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- Low energy index: 1.45
- Cutoff energy: 4.87 GeV
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The slope of the exponential as a function of energy is then: |
Γ Γ(E) = 1.45+E/4.87GeV. At the middle of the highest energy band this is |
Γ Γ(31.6GeV)=7.94. A power law with this slope and integral flux given above has a flux constant at the middle of the energy band of N_0_=1.25e-09*(7.94-1)/31.6/ |
(194194)94^\]=9.35e-14 ph/cm^2/s/GeV, i.e. |
- dN/dE = 9.35e-14 (E/31.6GeV)-7.94 ph/cm^2/s/GeV
This power law is depicted on my plot as a red power law covering the range 10-100 GeV (the PL fits from the other bands are also shown). Numerically integrating the red PL function also gives 1.25e-09. Calculating E^2dN/dE at the mid point gives 31.6^2*9.3e-14 = 9.3e-11 GeV/cm^2/s = 1.5 erg/cm^2/s, in agreement with the point depicted on the my plot.
This discrepancy occurs is present between Jean's and my plots for all the PLEXP models, for points above the cutoff energy. Flux points for sources with power-law spectra look to agree. I have not studied the LOGP models in much detail. Further examples of PLEXP sources with significant highest energy points (i.e. not an upper limit) are shown below.
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