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CHAPTER 2: AGN SURVEYS WITH XMM-Newton
2.1.3 X-ray properties of the sources
We have fitted the count rates of the sources in several bands to those expected
from a power-law spectrum in order to study their spectral characteristics. The
model has a slope Γ and Galactic Hydrogen column density N H obtained from
21 cm radio measurements ([55], see Table 2.1). Obviously not all the sources
have their spectrum well represented by a power law (for instance, stars and
galaxy clusters show thermal spectra) but for the purpose of calculating fluxes
in the same bands as those in which the fit is performed this is an accurate and
simple model.
We have calculated the expected count rates for different values of Γ ranging
from -10 to 10 in steps of 0.5, linearly interpolating for intermediate values,
using LSIF1;1A
([7]) with the on-axis redistribution matrix files and effective areas
for each field generated by the SAS TJUV§;7W task . The count rates obtained from
are already corrected from vignetting, so the effective areas were
generated disabling the vignetting and PSF corrections in TJ0UV§;7W .
;D=2?§;2@B;BAD@
The fluxes obtained for bands 2 to 5 (in the case of band 5 the flux was calculated
in the range 7.5-10 keV) were also calculated for the same Γ values but
setting N H to zero, i.e. they were calculated ’before the atmosphere’. We have
also checked that the chosen step size in Γ does not significatively affect the
calculations by repeating the spectral fits in a single field with a step of 0.001,
finding that the differences in the slopes were smaller than the uncertainties.
Spectral fits were performed in bands 2 and 3 for the soft and XID fluxes, and
in bands 3, 4 and 5 for the hard and ultrahard fluxes. The average count rates
of our sources in the XID and hard bands were 0.0095 and 0.0032, respectively,
which give (for a typical exposure time of 15 ks) an average of more than 10
counts per bin thus ensuring the validity of Gaussian statistics. The best fit
Γ and flux were calculated by minimising the χ 2 between the observed and
expected count rates. The minimisation was done in Γ, setting the flux from the
normalisation that minimised the χ 2 in the corresponding band. 1-σ error bars
for Γ and flux were obtained from the values which produced ∆χ 2 = 1 from the
minimum. In most cases these error bars were assymetric but we have used a
symetric error bar obtained from the average of the upper and lower error bars
for the weighted Γ and the source counts study (see section 3). In some cases the
fitted slopes are very steep (|Γ| ∼ 10): this corresponds to sources with positive
count rates in only one of the fitted bands, which forces the power law to the
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