Index: trunk/MagicDoku/strategy_mc_ana.tex =================================================================== --- trunk/MagicDoku/strategy_mc_ana.tex (revision 779) +++ trunk/MagicDoku/strategy_mc_ana.tex (revision 780) @@ -14,5 +14,5 @@ \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}} @@ -118,6 +118,13 @@ 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 :\\ @@ -143,5 +150,7 @@ 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 @@ -170,20 +179,24 @@ \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} @@ -192,5 +205,5 @@ \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} @@ -200,8 +213,11 @@ 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} @@ -210,4 +226,13 @@ \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 @@ -221,4 +246,11 @@ \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}{} @@ -329,5 +361,9 @@ 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 @@ -382,4 +418,8 @@ \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}{} @@ -841,4 +881,53 @@ \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}