source: trunk/MagicSoft/GC-Proposal/GC.tex@ 6737

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\title{Proposal: Observations of the Galactic Center \\
Key Programs: Galactic Center / Dark Matter
}
\author{H. Bartko, A. Biland, S. Commichau, P. Flix, W. Wittek}
\date{March dd, 2005\\}
\TDAScode{}%MAGIC 05-xx\\ 04mmdd/HBartko
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\begin{abstract}  
The Galactic Center (GC) is a very interesting region. Gamma radiation above  a few hundred GeV has been detected recently by Whipple, Cangaroo and HESS. The reconstructed spectra from Cangaroo and HESS show significant differences. Source and acceleration mechanism have still to be identified.

Various possibilities for the acceleration of the very high energy gamma rays
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 SUSY-neutralino particle
dark matter (DM) annihilation, other models like Kaluza-Klein dark matter are not ruled out. Moreover, assuming a universal DM distribution profile, the GC is expected to yield the largest DM flux due to its relative vicinity.


The GC culminates at about 58 deg ZA in La Palma. 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 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 to participate in the exciting physics of the Galactic Center. The main motivations are:

\begin{itemize}
\item To solve the flux discrepancies between HESS and Cangaroo, inter-calibration between the instruments.
\item Extend the observed spectrum to higher energies due to large ZA.
\item Determine the nature and acceleration mechanism of the source. Set constraints to models for particle dark matter annihilation.
\end{itemize}


To get a comparable data set to the other experiments and to be able to reconstruct the spectrum, an observation of 20 hours plus 20 hours of dedicated OFF data would be needed and hereby applied for. Moreover due to the large threshold moon observations are envisaged and 60 hours are applied for.
\end{abstract}

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\section{Introduction}



The Galactic Center (GC) region, excepting the famous source Sgr A$^*$, contains many unusual objects which may be responsible for the high energy processes generation 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 within the volume of 300 pc and the mass of $2.7 \cdot 10^7 M_{\odot}$, young supernova remnants e.g. G0.570-0.018 or Sgr A East, and nonthermal radio arcs. An overview of the sources in the GC region is given in figure \ref{fig:GC_sources}. Some data about the Galactic Center 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  & $8\pm0.5$ kpc (1 deg = 24 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 the index 1.3 below the bread at a few GeV. If in the GC, the gamma ray luminosity of this source is very large $~2 \cdot 10^{37} \mathrm{erg}/\mathrm{s}$, which is equivalent to about 10 Crab pulsars. 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 different reconstructed positions of the GC source. Recently a second TeV gamma source only about 1 degree away from the Galactic Center has been discovered \cite{SNR_G09+01}. Its integral flux above 200 GeV represents about 2\% of the gamma flux from the Crab nebula.

\begin{figure}[h!]
\begin{center}
\includegraphics[totalheight=6cm]{sgr_figure4.eps}
\end{center}
\caption[Gamma flux from GC.]{The observed VHE gamma flux with the other IACTs and the EGRET satellite \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 observed VHE source locations with the other IACTs \cite{Horns2004}.} \label{fig:GC_source_location}
\end{figure}

The different reconstructed spectra in VHE gammas 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.



\section{Investigators and Affiliations}

The investigators of the proposed observations of the Galactic Center 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.


\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 & OFF pointing, Moon observations
\\ Sebastian Commichau & ETH Zurich    & commichau@particle.phys.ethz.ch &
 data analysis, MC generation, spectra
\\ Pepe Flix           & IFAE Barcelona& jflix@ifae.es & data analysis, disp
\\ Wolfgang Wittek     & MPI Munich    & wittek@mppmu.mpg.de & padding
\\ 
\hline
\end{tabular}
}
\caption{The investigators and assigned tasks.}\label{table:GC_investigators}}}
\end{table}

\section{Scientific Case} 


High energy gamma rays can be produced in the GC 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$^*$, supernovae or an energetic pulsar. 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}.


In order to shed new light on the high energy phenomena in the GC region, and constrain the models mentioned above, new observations with high sensitivity, good spectra reconstruction and angular resolution are necessary.

For the interpretation of the observed gamma flux the following observables are very important:

\begin{itemize}
\item{source location, source extension}
\item{time variability}
\item{energy spectrum}
\end{itemize} 






\subsection{Leptonic Models}


\subsection{Hadronic Models}


\subsection{Dark Matter}


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}.

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*}
\frac{\text{d} N_{\gamma}(E_{\gamma}>E_{\mathrm{thresh}})}{\text{d}t\  \text{d}A\  \text{d}\Omega }= N_{\gamma}(E_{\gamma}>E_{\mathrm{thresh}}) \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 cross section, $m_{\chi}$ the mass and $\rho_{\chi}$ the spatial density distribution of the hypothetical dark matter particles. $N_{\gamma}(E_{\gamma}>E_{\mathrm{thresh}})$ is the gamma yield above the threshold energy per annihilation. The flux prediction depends on the choose of SUSY parameters and the spatial distribution of the dark matter. The spectra 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 density enhancement in the center of the dark halos. In the very center the dark matter density can even more enhanced through an adiabatic compression due to the baryons \cite{Prada2004} present. 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 distribution of the dark matter can be made \cite{Fornego2004,Evans2004}. 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 predictions for the gamma flux from SUSY particle dark matter annihilation are derived.

Figure \ref{fig:exclusion_lmits} shows exclusion limits taking the sensitivity of MAGIC from MC simulations into account for different sources and predictions from typical allowed SUSY modells in the plane $N_{\gamma}(E_{\gamma}>E_{\mathrm{thresh}})\langle \sigma v \rangle$ vs $m_{\chi}$. Due to its relative vicinity the Galactic Center yield the largest expected flux from particle dark matter annihilation. Nevertheless this flux is more than one order of magnitude below the current MAGIC sensitivity. Also the observed flux from the HESS experiment way above the theoretical expectation.


\begin{figure}[h!]
\begin{center}
\includegraphics[totalheight=6cm]{Dark_exclusion_limits.eps}
\end{center}
\caption[DM exclusion limits.]{Exclusion limits for different possible sources of dark matter annihilation radiation. The galactic center is expected to give the largest flux from all sources. The observed flux by the HESS experiment is within the reach of MAGIC for energies above about 700 GeV. Nevertheless it is more than one order of magnitude above the typical model predictions.  -- figure to be updated --} \label{fig:exclusion_lmits}
\end{figure}


Detailed discussion of the observed gamma flux from the Galactic Center 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 theoretical expectation in most models. This leads to the conclusion that most likely the dominating part of the observed gamma flux from the Galactic Center 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 there is only 2.9 hours of ON data available at a very large zenith
angle range. 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 $[^\circ]$ & Zd $[^\circ]$\\ \hline
   09/08/2004 & 21:00 - 22:00 & 198.3 - 214.7 & 60.3 - 67.8
\\ 09/09/2004 & 21:17 - 22:12 & 203.4 - 214.7 & 62.2 - 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 for the gamma
hadron separation. For this purpose high
ZA (65$^\circ$ Zd and 205$^\circ$ Az) Monte Carlo gammas were generated, 
99500 events in all, with energies between 200
and 30,000 GeV. The slope of the generated spectrum is $-2.6$, conforming the
energy spectrum of the Crab nebula... 

The MC sample is divided into training
and test sample. Since there is no dedicated OFF data available, we used a
subsample of Sgr A$^*$ ON data for the Random Forest training. As trainings
parameters we used SIZE, DIST, WIDTH, LENGTH, CONC, and M3Long...


%\begin{figure}[!h]
%\centering
%\subfigure[The Hadronness distribution.]{
%\includegraphics[scale= .3]{hadronness}}
%\subfigure[SIZE $> 300$ Phe]{
%\includegraphics[scale= .3]{size300}}
%\subfigure[SIZE $> 500$ Phe]{
%\includegraphics[scale= .3]{size500}}
%\subfigure[SIZE $> 1000$ Phe]{
%\includegraphics[scale= .3]{size1000}}
%\caption{Hadronness distribution and ALPHA plots for three different lower SIZE cuts. The
%  Hadronness cut is made at 0.4.}\label{fig:prelresults}
%\end{figure}


\section{Feasibility} 

Plot: sensitivity limits from MAGIC compared to predicted gamma flux.

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}

Cangaroo (fit to Cangaroo data):

\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:

\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 expected 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 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 MAGIC shall be able to get an excess at the 5
$\sigma$ significance level in $1.8 \pm 0.5$ h observation time for both the
Cangaroo and HESS spectrum. 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. 

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.



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



\section{Observational Constraints}


The galactic center culminates at about 58 deg ZA in La Palma. It is visible
at up to 60 deg ZA between April and late August for in total about 150 hours. The galactic center has a quite large LONS background. This together with the large ZA requires to take dedicated OFF data. Since the LONS level is in any case very large moon observations can be considered in addition to the normal observations.


\begin{itemize}
\item{possible months of observation: April - August}
\item{observation mode (ON/OFF)}
\item{moon observation in addition possible}
\end{itemize}


\section{Requested Observation Time}

Based on the above estimations a 5 $\sigma$ excess is expected to be observed in about 2 hours assuming the HESS flux. To acquire a comparable data set to the other experiments at least 20 hours of good ON data and 20 hours of good dedicated OFF data are needed. 

To get the lowest possible threshold all data shall be taken under 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. Nevertheless, the proposed maximum ZA of 60 deg should not be exceeded during moon observations.

In order to take part in exploring the exciting physics of the galactic center
we propose to start taking data as soon as possible beginning in April. In this way first results may be presented in the summer conferences 2005.


\section{Outlook and Conclusions}

The galactic center is an interesting target in all wavelengths. A great wealth of scientific publications is available, over 600 since 1999. First detections of the Galactic Center 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 galactic center 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.






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\appendix

\section{Acknowledgements}

The authors thank ...  is acknowledged. 


\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}