# Changeset 780 for trunk/MagicDoku/strategy_mc_ana.tex

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Timestamp:
May 7, 2001, 3:04:40 PM (20 years ago)
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Corrections by Rudy and Wolfgang added, 7 May 2001

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 r779 \title{Outline of a standard analysis for MAGIC \\ (including Monte Carlo work)} \author{H. Kornmayer, W. Wittek\\ \author{R. B\"ock, H. Kornmayer, W. Wittek\\ \texttt{h.kornmayer@web.de, wittek@mppmu.mpg.de}} obtained by some procedure. Open questions : - how should $\Delta \beta$ be defined - how big should $\Delta \beta$ be chosen We propose to define $\Delta \beta$ as a direction difference in the local azimuthal angle $\phi$ : $\Delta \phi\;=\;\Delta \beta\;/\;sin(\Theta)$. For very small $\Theta$ ($\Theta\;<\; 1$ degree) $\Delta \beta$ should be defined differently, also to avoid large rotation speeds of the telescope. Since the radius of the trigger area is 0.8 degrees, we propose to choose $\Delta \beta\;=\;0.4$ degrees. \item Pedestals :\\ The gamma/hadron separation will be given in terms of a set of cuts on quantities which are derived from the measurable quantities, which are : (or certain conditions) on quantities which in general are not identical to the measured quantities but which are derived from them. The measurable quantities are : \begin{itemize} \item[-] the direction $\Theta$ and $\phi$ the telescope is pointing to \begin{itemize} \item Image parameters :\\ The standard definition of the image parameters is assumed. See for example \cite{hillas85,fegan96,reynolds93}. \item Impact parameter :\\ The impact parameter $p$ is defined as the vertical distance of the telescope from the shower axis. It is not directly measurable. It may be estimated from the image parameters. \item Energy :\\ The energy of the shower is not directly measurable either, but may be estimated from the image parameters too. \item The direction $(\Theta,\phi)$ :\\ $(\Theta,\phi)$ denotes the direction the telescope is pointing to, not the position of the source being observed. \item Image parameters :\\ The standard definition of the image parameters is assumed. See for example \cite{hillas85,fegan96,reynolds93}. We should also make use of additional parameters like asymmetry parameters, number of islands or mountains etc. \end{itemize} Quantities which are not directly measurable, but which can be estimated from the image parameters are : \begin{itemize} \item Impact parameter :\\ The impact parameter $p$ is defined as the vertical distance of the telescope from the shower axis. \item The energy of the shower \end{itemize} \subsubsection{Differential gamma flux and collection area for a point source} The differential gamma flux from a point sourse $s$ is given by The differential gamma flux from a point source $s$ is given by \begin{eqnarray} where $dN^{\gamma}_s$ is the number of gammas from the source $s$ in the bin $dE,\;dF,\;dt$ of energy, area and time respectively. We denote the probability for reconstructing a gamma shower with energy denote the probability for 'observing' a gamma shower with energy $E$, zenith angle $\Theta$ and position $F$ in a plane perpendicular to the source direction by $R^{\gamma}(E,\Theta,F)$. The effective collection area is defined as to the source direction by $R^{\gamma}(E,\Theta,F)$. Depending on the special study, the term 'observing' may mean triggering, reconstructing, etc. The effective collection area is defined as \begin{eqnarray} \end{eqnarray} A side remark : The well known behaviour that the effective collection area (well above the threshold energy) is larger for larger zenith angles $\Theta$, is due to the fact that at higher $\Theta$ the distance of the shower maximum (where the majority of Cherenkov photons is emitted) from the detector is larger than at smaller $\Theta$. The area in which $R^{\gamma}(E,\Theta,F)$ contributes significantly to the integral (\ref{eq:form-1}) is therefore larger, resulting in a larger $F^{\gamma}_{eff}(E,\Theta)$. For the simulation this means, that the maximum impact parameter should be chosen larger for larger $\Theta$. The number of $\gamma$ showers observed in the bin $\Delta \Theta$ of \int_{\Delta E}{} \Phi^{\gamma}_s(E)\cdot F^{\gamma}_{eff}(E,\Theta)\cdot dE \\ \end{eqnarray} Assuming that $F^{\gamma}_{eff}(E,\Theta)$ depends only weakly on $E$ in the (sufficiently small) interval $\Delta E$ gives \begin{eqnarray} \Delta N^{\gamma,obs}_s(E,\Theta) &\approx   &\Delta T_{on}(\Theta) \cdot F^{\gamma}_{eff}(E,\Theta) \cdot \int_{\Delta E}{} which $R^{\gamma}(E,\Theta,F)$ is greater than zero were simulated. This means in particular that the MC simulation of gammas extends to sufficiently large impact parameters. extends to sufficiently large impact parameters. In reality, in order to save computer time showers will be generated up to a maximum value of the impact parameter (possibly depending on the zenith angle). An appropriate correction for that has to be applied later in the analysis. Knowing $F^{\gamma}_{eff}(E,\Theta)$, the gamma fluxes can be obtained \int_{\Delta E}{} \Phi^{h}(E)\cdot F^{h}_{eff}(E,\Theta)\cdot dE \\ \end{eqnarray} \begin{eqnarray} \Delta N^{h,obs}(E,\Theta) &\approx   &\Delta T_{on}(\Theta) \cdot F^{h}_{eff}(E,\Theta) \cdot \int_{\Delta E}{} \end{itemize} \subsection{A suggestion for an initial workplan} We propose in the following a list of tasks whose common goal it is to provide and use data files with a definition of data suitable for initial studies, e.g. trigger rates, and for subsequent further analysis in MARS, e.g. $\gamma$/h-separation. We consider this list to be minimal and a first step only. Given the amount of work that will have to be invested, the detailed assumptions below should be backed up by collaboration-wide agreement; also, some input from groups is essential, so PLEASE REACT. Event generation should be done with the following conditions: \begin{itemize} \item Signal definition: we will use the Crab, over a range of zenith angles (define!!). A minimum of 20,000 (can we get that?) triggers will be generated, starting from existing MMCS files; \item Observation mode: observations are assumed off-axis, with an offset of $\pm 0.4 \deg$ in $\Delta \beta$ along the direction of the local azimuthal angle $\phi$, switching sign every 500 events (see 'Assumptions' above); \item Adding star field: adapt starfieldadder and starresponse to the Crab. Ignore star field rotation problems for the moment, until a separate study is available (??); \item Pedestal fluctuations: all pixel values are smeared by a Gaussian centered at zero with a sigma of 1.5 photoelectrons; \item Trigger:  Padova to define (!!) the grouping of pixels, the trigger thresholds, and a method to avoid triggering on stars. We assume only a first-level trigger. \end{itemize} With this event sample available, we suggest to embark on several studies, which will help us in understanding better the MAGIC performance, and will also pave our way into future analysis. \begin{itemize} \item determine trigger rates (1st level only), as function of energy and zenith angle (also of impact parameter?); \item determine gamma acceptance, as function of energy and zenith angle (also of impact parameter?); \item determine effective collection area (gammas and hadrons), as function of energy and zenith angle (also of impact parameter?); \item show the position of the shower maximum (Xmax); \item start comparing methods for $\gamma$/h-separation, i.e. the generation of ON and OFF samples from the observations; \item start magnetic field studies ($\phi$-dependence); \item eventually, study the effect of the rotating star field. \end{itemize} \section{Analysis of the real data}