Version 14 (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.