Algorithm

XMM-Newton Science Analysis System

epicspeccombine (epicspeccombine-0.6) [xmmsas_20230412_1735-21.0.0]

Algorithm

The input files are combined such that the output files contain:

Source Spectrum: the sum of the counts in all of the input source spectra.
Background Spectrum: the sum of the counts in all of the background spectra.
Exposure time: the exposure time is set to the mean of the sum of the exposure times for each instrument. i.e. exposure time is added for spectra of a given instrument and then averaged over the instruments.
the response matrix contains the sum of the exposure-weighted average of the individual responses. e.g. if each instrument has the same total exposure time then the output effective area will be the sum of the individual instrument effective areas.
the backscale value is the sum of the exposure-weighted averages of the individual instrument BACKSCAL values.
Background Spectrum: the sum of the counts in all of the input background spectra.

Mathematically this is given by:

$\begin{code} \par$ S = \sum_{i}{S_{i}} $ \par$Exposure = \sum_{i}{exp_{i}} / num... ..._{i} \times exp_{i}} / \sum_{i}{exp_{i}}$ \par$ B = \sum_{i}{B_{i}} $ \end{code}$

where i is the instrument, o is the observation, $S_{i}$ are the source counts in each spectrum (i), $R_{i}$ are the response elements for each spectrum (i), $BACKSCAL_{i}$ are the backscale values for each spectrum, $number\_of\_insts$ is the number of independent cameras contained in the source spectra and $exp_{i}$ is the exposure time of each spectrum. $B_{i}$ are the background counts in each background spectrum (i),

XMM-Newton SOC -- 2023-04-16