Changes between Version 50 and Version 51 of DatabaseBasedAnalysis/Spectrum


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Timestamp:
Dec 3, 2019, 7:09:02 PM (10 months ago)
Author:
tbretz
Comment:

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  • DatabaseBasedAnalysis/Spectrum

    v50 v51  
    4444As the simulated energy spectrum is independent of zenith angle, it can be expressed as
    4545
    46 \[dN_0'(E,\theta) = N_0\cdot d\eta(E)\cdot d\eta(\theta)\]
     46\[dN_0(E,\theta) = N_0\cdot d\eta(E)\cdot d\eta(\theta)\]
    4747
    4848with the differential energy spectrum \(\eta(E)\) and the zenith angle distribution \(\eta(\theta)\), for the total production range \(E_\textrm{min}\)  to \(E_\textrm{max}\) and \(\theta_\textrm{min}\) to \(\theta_\textrm{max}\)
     
    5050
    5151
    52 \[N_0' = \int_{E_\textrm{min}}^{E_\textrm{max}}\int_{\theta_\textrm{min}}^{\theta_\textrm{max}} dN_0(E,\theta) = N_0\int_{E_\textrm{min}}^{E_\textrm{max}}\int_{\theta_\textrm{min}}^{\theta_\textrm{max}}\eta(E) dE \cdot \eta(\theta) d\theta= N_0\int_{E_\textrm{min}}^{E_\textrm{max}}\eta(E) dE\cdot \int_{\theta_\textrm{min}}^{\theta_\textrm{max}}\eta(\theta) d\theta\]
     52\[N_0 = \int_{E_\textrm{min}}^{E_\textrm{max}}\int_{\theta_\textrm{min}}^{\theta_\textrm{max}} dN_0(E,\theta) = N_0\int_{E_\textrm{min}}^{E_\textrm{max}}\int_{\theta_\textrm{min}}^{\theta_\textrm{max}}\eta(E) dE \cdot \eta(\theta) d\theta= N_0\int_{E_\textrm{min}}^{E_\textrm{max}}\eta(E) dE\cdot \int_{\theta_\textrm{min}}^{\theta_\textrm{max}}\eta(\theta) d\theta\]
    5353
    5454consequently
     
    5858or
    5959
    60 \[N_0' = N_0\cdot \sum_{E_\textrm{min}}^{E_\textrm{max}}\omega_i(E) \cdot \sum_{\theta_\textrm{min}}^{\theta_\textrm{max}}\omega_i(\theta)\]
     60\[N_0 = N_0\cdot \sum_{E_\textrm{min}}^{E_\textrm{max}}\omega_i(E) \cdot \sum_{\theta_\textrm{min}}^{\theta_\textrm{max}}\omega_i(\theta)\]
    6161
    6262with