Changeset 780

Timestamp:

05/07/01 15:04:40 (24 years ago)

Author:

wittek

Message:

Corrections by Rudy and Wolfgang added, 7 May 2001

File:

• trunk/MagicDoku/strategy_mc_ana.tex (modified) (11 diffs)

trunk/MagicDoku/strategy_mc_ana.tex

@@ -14 +14 @@
 \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 +118 @@
 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 +150 @@
 
 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 +179 @@
 
 \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 +205 @@
 \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 +213 @@
 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 +226 @@
 \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 +246 @@
  \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 +361 @@
 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 +418 @@
  \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 +881 @@
 \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}