XMM-Newton Science Analysis System


evigweight (evigweight-1.8) [xmmsas_20230412_1735-21.0.0]

Definitions

The spectroscopic model of the source gives $s_{\alpha,\delta}(E)$, the number of photons received per cm$^{2}$ and per second at the earth, from sky position $\alpha,\delta$ and at energy $E$ (differential per solid angle and energy).

The number of photons, $m_{detx,dety}(I)$, detected (per second) in pixel $detx,dety$ and in PI energy bin $I$ centered at $E_I$ is obtained by multiplying by the effective area and applying the response matrix:

  $$m_{detx,dety}(I) \; = \; \int_e \: R_{detx,dety}(e,I) \: A_{detx,dety}(e) \: s_{\alpha,\delta}(e) \: \mathrm d e \: \Delta \Omega$$ (1)

$A_{detx,dety}(E)$ is the effective area at position $detx,dety$ for energy $E$ and includes all instrumental effects (telescope, RGA, filter, detector). $R_{detx,dety}(E,I)$ is the redistribution of photons of energy $E$ at position $detx,dety$ into PI bin $I$. The correspondence between sky position and detector coordinates depends on the telescope's pointing. In theory this correspondence is not direct, but via a convolution with the Point Spread Function. This complication is ignored here (see Sect.3.7).