Flux distribution and angular clustering of
sources in the X-ray Universe
J. Ebrero1 and F.J. Carrera2
1
2
Instituto de Fı́sica de Cantabria (CSIC-UC), Av. Los Castros, 39005 Santander
(Spain) ecarrero@ifca.unican.es
Instituto de Fı́sica de Cantabria (CSIC-UC), Av. Los Castros, 39005 Santander
(Spain)carreraf@ifca.unican.es
Summary. AXIS (An XMM-Newton International Survey) is one of the best calibrated, extended and homogeneous sample of serendipitous X-ray sources detected
by XMM-Newton. It comprises 1433 X-ray sources in 36 high galactic latitudes observations that cover a sky area of 4.8 deg2 between 0.5 and 10 keV.
We have studied the flux distribution of these sources (log N − log S relations)
combining them with others from deeper and shallower samples. The models fitted
to these distributions reveal differences in detail between the simple models and
the data and extend the results obtained at energies above 4.5 keV by an order of
magnitude in flux. We have assessed the contribution of these sources to the cosmic
X-ray background as well, checking out that medium-deep samples like AXIS and
2XMM are essential to determine the evolution of the X emission in the Universe
at energies below 10 keV.
We have detected evidences of large-scale structures of the sources below 4.5 keV.
These results are among the most significative clustering detections found in X-rays
so far. We have not detected clustering at higher energies, although we have checked
that this absence of signal could be due to the low number of sources in this sample
above 4.5 keV.
Key words: X-ray sources; logN-logS; angular clustering; cosmic X-ray background
1 Introduction
The cosmic X-ray background (CXB hereafter) is a testimony of the accretion
power in the Universe. It has been resolved in more than a 90% into individual
sources in the 0.5-2 keV energy band, whereas at higher energies (2-10 keV)
only about a 50% of the CXB has been resolved.
Deep pencil-beam surveys [9] are able to resolve many sources although
their sky coverage is short. On the other hand, shallower surveys only resolve
bright sources but cover large sky areas. The bulk of the CXB emission occurs
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J. Ebrero and F.J. Carrera
at medium fluxes and therefore medium-depth surveys with relatively wide sky
coverage have proven essential to determine the evolution of the X emission
below 10 keV.
It is well known that Active Galactic Nuclei (AGN) are the dominant
population of objects at medium fluxes and that they tend to cluster forming large-scale structures [13],[10]. Ideally, clustering analysis would require a
samples both deep (great angular density) and wide (large effective area to
prevent espurious effects coming from isolated structures). AXIS (An XMMNewton International Survey) is close to this ideal sample [5].
AXIS consists in 1433 different sources from 36 XMM-Newton pointings
at high galactic latitudes (|b| > 20 deg) with exposure times larger than 15 ks.
Bright or extended targets have been removed from these observations. The
overall 0.5-10 keV sky coverage of the sample is 4.8 deg 2 (Fig. 1).
We have built the log N − log S relations, calculated the contribution to
the CXB, and performed an angular clustering analysis in 4 different energy
bands: 0.5-2 keV (Soft), 2-10 keV (Hard), 0.5-4.5 (XID) and 4.5-7.5 (Ultrahard). We have added to our sample data from other deeper and shallower
surveys which have allowed us to span over 4 orders of magnitude in flux.
These samples are the CDF-N and CDF-S [4], BSS and HBSS [6] and AMSS
[12]. In Table 1 is summarized the total number of sources in each sample and
the corresponding energy band in which we have used them.
Fig. 1. Sky coverage of AXIS sample
2 The log N − log S
Some previous works on X-ray source counts ([4],[11],[1]) have already shown
that the log N − log S is well approximated by a steep power law at bright
fluxes that flattens at fainter fluxes. Taking this into account, we have therefore chosen a broken power law model for our log N − log S. We have carried
out a fit using a Maximum Likelihood algorithm over the individual sources
Flux distribution and angular clustering of sources in the X-ray Universe
3
Table 1. Samples used and number of sources breakdown
Sample Soft Hard XID Ultrahard
AXIS 1267 397 1359
CDF-N 442 313
CDF-S 282 186
AMSS 606
BSS
389
HBSS
-
89
65
(without binning) in each band. As expected, our results confirm the presence of a break around 10−14 cgs in Soft, Hard and XID bands, whereas in
the Ultrahard band no such break was found and hence a simple power law
model was applied to this case. The values for the slopes are in good agreement with other works like [11], fixing the uncertainties that [1] had at faint
fluxes in the Soft band (probably due to incompleteness at those fluxes). In
the Hard band, although the overall fit results are consistent with those of
previous works, we found slight differences in detail. It might be due to recent
changes in the internal calibration of Chandra or perhaps a smoother model
is required to explain properly the superposition of different populations at
different redshifts. For further details see [5].
Fig. 2. Integral log N − log S in Soft (left) and Hard (right) bands
3 Contribution to the X-ray background
Using the best fit parameters from our log N − log S we can estimate the
contribution of our sources in different flux intervals to the total CXB intensity. Figure 3 shows the relative contribution to the total CXB intensity for
the four bands, showing that the maximum contribution comes from fluxes
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J. Ebrero and F.J. Carrera
around the break flux at ∼ 10−14 cgs. The extrapolation of the Soft and Hard
log N − log S to zero flux using our best fit model does not saturate the CXB,
which could suggest the presence of a dominant non-resolved population at
fainter fluxes, especially in the Hard band. This non-resolved component may
consist of galaxies or obscured AGNs. We have resolved up to a 87% of the
CXB in the Soft band, 85% in the Hard band, 60% in the XID band and 25%
in the Ultrahard band, respectively.
Fig. 3. Relative contribution to the total CXB intensity in each band.
4 Angular clustering
If there is cosmic structure in all or most of our fields, the sources in them
will tend to appear together projected in the sky with respect an unclustered
distribution of sources. The angular correlation function W (θ) measures the
excess of source pairs at a given angular separation θ with respect a simulated
uniform sample. The estimator we have used is the one proposed by [7]:
DD
W (θ) = f
−1
(1)
DR
where DD is the number of pairs with angular separation θ, and DR is
the number of pairs of one real and one random source at the same angular
separation. f is a normalization constant defined in [7]. The random sample
has been drawn from our own source list taking into account the variations
in sensitivity with the position in a given field. We have simulated up to 1
million sources in each energy band.
This way, we have found evidences of angular clustering in Soft and XID
bands. A F-test suggest a significance in the detection ∼ 99% in these bands.
In both cases W (θ) was fitted to a simple power law which yielded to slope
values a bit steeper than the canonical value of γ = −0.8 though consistent
Flux distribution and angular clustering of sources in the X-ray Universe
5
with the results of other works within the error bars [3], [8]. On the other hand,
we have not found a significant clustering signal in Hard and Ultrahard bands.
In order to see if this could be caused by the lack of a sufficient number of
sources in these bands we have performed a simple test. Since we have clearly
detected a clustering signal in the Soft band, we have rejected at random
two thirds of the Soft sample sources leaving a number comparable to that
of the Hard band and repeated the analysis with this new sample. We found
no significative signal and hence we conclude that the clustering in the Hard
band may exist and be as strong as in the Soft band but our relatively low
number of sources do not allow us to detect it.
However, the W (θ) bins are not independent so we have tried and alternative test based in the Poissonian statistics, comparing the expected number
of pairs in the absence of correlation (from DR pairs) with the number of observed pairs at distances equal or lower than each individual observed distance.
We have repeated this exercise 10000 times replacing the real data by random
sources in order to estimate the signal in the absence of correlation and the
99% percentiles of the simulations which allows us to estimate the significance
of the clustering (see Figure 4 for an example in the Soft band). Hence, we
have found in the Soft and XID bands a > 99% (but mostly < 99.9%) significant detection of correlation in the angular positions at separations 200-700
arcsec.
Fig. 4. Left: W (θ) for the Soft band. Solid dots are the observed values, grey
triangles are the zero points from the integral constraint (displaced to the left for
clarity), and the solid line is the χ2 fit to the data. Right: 1 − Pλ vs. θ for the soft
band (black jagged line). The gray jagged lines correspond to the median, 99% and
99.9% levels from random simulations.
5 Conclusions
We present the results from AXIS (An International XMM-Newton Survey),
a sample of 1433 serendipitous X-ray sources which covers 4.8 deg 2 in the sky,
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J. Ebrero and F.J. Carrera
at the fluxes in which more than a half of the acretion power of the Universe
is emitted.
We have determined very accurately the number of sources per flux unit
in four differente energy bands: 0.5-2 keV (Soft), 2-10 keV (Hard), 0.5-4.5 keV
(XID) and 4.5-7.5 keV (Ultrahard) using a combination of deeper and shallower surveys along with our sources.
With the best fit parameters from the source counts we have determined
the contribution to the cosmic X-ray background (CXB), resolving ∼ 85%
of the CXB intensity in the Soft and Hard bands, using jointly sources from
XMM-Newton and Chandra surveys like AXIS and CDF. At intermediate
fluxes, where the bulk of the CXB is emitted, AXIS sources resolve around
∼ 50% of the CXB.
We have found evidences of strong angular clustering in the Soft and XID
bands, but not in the Hard and Ultrahard bands which could be due to the
low number of sources present in those bands. To carry out this analysis we
have used the standard angular correlation function and a new method based
in Poissonian statistics, obtaining results compatible with previous works. For
further details on the AXIS X-ray properties, see [5].
Future work implies the use of redshifts in order to build luminosity functions and to determine the spatial clustering of the sources. To achieve this,
we will use XMS (XMM-Newton Medium Survey), a flux-limited subsample
of AXIS on which we have carried out an extensive program of optical identifications. This results will be presented in a forthcoming paper ([2]).
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Baldi, A. et al., 2002, ApJ, 564, 190
Barcons, X. et al., 2007, in preparation
Basilakos, S. et al., 2005, MNRAS, 356, 183
Bauer, F.E. et al., 2004, AJ, 128, 2048
Carrera, F.J. et al., 2006, A&A, submitted
Della Ceca, R. et al., 2004, A&A, 428, 383
Efstathiou, G. et al., 1991, ApJ, 380, L47
Gandhi, P. et al., 2006, A&A, 457, 393
Giacconi, R. et al., 2002, ApJS, 139, 369
Gilli, R. et al., 2005, A&A, 430, 811
Moretti, A. et al., 2003, ApJ, 588, 696
Ueda, Y. et al., 2005, ApJS, 161, 185
Yang, Y. et al., 2006, ApJ, in press