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A statistical evaluation of the EPIC flux
calibration
XMM­SOC­CAL­TN­0023
Version 2.0
R. D. Saxton
April 4 2003
Abstract
The 1XMM catalogue of XMM­Newton sources provides an important dataset for investi­
gating the performance of the EPIC instrumentation. We have used the catalogue to perform
a detailed comparison of the recorded flux in each camera and have investigated the fidelity
of the instrumental calibration. The two MOS cameras agree remarkably well implying that
the on­axis cross­calibration of these cameras is good to within 4%. The dispersion of the
on­axis flux distribution is tight and consistent with residual small calibration uncertainties.
Off­axis the distribution is broader illustrating the importance of a correct modelling of the
chip­to­chip variation in the MOS point spread function. The EPIC­pn camera agrees with
the MOS cameras at low energies but records 5­10% less flux above 2 keV. This may be partly
explained by the simplified encircled energy correction used in the catalogue construction
but implies the presence of a residual calibration error, possibly related to the MOS quantum
efficiency or the throughput of the gratings. The dispersion of the on­axis MOS/PN flux
distribution is wider than expected and not understood. Off­axis the discrepancy between
the MOS and EPIC­pn fluxes increases although the dispersion is similar.
1 Introduction
The objective of this paper is to assess the relative calibration of the EPIC instrumen­
tation by using a large sample of sources jointly observed by the MOS and PN cameras.
This second version of the document is based on sources from the XMM catalogue [1]
which has been constructed using the pipeline processing system (PPS), SAS version
xmmsas 20020507 1701, run at the Science Survey Centre (SSC; [2]). The catalogue con­
tains the position and parameters of about 30,000 sources and represents a rich resource
for the XMM­Newton project. It samples a wide range of observational parameters and
may be used for investigating instrumental effects such as detector quantum efficiency,
the point spread function, the vignetting function and telescope astrometry as well as
having a fundamental astronomical value.
Where sources have been detected in more than one camera, their observed fluxes have
been compared to identify any systematic differences in the camera calibrations.
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2 Sample selection
The large number of sources available in the catalogue has allowed tighter constraints
to be used when selecting sources compared to the previous version of this study. The
relative flux difference between the EPIC cameras has been calculated from the following
source subset:
ffl All catalogue sources have been manually screened to identify spurious detections,
sources contaminated by extended emission and sources lying near to the edge of
the field­of­view or to a CCD boundary. Sources meeting any of these conditions
have been excluded from the sample.
ffl Sources at an off­axis angle greater than 5 arcminutes in the MOS cameras have
been excluded
ffl Sources with ! 250 counts in the MOS­1 observation have been excluded (see below)
ffl The catalogue is constructed from FullFrame,ExtendedFullFrame and LargeWindow
EPIC­pn observations. EPIC­pn SmallWindow observations are hence implicitly
excluded from this comparison. All the major MOS imaging modes are included in
the catalogue.
ffl The majority of the catalogued sources have been observed prior to revolution 300.
2.1 Source counts
The creation of a sample from catalogued sources means that at the low flux end the data
will contain sources which have been artificially boosted by a statistical fluctuation ­ the
Eddington effect. Simulations have been run to quantify this effect on low significance
sources in the catalogue and the relationship between recovered and input counts is shown
in Figure 1. There is a constant offset between the ratio of recovered to input counts due
to a known problem with the PSF used in the simulations (I.M.Stewart, p.comm.) but
it can be seen that the ratio tends to this offset for an input of about 250 counts. Fluxes
calculated from a smaller number of counts than this will be biased upwards. This effect
will result in a broadening of the flux comparison between the MOS detectors for low­
count sources but will cause an artificial excess for the MOS compared to the pn because of
the extra effective area and hence higher number of counts seen by the EPIC­pn detector.
Therefore a limit of 250 source counts in the MOS cameras has been set to remove this
bias.
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10 20 50 100 200 500 1000 2000 5000
0.5
1
1.5
SCTS (counts)
RATE/SIM_RATE
M1 recovered count rate.
Figure 1: The ratio of detected to input counts from simulations involving the EPIC source parameterisation
chain.
3 Method of flux determination
The flux (in units of ergs cm \Gamma2 s \Gamma1 ) of a given source in a given energy band is given by
Flux = counts / exposure—time / energy—conversion—factor (i)
Counts are calculated by extracting the number of events from a circle around the source,
subtracting the background and correcting for the fraction of the PSF outside the source
circle (the encircled energy fraction or EEF).
counts = (source—cnts—in—circle ­ background) / EEF (ii)
The source is centroided and counts extracted from a circle of radius 18--28 arcseconds,
dependent on source strength and off­axis angle.
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Table 1: Relative encircled energy factor for an on­axis source extracted from a circle
of 20 arcsec radius.
Camera Energy
1.0 keV 7.0 keV
MOS­1 1.0 1.0
MOS­2 1.032 0.996
PN 1.046 1.057
3.1 Background subtraction
The background has been calculated for each catalogue field by removing all the detected
sources and fitting a spline surface to the remaining image. This technique can introduce
errors, especially when strong sources are present in the field.
3.2 The encircled energy fraction
The pipeline code uses a single model to represent the PSF of all three cameras. This
is a reasonable approximation as the three telescopes are of very similar construction.
In practise small differences will be present and are visible in parameterisations of the
in­orbit PSF [3,4]. The relative EEF of the telescopes, predicted by these studies for an
on­axis source, extracted with the mean radius used in the catalogue of 20 arcseconds is
shown in Table 1. It is known that the King function, used in the PSF parameterisations,
underpredicts the core of the real PSF and hence introduces an error in the EEF of small
circles (or annuli). This effect, presumably different for each telescope, has not been
quantified and so the values in Table 1 should only be used as a guideline.
3.3 The exposure time
This is calculated at the source centre from an exposure map which is derived from the
sum of the frame times multiplied by the fractional exposure time, modulated by the
spectrally dependent vignetting.
A correction for the dead­time due to the chip readouts which cause the out­of­time (OOT)
event stripes has been applied to the exposure time by the source detection software.
3.4 Vignetting
Recent studies have shown that the optical­axis is not centred around a detector coordi­
nate of DETX=0, DETY=0 as was previously supposed [5]. The best measurement of the
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Table 2: The optical­axis positions used for recalculating the vignetting correction
Camera DET­X DET­Y
MOS­1 60 ­230
MOS­2 400 ­1350
PN 1250 280
Table 3: Percentage variation in PN v MOS flux ratio with spectral shape
Nh a Index Flux difference per band (%) b
1 (0.2­0.5 keV) 2 (0.5­2 keV) 3 (2.0­4.5 keV) 4 (4.5­7.5 keV) 5 (7.5­12.0 keV)
3 1.7 0.0 0.0 0.0 0.0 0.0
0 2.45 5.8 8.3 2.0 ­2.6 ­1.5
0 1.15 3.1 ­2.3 ­0.6 1.3 1.7
9.8 1.15 0.5 ­5.0 ­0.3 1.2 0.8
9.8 2.45 ­3.3 2.4 1.5 ­1.9 ­1.4
a Absorption column, 10 20 cm \Gamma2 .
b Fluxes calculated using the Thin filter matrices.
real optical­axis positions (Table 2) have been used to recalculate the vignetting function
and consequently the exposure time and source flux.
3.5 ECF
The energy conversion factors (ECF) have been reworked during this analysis (see SSC­
LUX­TN­0059, issue 3.0 for the new values). They have been calculated assuming, what
we expect to be, an average spectrum of an absorbed power law of slope \Gamma = 1:7 and
N h = 3:0 \Theta 10 20 cm \Gamma2 . A deviation of source spectra from this average will affect the ECFs
and modify the relative flux seen between the cameras. To quantify this effect we have
performed a fit of an absorbed power­law on the band 2 (0.5--2 keV) spectra of 1900 PN
sources detected over the field of view. The mean spectral slope is \Gamma = 1:80 \Sigma 0:65 (Fig.
2) and the limits on the absorption column which contain 1 sigma (68.3%) of the sources
are NH = 0 \Gamma 9:8 \Theta 10 20 cm \Gamma2 (Fig. 3). The effect of this dispersion in the source spectra
on relative flux estimates is given in Table 3 . It can be seen that the effect is small except
in band 2, where an apparent excess of a few percent will be seen in the MOS cameras
for a source spectrum flatter than the average and an excess in the PN camera will be
seen if the spectrum is steeper, and band 1 where a smaller NH will give an apparent
increase in MOS flux. This can be understood from the shape of the effective area curves
for MOS and PN (Fig. 4) which are reasonably parallel above 1.5 keV but diverge at
lower energies.
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Figure 2: A histogram of spectral slopes derived from an absorbed powel­law model fit to EPIC­pn spectra.
Figure 3: The distribution of nH derived from an absorbed powel­law model fit to EPIC­pn spectra.
6

Figure 4: The effective area of the EPIC MOS and PN cameras with the Medium filter
These factors have been calculated using the on­axis redistribution matrices, m11 im all 2002­
04­18.rmf, m21 im all 2001­04­18.rmf and epn ff20 sdY9.rmf in conjunction with effec­
tive area files produced by arfgen using the quantum efficiency files,
EMOS1 QUANTUMEF 0014.CCF, EMOS2 QUANTUMEF 0014.CCF
and EPN QUANTUMEF 0012.CCF. This form of calculating the ECFs makes the fol­
lowing implicit assumptions.
ffl The filter transmission is spatially invariant over the field
ffl The quantum efficiency of the detectors is spatially invariant
ffl Source counts are taken with event patterns 0­12 for the MOS and 0­4 for the PN
(bands 2--5) and pattern 0 for PN band 1.
Pipeline images were actually created using event patterns 0--25 for MOS. The count rates
extracted in the pipeline analysis therefore include patterns which are excluded in the ECF
calculation. The effect of these extra events on the MOS ECFs is energy­dependent and
is given as a set of percentages in Table 4. In this study, the extra patterns have been
corrected for by increasing the ECFs and hence decreasing the EPIC fluxes by the factors
in Table 4.
3.6 Outliers
Many sources exhibiting large flux differences between the cameras were evident in Version
1 of this study. From Figures 5 & 6 it can be seen that the situation is much improved in
this version; this is principally due to the manual flagging present in the catalogue which
allows suspect sources to be excluded from the sample. It should also be noted that
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Table 4: The flux contribution of MOS pattern 13--25 events
Band Correction percentage
MOS
1 0.0
2 0.0
3 0.1
4 2.3
5 2.8
some problem fields, e.g. 0257/0112670601, which gave multiple sources with large flux
differences in the previous study, were excluded from the construction of the catalogue.
The major effect of the flagging has been to identify sources which lie close to CCD gaps,
the edge of the field­of­view and bad pixels/columns.
Figure 5: Observed flux in the EPIC MOS cameras
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Figure 6: Observed flux in the EPIC PN and MOS­1 cameras
4 Results and Discussion
4.1 Mean offsets
A comparison of fluxes using the clean sample of sources described in section 2 is shown in
Table 5. The MOS cameras are well calibrated with each other on­axis although MOS­1
records a small excess of flux at higher energies.
The MOS­PN on­axis comparison is good for the two low­energy bands. At energies
above 2 keV the two MOS cameras predict 5--10% more flux than EPIC­pn. This was
seen in the previous study where the MOS excess was ascribed to errors in the quantum
efficiency (QE) of one or all the cameras. The QE has been reexamined and modified for
each camera [6,7] recently but clearly has not resolved the discrepancy. The vignetting
function has also received considerable attention since the last study and the optical­axis
shifts ,applied here, should remove this as a source of possible error. Catalogue fluxes have
been produced using the encircled energy fraction calculated from the MEDIUM mode
PSF, which is identical for each camera. The effects of this simplification were discussed in
section 3.2 and estimated in Table 1. If taken at face value these discrepancies introduce
an offset of ¸ 3 \Gamma 6% in the EPIC­pn fluxes which will significantly improve the comparison
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Table 5: The mean on­axis flux differences in the EPIC cameras.
Band Energy Mean flux difference (%) a
(keV) (M1­M2)/M1 (M1­PN)/PN (M2­PN)/PN
1 0.2--0.5 \Gamma1:4 \Sigma 0:5 2:6 \Sigma 0:7 4:4 \Sigma 0:7
2 0.5--2.0 \Gamma1:6 \Sigma 0:4 0:6 \Sigma 0:7 3:0 \Sigma 0:7
3 2.0--4.5 1:8 \Sigma 0:4 8:8 \Sigma 0:6 7:6 \Sigma 0:6
4 4.5--7.5 3:2 \Sigma 0:6 7:9 \Sigma 0:8 5:3 \Sigma 0:8
5 7.5--12.0 3:0 \Sigma 1:2 10:9 \Sigma 1:5 8:9 \Sigma 1:5
a The percentage flux difference between the cameras using the source sample described in section 2.
Errors quoted are 90% for 1 free parameter.
Table 6: The mean flux differences for band 2 for different source populations.
cnts offax Mean flux difference (%)
in MOS (arcmin) (M1­M2)/M1 (M1­PN)/PN (M2­PN)/PN
50--250 0--5 1:0 \Sigma 0:9 4:9 \Sigma 0:6 7:1 \Sigma 0:7
50--250 5--12 4:3 \Sigma 0:5 7:5 \Sigma 0:4 7:2 \Sigma 0:4
250--10000 0--5 \Gamma1:6 \Sigma 0:4 0:6 \Sigma 0:7 3:0 \Sigma 0:7
250--10000 5--12 2:7 \Sigma 0:5 6:1 \Sigma 0:5 4:8 \Sigma 0:6
with the MOS. Application of these values would, however, give a ¸ 4% excess of MOS­2
over MOS­1 in bands 1 and 2.
The effects of using fainter sources for the flux comparison has been investigated for band
2 (Table 6). This shows a widening of the discrepancy between the MOS and PN cameras
in agreement with the effect of low­counts on measured fluxes discussed in section 2.1.
A sample of sources at off­axis angles of 5--12 arcminutes (i.e. excluding the central chip
of the MOS cameras) has been analysed. The band 2, MOS/PN difference for this sample
is ¸ 6%.
4.2 Dispersion
In this study we have access to a sufficient number of sources to investigate the dispersion
of the flux differences. This number reflects the total systematic error involved with the
measurement of each camera flux which in turn allows a comparison to be made between
the estimated systematics for each calibration quantity [8] and the actual performance of
the system.
It can be seen immediately from Figs. 7 & 8 that the MOS­PN distribution is significantly
broader than that of the two MOS cameras. As shown in section 3.5 the distributions of
bands 1 and 2 are influenced by spectral shape and so we have selected band 3 fluxes, to
investigate instrumental uncertainties. The total percentage error may be obtained from
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Table 7: The dispersion of the band­3 flux difference distribution
Selection M1/M2 M1/PN M2/PN
cnts offax a sigma b syserr c sigma syserr sigma syserr
250--10000 0--5 1:32 \Sigma 0:08 2:7 \Sigma 0:2 1:94 \Sigma 0:20 4:9 \Sigma 0:2 1:79 \Sigma 0:16 5:0 \Sigma 0:2
250--10000 5--12 1:51 \Sigma 0:17 7:3 \Sigma 0:5 0:88 \Sigma 0:16 0:0 \Sigma 1:9 1:28 \Sigma 0:17 5:2 \Sigma 0:9
50--250 0--5 1:29 \Sigma 0:06 10:3 \Sigma 0:7 1:15 \Sigma 0:05 7:2 \Sigma 0:8 1:33 \Sigma 0:07 11:4 \Sigma 0:7
50--250 5--12 1:37 \Sigma 0:06 13:7 \Sigma 0:6 1:23 \Sigma 0:06 9:5 \Sigma 0:8 1:28 \Sigma 0:06 10:7 \Sigma 0:7
a Off­axis angle range (arcminutes).
b The width of the flux difference distribution in units of the statistical error.
c The systematic error calculated from the width of the flux difference distribution (%).
Table 8: Estimated systematic errors in calibration quantities
Effect MOS­1 MOS­2 PN
On­axis Off­axis On­axis Off­axis On­axis Off­axis
PSF a 1 4 1 4 1 2
Vignetting b 1 1.5 1 1.5 1 1.5
Spectrum [band 2] 0 0 0 0 7 7
Spectrum [band 3] 0 0 0 0 1.5 1.5
a The spread in flux due to the uncertainties introduced by the MEDIUM mode PSF encircled energy
correction used in the pipeline. The values for the MOS off­axis reflect the individual placement of each
CCD which results in an azimuthal variation not reflected in the calibration.
b The spread in flux caused by the residual uncertainty of 10 arcseconds in the position of the optical
axes.
Figures 7 & 8 and the systematic error of the combined measurement derived by subtract­
ing the statistical error of each flux pair (Table 7). The dispersion of the MOS­1/MOS­2
stronger near­on­axis sources is ¸ 2% and is consistent with residual uncertainties in the
vignetting and PSF functions (see Table 8). A larger systematic error is evident for fainter
sources which is associated with the effect of low­counts as discussed in section 2.1 and
also by errors introduced in the processing, such as the background subtraction (see sec­
tion 3.1) which will gain in importance at low fluxes. The off­axis systematic error rises
to ¸ 6% for the stronger detections; which can be explained by an uncertainty introduced
in the off­axis PSF of the MOS cameras. As noted in section 3.2 the same PSF is used for
all three cameras and is only dependent on off­axis angle and photon energy. The MOS
CCDs have been placed in three layers to follow the focal surface which means that the
PSF of the outer CCDs is azimuthally dependent [9] . This introduces a ¸ \Sigma4% error in
the encircled energy fraction contained in a 20 arcsecond circle.
The derived MOS/PN systematic errors are larger (¸ 5%) with apparently little de­
pendence on off­axis angle. Off­axis this is consistent with the expected instrumental
systematics, again principally due to the off­axis PSF of the MOS cameras. It is not clear
why the on­axis dispersion should be so broad; this result implies an unknown random
element of magnitude 3--4% in the MOS/PN flux ratio.
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Figure 7: Percentage flux difference in the EPIC MOS cameras [(Mos­2 ­ Mos­1) / Mos­1]
Figure 8: Percentage flux difference in the EPIC MOS­1 and PN cameras [(PN ­ Mos­1) / Mos­1]
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5 Conclusions
The MOS cameras appear to be well calibrated with respect to each other except for a
small excess in MOS­1 at high energies. The dispersion of the flux ratio distribution is
small and consistent with expected instrumental systematics on axis. Off­axis the disper­
sion is broader but can be reasonably interpreted as errors introduced by an azimuthal
variation in the MOS PSF which is not currently modelled.
Both MOS cameras show a significant excess of flux compared with EPIC­pn above 2
keV. This may be partly due to the simplified PSF used in the calculation of catalogue
fluxes and partly due to an unknown element, possibly the MOS QE or the grating
obscuration factor. Off­axis, the flux difference between the cameras is greater. The
dispersion of the MOS/PN distribution is broader than that of the two MOS cameras;
off­axis it is compatible with the expected instrumental uncertainties but there appears
to be an unknown element of 3 \Gamma 4% which is affecting the on­axis dispersion.
5.1 Pipeline, catalogue and calibration issues
This study has exposed the following issues with the calculation of source fluxes by the
pipeline.
ffl The current erroneous positioning of the optical­axes strongly affects measured
source flux, particularly off­axis and should be corrected.
ffl The PSF measured from in­orbit data should be used to calculate the encircled
energy fraction.
ffl A greater effort needs to be spent on quantifying the off­axis EPIC PSF, particularly
the azimuthal, chip­to­chip, variations present in the MOS detector.
ffl Fluxes calculated from low numbers of source counts are biased due to selection
effects.
Acknowledgements. This survey has been made possible by the quality and consistency
of the pipeline and source searching software developed by Hermann Brunner, Jean Bal­
let, Michael Freyberg, Matthias Ehle, Dean Hinshaw, Georg Lamer and Uwe Lammers.
Thanks are also due to all the members of the SSC who have helped to produce the
1XMM catalogue in record time. Finally, I'd like to express my appreciation for the rig­
orous simulation work undertaken by Ian Stewart which has illuminated and quantified
the subtle effects of low source counts on measured flux.
References
[1] Watson, M.G., et al. 2003, Astron. Nachr., 324, 89
13

[2] Watson, M.G., et al. 2001, ''The XMM­Newton Serendipitous survey: 1. The role of
XMM­Newton Survey Science Centre'', A&A, 365, L51.
[3] Ghizzardi, S., ''In­flight calibration of the on­axis and near off­axis PSF for the Mos­1
and Mos­2 cameras'', EPIC­MCT­TN­011.
[4] Ghizzardi, S., ''In­flight calibration of the PSF for the PN camera'', EPIC­MCT­TN­
012.
[5] D. H. Lumb, A. Finoguenov, R. Saxton, B. Aschenbach, P. Gondoin,M. Kirsch, I. M.
Stewart, 2003, ''In­orbit Calibrations of XMM­Newton Telescopes'', Proc SPIE 4851 2003
in press
[6] Saxton, R., Lumb, D., ''EPIC spectral Response Distribution'', XMM­SOC­CAL­SRN­
0121.
[7] Saxton, R., ''EPIC pn quantum efficiency'', XMM­SOC­CAL­SRN­0139.
[8] Kirsch, M., ''EPIC status of calibration and data analysis'', XMM­SOC­CAL­TN­0018.
[9] Saxton, R.D., Denby, M., Griffiths, R.G., Neumann, D.M., 2003, Astron. Nachr., 324,
138.
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