Changes between Version 251 and Version 252 of DatabaseBasedAnalysis/Spectrum


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Timestamp:
12/10/19 14:26:28 (5 years ago)
Author:
tbretz
Comment:

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  • DatabaseBasedAnalysis/Spectrum

    v251 v252  
    1717For simplicity, in the following, \(\Delta E\) will be replaced by just \(E\) but always refers to to a given energy interval. If data is binned in a histogram, the relation between the x-value for the bin \(E_\textrm{x}\) and the corresponding interval \(\Delta E_\textrm{x}\) is not well defined. Resonable definitions are the bin center (usually in logarithmic bins) or the average energy.
    1818
    19 === Efficiency and eff. Area ===
     19=== Efficiency ===
    2020
    2121The 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
    … …  
    2424
    2525where \(N_0\) 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.
    26 
    27 The effective collection area is then defined as \(A_\textrm{eff}(E) = A_0\cdot\epsilon(E)\). The result is idependent of the simulated area as long as the simulated area is large enough. In this case, the efficiency degrades inversely proportional to the increase of the area.
    2826
    2927Note that the exact calculation of the efficiency \(\epsilon(\Delta E)\) depends on prior knowledge of the correct source spectrum \(N_0(E)\). Therefore, it is strictly speaking only correct if the simulated spectrum and the real spectrum are identical. As the real spectrum is unknown, special care has to be taken of the systematic introduced by the assumption of \(N_0(E)\).