get def
+    /y3 SplinePoints 5 get def
+
+    /dx x1 x2 sub def
+    /dy y2 y1 sub def
+    /len1 dx dx mul dy dy mul add sqrt def
+    len1 0.0 eq {
+	/theta1 0.0 def
+    } {
+	/theta1 dy dx atan def
+	theta1 0 lt {
+	    /theta1 theta1 360 add def
+	} if
+    } ifelse
+
+    /dx x3 x2 sub def
+    /dy y2 y3 sub def
+    /len2 dx dx mul dy dy mul add sqrt def
+    len2 0.0 eq {
+	/theta2 0.0 def
+    } {
+	/theta2 dy dx atan def
+	theta2 0 lt {
+	    /theta2 theta2 360 add def
+	} if
+    } ifelse
+
+    % compute and store the left and right control points
+    x2 y2 len1 len2 theta1 theta2 CPoint
+    /yright exch def
+    /xright exch def
+    /yleft  exch def
+    /xleft  exch def
+
+    x1 y1 moveto
+
+    x1 3 xleft mul add 4 div
+    y1 3 yleft mul add 4 div
+    xleft 3 mul x2 add 4 div
+    yleft 3 mul y2 add 4 div
+    x2 y2 curveto
+
+    /xsave xright def
+    /ysave yright def
+    
+    6 2 elems 1 sub {
+	/index exch def
+
+	/x2 x3 def
+	/y2 y3 def
+	/len1 len2 def
+
+	theta2 180 ge {
+	    /theta1 theta2 180 sub def
+	} {
+	    /theta1 theta2 180 add def
+	} ifelse
+
+	/x3 SplinePoints index get def
+	/y3 SplinePoints index 1 add get def
+
+	/dx x3 x2 sub def
+	/dy y2 y3 sub def
+	/len2 dx dx mul dy dy mul add sqrt def
+	len2 0.0 eq {
+	    /theta2 0.0 def
+	} {
+	    /theta2 dy dx atan def
+	    theta2 0 lt {
+		/theta2 theta2 360 add def
+	    } if
+	} ifelse
+
+	x2 y2 len1 len2 theta1 theta2 CPoint
+	/yright exch def
+	/xright exch def
+	/yleft  exch def
+	/xleft  exch def
+
+	xsave ysave xleft yleft x2 y2 curveto
+	/xsave xright def
+	/ysave yright def
+    } for
+
+    xright 3 mul x2 add 4 div
+    yright 3 mul y2 add 4 div
+    xright 3 mul x3 add 4 div
+    yright 3 mul y3 add 4 div
+    x3 y3 curveto
+end
+} def
+
+end
+
+
+/Spline
+{
+    SplineDict begin ComputeCP end
+} def
+%%%%%%%%%%%%%%%%%%%%
+% General Rotated ellipses.
+%   x y a0 xrad yrad a1 a2 ellipse
+%   N.B. xrad and yrad must be != 0 
+% Chris Beecroft (chrisb@netcom.com)
+%%%%%%%%%%%%%%%%%%%%
+/ellipsedict 9 dict def
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+/ellipse
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+      /endangle exch def
+      /startangle exch def
+      /yrad exch def
+      /xrad exch def
+      /rotation exch def
+      /y exch def
+      /x exch def
+
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+      x y translate
+      rotation rotate
+      xrad yrad scale
+
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+      % divide in x,y scaling and convert back to polar.
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+      % to be a small negative number to atan rseults in
+      % a degree of 360 rather than 0. If startangle is 0
+      % then a surprise appears and no ellipse is drawn.
+
+      /endangle endangle 0.001 sub sin yrad div endangle cos xrad div atan def
+      /startangle startangle sin yrad div  startangle cos xrad div  atan def
+
+      0 0 1 startangle endangle arc
+      savematrix setmatrix
+      end
+    } def
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+/lstr { newpath moveto show } def
+
+% Define r-justified string: (..) x y rstr
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+  show        % show the string
+} def
+
+% Define centered string: (..) x y cstr
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+  show        % show the string
+} def
+
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+(RA:) 124 193 rstr (17:45:12.0) 134 193 lstr
+(Declination:) 124 182 rstr (-29:00:36) 134 182 lstr
+(Epoch:) 124 171 rstr (2000.00) 134 171 lstr
+(Altitude:) 124 160 rstr (-0:37:50) 134 160 lstr
+(Azimuth:) 124 149 rstr (225:26:15) 134 149 lstr
+(Field Width:) 124 138 rstr (10:00) 134 138 lstr
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+(UTC Date:) 460 171 rstr (3/15/2005) 470 171 lstr
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+(Grid Steps:) 306 171 cstr
+(RA:   0:05:00) 306 160 cstr
+(Dec:   1:00:00) 306 149 cstr
+(Largest Eyepiece: 3:33) 306 138 cstr
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+(Copyright (c) 1990-2002 by Elwood Charles Downey) 306 94 cstr
+(http://www.ClearSkyInstitute.com) 306 83 cstr
+(Generated Tue Mar 15 12:31:33 2005 UTC) 306 72 cstr
+
+% All finished
+showpage
Index: /trunk/MagicSoft/GC-Proposal/bibbib.bib
===================================================================
--- /trunk/MagicSoft/GC-Proposal/bibbib.bib	(revision 6824)
+++ /trunk/MagicSoft/GC-Proposal/bibbib.bib	(revision 6825)
@@ -6,4 +6,13 @@
      eprint    = "astro-ph/0212509",
      SLACcitation  = "%%CITATION = ASTRO-PH 0212509;%%"
+}
+
+@Article{ECO-1000,
+     author    = {{Martinez}, M. and others},
+     title     = "ECO, the European Gamma-Ray Observatory: Low-threshold 
+Telescopes at La Palma",
+     year      = "2003",
+     eprint    = "",
+     SLACcitation  = "%%CITATION = ASTRO-PH xxxxx;%%"
 }
 
