wiki:DatabaseBasedAnalysis/Spectrum

Version 15 (modified by tbretz, 10 months ago) (diff)

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Spectrum Analysis

The differential flux \(\phi(E)\) per area, time and energy interval is defined as \[\phi(E) = \frac{dN}{dA\cdot dt\cdot dE}\]

Often \(\phi(E)\) is also referred to as \(\frac{dN}{dE}\) as observation time and effective collection area is a constant. The effective area is then defined as \(A_\textrm{eff}(E)=\epsilon(E)\cdot A_0\). Note that at large distances the efficiency vanishes, so that the effective area is an (energy dependent) constant while \(A_0\) and the efficiency \(\epsilon(E)\) are mutually dependent.

For an observation with an effective observation time \(\Delta T\), this yields: \[\phi(E) = \frac{1}{A_0\cdot \Delta T}\frac{dN}{d\epsilon(E)\cdot dE}\]

The total area \(A_0\) and the corresponding efficiency \(\epsilon(E)\) are of course only available for simulated data. For simulated data, \(A_0\) is the production area and \(\epsilon(E)\) the corresponding energy dependent efficiency of the analysis chain. For a given energy bin, the efficiency is then defined as

\[\epsilon(E) = \frac{N_\textrm{exc}(E)}{N_0(E)} \]

where \(N_0\) is the number of simulated events in this energy bin and \(N=N_{exc}\) the number of *excess* events that are produced by the analysis chain.

The number of excess events, for data and simulations, is defined as

\[N_\textrm{exc} = N_\textrm{sig} - N_\textrm{bg}\]

where \(N_\textrm{sig}\) is the number of events identified as potential gammas from the source direction ('on-source') and \(N_\textrm{bg}\) the number of gamma-like events measured 'off-source'. Note that for Simulations, \(N_\textrm{bg}\) is not necessarily zero for wobble-mode observations as an event can survive the analysis for on- and off-events, if this is not protected by the analysis chain.

Define Binnings

Get Data File List

Get Observation Time

Get Monte Carlo File List

Get Zenith Angle Histogram

Analyze Data

Analyze Monte Carlo Data

Summarize Corsika Production

Result (Spectrum)

Result (Threshold)

Result (Migration)