Changes between Version 252 and Version 253 of DatabaseBasedAnalysis/Spectrum

Timestamp:

12/10/19 14:27:35 (5 years ago)

Author:

tbretz

Comment:

--

DatabaseBasedAnalysis/Spectrum

@@ -10 +10 @@
 \[\phi(E) = \frac{dN}{dA\cdot dt\cdot dE}\]
 
-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 \(R_0\) the efficiency \(\epsilon(R_0)\) vanishes, so that the effective area is an (energy dependent) constant while \(A_0=\pi R_0^2\) and the efficiency \(\epsilon(E)\) are mutually dependent.
+Often \(\phi(E)\) is also referred to as \(\frac{dN}{dE}\) as observation time and effective collection area is a constant.
 
 For an observation with an effective observation time \(\Delta T=\sum\delta t_i\), this yields in a given Energy interval \(\Delta E\):
@@ -26 +26 @@
 
 Note 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 \(N_0(E)\).
+
+=== Effective Collection Area ===
+
+The effective area is then defined as \(A_\textrm{eff}(E)=\epsilon(E)\cdot A_0\). Note that at large distances \(R_0\) the efficiency \(\epsilon(R_0)\) vanishes, so that the effective area is an (energy dependent) constant while \(A_0=\pi R_0^2\) and the efficiency \(\epsilon(E)\) are mutually dependent.
 
 === Excess and Error ===