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arfgen (arfgen-1.102) [xmmsas_20211130_0941-20.0.0]


A cross-region ARF

Due to the finite size of the PSF in XMM, a fraction of photons which are emitted from one part of the sky are detected at another position on the detector. This is generally not a problem for point sources but for regions of extended emission it can cause an extracted spectrum to be a mix of flux from different areas of an object. It may be possible to disentangle the true sky emission by simultaneously fitting different spectral files. In this case an ARF giving the expected contribution (effective area) of flux received in one area from a different area is needed. This can be achieved by finding the product of the usual effective area components at the position of the output area with the energy-dependent encircled-energy fraction contained in the output area due to flux from the input area.

i.e.


\begin{code}
\par
$A_{io} = F_{o} C_{o} Q_{o} \sum_{i}{I_{i}\psi_{io}V_{i}}/\sum_{i}{I_{i}}$\ \\
\par
\end{code}

where $F_{o}$ is the filter response, $C_{o}$ is the chip gap and bad pixel factor, $Q_{o}$ is the quantum efficiency, $I_{i}$ is the relative flux in a pixel $i$ of the input region, $\psi_{io}$ is the fraction of the PSF which falls in the output region from this input pixel and $V_{i}$ is the vignetting at the position of the input region pixel.

XMM-Newton SOC -- 2021-11-30