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CHAPTER 3: SOURCE COUNTS OF THE AXIS SOURCES
Table 3.2 Maximum likelihood fit results to the log N − log S in the Soft band for two
HR selected subsamples. The first column is the band used, the second is the powerlaw
slope above the flux break, the third is the slope below that break, the fourth is the
flux break, the fifth is the normalisation, and the sixth column indicate the number of
sources from each sample used in the fit.
N used /N tot
Band Γ u Γ d S b K AXIS
(10 −14 cg s) (deg −2 )
Soft HR < −0.2 2.33 +0.04
−0.04
1.69 +0.03
−0.04
1.40 +0.20
−0.10
88.7 +5.9
−7.9
1058/1058
Soft HR > −0.2 2.77 +0.07
−0.06
- 1.00 16.9 +0.05
−0.06
209/209
section 3.2.1), it produced gaps in those flux bins which have been depleted of
sources after the splitting of the sample. Since it is extremely difficult to deal
with this problem when the area varies rapidly with the flux (see Fig. 3.1), we
decided to use as a first approximation the Soft Ω(S) for both subsamples. A
similar approach has been used in [125] where they use the corresponding area
curve for each energy band under study.
It can be seen in Fig. 3.6 that the source counts of Soft sources with HR < −0.2
clearly still follows a broken power law model, while for the HR > −0.2 sources
it is a simple power law. The best fit parameters are listed in table 3.2. Those
for the softest sources (HR < −0.2) are fully compatible, well within the 1-σ
errors, with the best fit parameters obtained for the Soft AXIS-only sample (see
table 3.1). This is reasonable, since the AXIS Soft sources with HR < −0.2 are
over 83% of the total Soft sample. However, the Soft HR > −0.2 subsample
best fit parameters are more similar to those obtained for the hard AXIS-only
sample.
In [125] they found similar results using a discriminating value of HR = 0 for
all energy bands in the Chandra Multiwavelength Project (ChaMP). They demostrated
that the missing break is not due to small number statistics, since
the HR < 0 sources largely outnumbered the HR > 0 sources, by performing
simulations in randomly selected subsets of the HR < 0 sample with the same
number of sources as the HR > 0 subsample. They calculated the log N − log S
for these subsets finding that, in spite of the reduced statistics, they all showed
a detectable break. A possible explanation for this behavior is that spectrally
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