Changeset 780


Ignore:
Timestamp:
May 7, 2001, 3:04:40 PM (20 years ago)
Author:
wittek
Message:
Corrections by Rudy and Wolfgang added, 7 May 2001
File:
1 edited

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  • trunk/MagicDoku/strategy_mc_ana.tex

    r779 r780  
    1414\title{Outline of a standard analysis for MAGIC \\
    1515(including Monte Carlo work)}
    16 \author{H. Kornmayer, W. Wittek\\
     16\author{R. B\"ock, H. Kornmayer, W. Wittek\\
    1717\texttt{h.kornmayer@web.de, wittek@mppmu.mpg.de}}
    1818
     
    118118obtained by some procedure.
    119119
    120 Open questions : - how should $\Delta \beta$ be defined
    121                  - how big should $\Delta \beta$ be chosen
     120We propose to define $\Delta \beta$ as a direction difference in the
     121local azimuthal angle $\phi$ :
     122$\Delta \phi\;=\;\Delta \beta\;/\;sin(\Theta)$. For very small
     123$\Theta$ ($\Theta\;<\; 1$ degree) $\Delta \beta$ should be defined
     124differently, also to avoid large rotation speeds of the telescope.
     125
     126Since the radius of the trigger area is 0.8 degrees, we propose
     127to choose $\Delta \beta\;=\;0.4$ degrees.
     128 
    122129
    123130\item Pedestals :\\
     
    143150
    144151The gamma/hadron separation will be given in terms of a set of cuts
    145 on quantities which are derived from the measurable quantities, which are :
     152(or certain conditions) on quantities which in general are not
     153identical to the measured quantities but which are derived from them. The
     154measurable quantities are :
    146155 \begin{itemize}
    147156 \item[-] the direction $\Theta$ and $\phi$ the telescope is pointing to
     
    170179
    171180\begin{itemize}
    172 \item Image parameters :\\
    173 The standard definition of the image parameters is assumed. See for
    174 example \cite{hillas85,fegan96,reynolds93}.
    175  
    176 \item Impact parameter :\\
    177 The impact parameter $p$ is defined as the vertical distance
    178 of the telescope from the shower axis. It is not directly
    179 measurable. It may be estimated from the image parameters.
    180 
    181 \item Energy :\\
    182 The energy of the shower is not directly measurable either, but may be
    183 estimated from the image parameters too.
    184 
    185181\item The direction $(\Theta,\phi)$ :\\
    186182$(\Theta,\phi)$ denotes the direction the telescope is pointing to,
    187183not the position of the source being observed.
     184
     185\item Image parameters :\\
     186The standard definition of the image parameters is assumed. See for
     187example \cite{hillas85,fegan96,reynolds93}. We should also make use of
     188additional parameters like asymmetry parameters, number of islands or
     189mountains etc.
     190\end{itemize}
     191 
     192Quantities which are not directly measurable, but which can be
     193estimated from the image parameters are :
     194
     195\begin{itemize}
     196\item Impact parameter :\\
     197The impact parameter $p$ is defined as the vertical distance
     198of the telescope from the shower axis.
     199
     200\item The energy of the shower
    188201\end{itemize}
    189202
     
    192205\subsubsection{Differential gamma flux and collection area for a point source}
    193206
    194 The differential gamma flux from a point sourse $s$ is given by
     207The differential gamma flux from a point source $s$ is given by
    195208
    196209\begin{eqnarray}
     
    200213where $dN^{\gamma}_s$ is the number of gammas from the source $s$ in
    201214the bin $dE,\;dF,\;dt$ of energy, area and time respectively. We
    202 denote the probability for reconstructing a gamma shower with energy
     215denote the probability for 'observing' a gamma shower with energy
    203216$E$, zenith angle $\Theta$ and position $F$ in a plane perpendicular
    204 to the source direction by
    205 $R^{\gamma}(E,\Theta,F)$. The effective collection area is defined as
     217to the source direction by $R^{\gamma}(E,\Theta,F)$. Depending on the
     218special study, the term 'observing' may mean triggering,
     219reconstructing, etc.
     220
     221The effective collection area is defined as
    206222
    207223\begin{eqnarray}
     
    210226\end{eqnarray}
    211227
     228A side remark : The well known behaviour that the effective collection
     229area (well above the threshold energy) is larger for larger zenith angles
     230$\Theta$, is due to the fact that at higher $\Theta$ the distance of
     231the shower maximum (where the majority of Cherenkov photons is
     232emitted) from the detector is larger than at smaller $\Theta$. The
     233area in which $R^{\gamma}(E,\Theta,F)$ contributes significantly to
     234the integral (\ref{eq:form-1}) is therefore larger, resulting in a
     235larger $F^{\gamma}_{eff}(E,\Theta)$. For the simulation this means,
     236that the maximum impact parameter should be chosen larger for larger $\Theta$.
    212237
    213238The number of $\gamma$ showers observed in the bin $\Delta \Theta$ of
     
    221246 \int_{\Delta E}{} \Phi^{\gamma}_s(E)\cdot
    222247 F^{\gamma}_{eff}(E,\Theta)\cdot dE \\
     248\end{eqnarray}
     249
     250Assuming that $F^{\gamma}_{eff}(E,\Theta)$ depends only weakly on $E$
     251in the (sufficiently small) interval $\Delta E$ gives
     252
     253\begin{eqnarray}
     254\Delta N^{\gamma,obs}_s(E,\Theta) 
    223255                         &\approx   &\Delta T_{on}(\Theta) \cdot
    224256  F^{\gamma}_{eff}(E,\Theta) \cdot \int_{\Delta E}{}
     
    329361which $R^{\gamma}(E,\Theta,F)$ is greater than zero were
    330362simulated. This means in particular that the MC simulation of gammas
    331 extends to sufficiently large impact parameters.
     363extends to sufficiently large impact parameters. In reality, in order to save
     364computer time showers will be generated up to a maximum
     365value of the impact parameter (possibly depending on the zenith
     366angle). An appropriate correction for that has to be applied later in
     367the analysis.
    332368
    333369Knowing $F^{\gamma}_{eff}(E,\Theta)$, the gamma fluxes can be obtained
     
    382418 \int_{\Delta E}{} \Phi^{h}(E)\cdot
    383419 F^{h}_{eff}(E,\Theta)\cdot dE \\
     420\end{eqnarray}
     421
     422\begin{eqnarray}
     423\Delta N^{h,obs}(E,\Theta)
    384424                         &\approx   &\Delta T_{on}(\Theta) \cdot
    385425  F^{h}_{eff}(E,\Theta) \cdot \int_{\Delta E}{}
     
    841881\end{itemize}
    842882
     883
     884
     885\subsection{A suggestion for an initial workplan}
     886We propose in the following a list of tasks whose common goal
     887it is to provide and use data files with a definition of data suitable for
     888initial studies, e.g. trigger rates, and for subsequent further
     889analysis in MARS, e.g. $\gamma$/h-separation. We consider this list to be
     890minimal and a first step only.
     891Given the amount of work that will have to be invested, the detailed
     892assumptions below should be backed up by collaboration-wide agreement; also, some
     893input from groups is essential, so PLEASE REACT.
     894 
     895Event generation should be done with the following conditions:
     896\begin{itemize}
     897  \item Signal definition: we will use the Crab, over a range of zenith angles
     898  (define!!). A minimum of 20,000 (can we get that?) triggers will be
     899  generated, starting from existing MMCS files;
     900  \item Observation mode: observations are assumed off-axis,
     901  with an offset of $\pm 0.4 \deg $ in $\Delta \beta$ along the direction of the
     902  local azimuthal angle $\phi$,
     903  switching sign every 500 events (see 'Assumptions' above);
     904  \item Adding star field: adapt starfieldadder and starresponse to the
     905  Crab. Ignore star field rotation problems for the moment, until a separate study
     906  is available (??);
     907  \item Pedestal fluctuations: all pixel values are smeared by a Gaussian
     908  centered at zero with a sigma of 1.5 photoelectrons;
     909  \item Trigger:  Padova to define (!!) the grouping of pixels, the
     910  trigger thresholds, and a method to avoid triggering on stars. We assume
     911  only a first-level trigger.
     912\end{itemize}
     913With this event sample available, we suggest to embark on several studies,
     914which will help us in understanding better the MAGIC performance, and will
     915also pave our way into future analysis.
     916\begin{itemize}
     917  \item determine trigger rates (1st level only), as function of energy and
     918  zenith angle (also of impact parameter?);
     919  \item determine gamma acceptance,
     920  as function of energy and zenith angle (also of impact parameter?); 
     921  \item determine effective collection area (gammas and hadrons),
     922  as function of energy and zenith angle (also of impact parameter?); 
     923  \item show the position of the shower maximum (Xmax);
     924  \item start comparing methods for $\gamma$/h-separation, i.e. the generation
     925  of ON and OFF samples from the observations;
     926  \item start magnetic field studies ($\phi$-dependence);
     927  \item eventually, study the effect of the rotating star field.
     928\end{itemize}
     929
     930
     931
    843932\section{Analysis of the real data}
    844933
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