Version 7 (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: $\phi(E) = \frac{1}{A_0\cdot \Delta T}\frac{dN}{d\epsilon(E)\cdot dE}$