**XMM-Newton Science Analysis System
**

evigweight (evigweight-1.8) [xmmsas_20211130_0941-20.0.0]

##

Spectral analysis

One can then define (via evselect
called with withzcolumn=Y
withzerrorcolumn=N)
a `corrected' spectrum within region
(usually in sky coordinates)
and its associated error :

where
is the exposure time for the CCD/node where
the event was detected and the width of bin .
If the region extends over a single CCD, the exposure time may
be taken out of the sums.
is an estimate of the spectrum one would get if the detector was flat.
In terms of the usual `uncorrected' spectrum:

where the
denote the average over the photons in
bin .
The corresponding source spectrum is also obtained by summing
over the region, and the model spectrum (to be compared to the data)
by multiplying with the central effective area
and applying the response matrix.

Of course the response matrix should be taken (via rmfgen)
in the true detector region (not at the center) associated
with the sky region .
The central effective area may be obtained by calling arfgen
with special settings:
arfgen arfset=your_arf spectrumset=your_spectrum withbadpixcorr=N modelee=N \
withdetbounds=Y filterdss=N detmaptype=flat detxbins=1 detybins=1 \
withsourcepos=Y sourcecoords=tel sourcex=0 sourcey=0

Model fitting may be performed via XSPEC, entering as RATE,
and as STAT_ERR, with
and in the Ancillary Response File and
Redistribution Matrix File, respectively.

Note that the weighting procedure is incompatible with using the Poisson
model (C-statistic) in XSPEC (the formula must be used).
This means that care must be taken to have enough counts per spectral bin.

XMM-Newton SOC -- 2021-11-30