The XMM-Newton wide-field survey in the COSMOS field II: X-ray data and the logN-logS

3.3 MB·English

by  N. Cappelluti

Draftversion February5,2008
PreprinttypesetusingLATEXstyleemulateapjv.12/01/06
THE XMM–NEWTON WIDE-FIELD SURVEY IN THE COSMOS FIELD II: X-RAY DATA AND THE
LOGN-LOGSA
N. Cappelluti1, G. Hasinger1, M. Brusa1, A. Comastri2, G. Zamorani2, H. Bo¨hringer1, H. Brunner1, F. Civano2,4,
A. Finoguenov1, F. Fiore5, R. Gilli2, R. E. Griffiths3, V. Mainieri1, I. Matute1, T. Miyaji3, J. Silverman1
Draft versionFebruary 5, 2008
ABSTRACT
We presentthe dataanalysisandthe X–raysourcecountsforthe firstseasonofXMM–Newton ob-
servations in the COSMOS field. The survey covers ∼2 deg2 within the region of sky bounded by
9h57.5m < R.A. < 10h03.5m; 1d27.5m < DEC < 2d57.5m with a total net integration time of 504
7 ks. A maximum likelihood source detection was performed in the 0.5–2 keV, 2–4.5 keV and 4.5–10
0 keV energy bands and 1390 point-like sources were detected in at least one band. Detailed Monte
0 Carlo simulations were performed to fully test the source detection method and to derive the sky
2
coverage to be used in the computation of the logN-logS relations. These relations have been then
n derived in the 0.5–2keV, 2–10keV and 5–10 keV energy bands, down to flux limits of 7.2×10−16 erg
a cm−2 s−1, 4.0×10−15 erg cm−2 s−1 and 9.7×10−15 erg cm−2 s−1, respectively. Thanks to the large
J number ofsourcesdetected inthe COSMOSsurvey,the logN-logScurvesaretightly constrainedover

8 a range of fluxes which were poorly coveredby previous surveys, especially in the 2–10 and 5–10 keV
bands. The 0.5–2keVand2–10keVdifferentiallogN-logSwerefittedwith abrokenpower-lawmodel

1 which revealed a Euclidean slope (α ∼2.5) at the bright end and a flatter slope (α ∼1.5) at faint
v fluxes. In the 5–10 keV energy band a single power-law provides an acceptable fit to the observed
6 source counts with a slope α ∼2.4. A comparison with the results of previous surveys shows good
9
agreementin allthe energybands under investigationin the overlappingflux range. We also notice a
1
remarkable agreement between our logN-logS relations and the most recent model of the XRB. The
1
slightly different normalizations observed in the source counts of COSMOS and previous surveys can
0
be largely explained as a combination of low counting statistics and cosmic variance introduced by
7
the large scale structure.
0
/ Subject headings: cosmology: observations — cosmology: large scale strutcure of universe — cosmol-
h
ogy: dark matter — galaxies: formation — galaxies: evolution —X-rays: surveys
p
-
o
1. INTRODUCTION 2005). At present the two deepest X–ray surveys, the
r
t Chandra Deep Field North (CDFN; Bauer et al. 2004)
s The source content of the X–ray sky has been in-
a vestigated over a broad range of fluxes and solid an- and Chandra Deep Field South (CDFS; Giacconi et al.
v: gles thanks to a large number of deep and wide surveys 2001), have extended the sensitivity by about two or-
ders of magnitude in all bands with respect to pre-
i performed in the last few years using ROSAT, Chan-
X dra and XMM–Newton (see Brandt & Hasinger 2005 vious surveys (Hasinger et al. 1993; Ueda et al. 1999;
Giommi et al. 2000), detecting a large number of faint
r for a review). Follow–up observations unambiguously
a X–ray sources. However, deep pencil beam surveys are
indicate that Active Galactic Nuclei (AGN), many of
limited by the area which can be covered to very faint
which are obscured, dominate the global energy output
fluxes (typically of the order of 0.1 deg2) and suffer
recorded in the cosmic X–ray background. The impres-
from significant field to field variance. In order to cope
sive amount of X–ray and multi-wavelength data ob-
with such limitations, shallower surveys over larger ar-
tained to date have opened up the quantitative study
eashavebeenundertakeninthelastfewyearswithboth
of the demography and evolution of accretion driven
Chandra (e.g. the 9 deg2 Bootes survey (Murray et al.
Supermassive Black Holes (SMBHs; Miyaji et al. 2000;
2005), the Extended Groth strip EGS (Nandra et al.
Hasinger et al. 2005; Ueda et al. 2003; La Franca et al.
2005), the Extended Chandra Deep Field South E-
1Max Planck Institut fu¨r Extraterrestrische Physik, D-85478 CDFS, (Lehmer et al. 2005; Virani et al. 2006) and the
Garching,Germany Champ(Green et al.2004;Kim et al.2004))andXMM–
2INAF-OsservatorioAstronomicodiBologna,viaRanzani1,I- Newton (e.g. the HELLAS2XMM survey (Fiore et al.
40132D7eBpaorlotmgnean,tItoaflyPhysics, Carnegie Mellon University, 5000 2003), the XMM–Newton BSS (Della Ceca et al. 2004)
and the ELAIS S1 survey (Puccetti et al. 2006) ).
ForbesAvenue,Pittsburgh,PA15213
4Dipartimento di Astronomia, Universita`di Bologna, viaRan- In this context the XMM–Newton wide field survey
zani1,I–40127 Bologna,Italy in the COSMOS field (Scoville et al. 2007), hereinafter
5INAF-Osservatorio astronomico di Roma, Via Frascati 33, I-
XMM–COSMOS (Hasinger et al. 2007), has been con-
00044MonteporzioCatone, Italy
aBased on observations obtained with XMM–Newton, an ESA ceivedanddesignedtomaximize the sensitivityandsur-
sciencemissionwithinstrumentsandcontributionsdirectlyfunded vey area product, and is expected to provide a major
by ESA Member States and NASA; also based on data collected step forward toward a complete characterization of the
at the Canada-France-Hawaii Telescope operated by the National
physical properties of X–ray emitting SMBHs. A con-
ResearchCouncilofCanada,theCentreNationaldelaRecherche
ScientifiquedeFranceandtheUniversityofHawaii. tiguous area of about 2 deg2 will be covered by 25 in-
2 N. Cappelluti et al.
dividual pointings, repeated twice, for a total exposure
time of about 60 ksec in each field. In the first ob-
serving run obtained in AO3 (phase A), the pointings
were disposed on a 5x5 grid with the aimpoints shifted
of 15’ each other, so as to produce a contiguous pat-
tern of coverage. In the second run, to be observed in
AO4 (phase B), the same pattern will be repeated with
eachpointing shifted by 1’with respect to phase A. The
above described approach ensures a uniform and rela-
tively deep coverage of more than 1 deg2 in the cen-
tralpartofthefield. Whencompleted,XMM–COSMOS
will provide an unprecedentedly large sample of about
2000 X–ray sources with full multi-wavelength photo-
metric coverage and a high level of spectroscopic com-
pleteness. As a consequence, the XMM–COSMOS sur-
vey is particularly well suited to address AGN evolution
inthecontextoftheLargeScaleStructureinwhichthey
reside. More specifically, it will be possible to investi-
gate if obscured AGN are biased tracers of the cosmic
webandwhethertheir spacedensity risesinthe proxim-
ity of galaxy clusters (Henry & Briel 1991; Cappi et al.
2001; Gilli et al. 2003; Johnson et al. 2003; Yang et al.
2003;Cappelluti et al.2005; Ruderman & Ebeling 2005;
Miyaji et al. 2007; Yang et al. 2006; Cappelluti et al.
2006). Fig. 1.— The background counts distribution in the PN ob-
The X–ray reduction of phase A data along with a de- servation of Field 6. The solid line represents the best gaussian
tailed analysis of the source counts in different energy fittothe distribution. Thecontinuous vertical linerepresents the
adopted3σcutabovewhichthecorrespondingtimeintervalshave
bands are presented in this paper which is organized as
beendiscarded.
follows. In Section 2 the data reduction procedure and
therelativeastrometriccorrectionsaredescribed. InSec-
tion3 the sourcedetection algorithmsandtechnique are 1 an example of the application of this method to Field
discussed. MonteCarlosimulationsarepresentedinSec- #6 is shown. Once the high energy flares were removed,
tion 4. The logN–logS relations and the analysis of the the 0.3–10 keV background counts distribution was pro-
contribution of the XMM-COSMOS sources to the X- cessed,withthesame3σclippingmethod,inordertore-
ray background are discussed in Section 5. The study move times during which low energy particle flares were
of sample variance is presented in Section 6 and a sum- important. These flares are not easily detected in the
mary of the work is reported in Section 7. The strategy 12–14keVband. Asa resultofthis selectionprocessthe
and the log of the observations of XMM–COSMOS are average time lost due to particle flares was <20% and
presented by Hasinger et al. (2007), the optical identifi- 2 observations were completely lost (see Hasinger et al.
cationsofX-raysourcesbyBrusa et al.(2007),theanal- 2007).
ysis of groups and clusters by Finoguenov et al. (2007), Animportantfeatureobservableinthebackgroundspec-
the spectral analysis of a subsample of bright sources trum of both MOS and PN CCDs is the Al Kα (1.48
by Mainieri et al. (2007) and the clustering of X-ray ex- keV) fluorescent emission. In the PN background two
tragalactic sources by Miyaji et al. (2007). Through- strong Cu lines are also present at ∼ 7.4 keV and ∼
out the paper the concordance WMAP ΛCDM cosmol- 8.0 keV. Since these emission lines could affect the sci-
ogy (Spergel et al. 2003) is adopted with H0=70 km s−1 entific results, the 7.2–7.6 keV and 7.8–8.2 keV energy
Mpc−1, ΩΛ=0.7 and Ωm=0.3 bands in the PN and the 1.45–1.54 keV band (in PN
andMOS) were excluded fromthe detectors events. Im-
2. EPIC DATA CLEANING
ages were then created in the 0.5–2 keV, 2–4.5 keV and
The EPIC data were processed using the XMM– 4.5–10 keV energy bands with a pixel size of 4 arcsec.
Newton Standard Analysis System (hereinafter SAS) Single and double events were used to construct the PN
version6.5.0. TheObservationalData Files (ODF,”raw images, while MOS images were created using all valid
data”)ofeachofthe25observations,werecalibratedus- eventpatterns. Out-of-Time(OOT)eventsappearwhen
ing the SAS tools epchain and emchain with the most a photon hits the CCD during the read-out process in
recentcalibrationdatafiles. Eventsinbadcolumns,bad the IMAGING mode. The result is that the x position
pixels and close to the chip gaps were excluded. of the event/photon is known, while the y position is
BoththeEPICPNandMOSeventfilesweresearchedfor unknown due to the readout and shifting of the charges
high particle background intervals. The distribution of at this time. For this reason artificial OOT event files
the backgroundcounts binned in 100 s intervals was ob- were created. A new y coordinate is simulated by ran-
tainedinthe12–14keVbandforthePNandinthe10–12 domly shifting the eventalongthe readoutaxisandper-
keVbandfor the MOS,which aredominatedby particle forming the gain and CTI (charge transfer inefficiency)
background, and then fitted with a gaussian model. All correction afterwards. For the PN, in full frame mode
timeintervalswithbackgroundcountratehigherthan3σ the OOT events constitute about 6.3% of the observ-
above the average best fit value were discarded. In Fig. ing time. Those files were filtered in the same way as
XMM-COSMOS survey II: the X-ray data and the logN-logS 3
3. EPIC SOURCE DETECTION
3.1. Background modeling
In order to perform the source detection a sophisti-
cated background modeling has been developed. In X-
ray observations the background is mainly due to two
components, one generated by undetected faint sources
contributing to the cosmic X-ray background and one
arisingfromsoftprotonstrappedbythe terrestrialmag-
netic field. For this reason two background templates
were computed for each instrument and for each point-
ing,oneforthesky(vignetted)background(Lumb et al.
2002)andoneforinstrumentalandparticlesbackground
(unvignetted). To calculate the normalizations of each
template of every pointing, we first performed a wavelet
sourcedetection(seeFinoguenov et al.2007)withoutso-
phisticated backgroundsubtraction, then we excised the
Fig. 2.— Shiftbetween the PN+MOSmosaic and the MEGA-
areas of the detector where a significant signal due to
CAM catalog for each pointing of the XMM-Newton COSMOS
field. sources was detected. The residual area is split into two
parts depending on the value of the effective exposure
(i.e. higher and lower than the median value). Using
the event files and the produced images were subtracted the two templates, we calculate the coefficients of a sys-
fromthe eventimages. Imageswere then addedin order tem of two linear equations from which we obtain the
to obtain PN+MOS mosaics. For each instrument and normalizations of both:
for each observation, spectrally weighted exposure maps
were created using the SAS task eexpmap, assuming a AM1+BM1 =C1 (1)
v unv
power law model with photon index Γ=2.0 in the 0.5–2 AM2+BM2 =C2 (2)
keVbandandΓ=1.7inthe 2–4.5and4.5–10keVbands. v unv
where A and B are the normalization factors, M1,2 the
v
2.1. Astrometry correction vignettedtemplatesintheregionwitheffectiveexposure
higherandlowerthanthemedian,M1,2 theunvignetted
In order to correct the astrometry of our XMM– unv
Newton observations for each pointing and for each in- templatesandC1,2 arethebackgroundcountsinthetwo
regions. The region with effective exposure lower than
strument, the produced X-ray source list (see next sec-
the median (i.e. high vignetting, &7’ off-axis) is domi-
tion) wascomparedwith the MEGACAMcatalogof the
nated by the instrumental background, while the region
COSMOSfield(Mc Cracken et al.2007)includingallthe
with higher effective exposure is dominated by the sky
sourceswithImagnitudesintherange18-23. Inorderto
background. Therefore with this method we have the
find the shift between the two catalogues, an optical-X-
advantage of better fitting the two components of the
ray positional correlationwas computed using the likeli-
hood algorithm included in the SAS task eposcorr. This background. The standard method for estimating the
background, based on the spline functions used in the
task uses in a purely statistical way all possible coun-
XMM–Newton pipelines,returnedinourcasesignificant
terparts of an X-ray source in the field to determine
residuals. The excellent result of this technique can be
the mostlikely coordinatedisplacement. This method is
seen in the signal-to-noise (SNR) map in Fig 3: despite
independent of actual spectroscopic identifications, but
the significant variations in exposure time and average
all post-facto checks using, for example, secure spectro-
backgroundlevel from pointing to pointing, a rather ho-
scopic identifications, have demonstrated its reliability
mogeneous signal–to–noise ratio is achieved across the
and accuracy. Using the magnitude range mentioned
whole mosaic. It is worth noting that also pixels with
above, systematic effects introduced by bright stars and
negative values are shown in the map; these are located
faintbackgroundobjectsareminimized. Inthe majority
wherethebackgroundmodelishigherthanthemeasured
of the observations the shift between the three cameras
background.
turned out to be < 1” (i.e. much smaller than the pixel
size of the images used here ). Since the shift between
theEPICcamerasisnegligible,acorrelationbetweenthe 3.2. Maximum likelihood detection
joint MOS+PN source list and the optical catalog was In each pointing the source detection was conducted
calculated to derive the astrometric correction. For the on the combined images of the different instruments in
23 pointings presented here, the shifts between the opti- the three energy bands mentioned above using the SAS
cal and X-ray catalog are never larger than 3”, with an taskseboxdetect andemldetect. Asafirststep,thesliding
average shift of the order of ∆α ∼1.4” and ∆δ ∼-0.17”. cell detection algorithm eboxdetect was run on the im-
Theaveragedisplacementinthetwocoordinatesbetween agesin the three energy bands. In this procedure source
the PN+MOS mosaic X-ray positions and the MEGA- countswerecollectedincellsof5×5pixelsadoptingalow
CAM catalog sources for each pointing of the XMM- threshold in the detection likelihood (i.e. likemin=4).
COSMOSfieldis showninFig 2. The appropriateoffset The sourcelist producedby eboxdetect was then used as
was applied to the event file of each pointing and im- inputforemldetect. Forallthesourcesdetectedwiththe
ages and exposure maps were then reproduced with the sliding cellmethod this task performs amaximum likeli-
corrected astrometry. hoodPSFfit. Inthiswayrefinedpositionsandfluxesfor
4 N. Cappelluti et al.
Fig. 3.— Signal–to–noise ratiomapinthe 0.5–2keV band ofthe XMM–Newtonraster scaninthe COSMOSfield. Thestretch ofthe
color map corresponds to [-0.1<S/N<1 per pixel]. The scale has been chosen to enhance the SNR contrasts. If S is the raw (sources +
background)imageandBisthemodelbackgroundimage,thentheSNRmapisobtainedbySNR= S√−SB. Theimagewassmoothedwith
agaussianfilterwithσ=2pixels. Negativevaluesareplaceswherethemeasuredbackgroundissmallerthanthemodelbackground.
the sources were determined. Due to the particular pat- trials,N . ForasimpleboxdetectionalgorithmN
trial trial
tern of our observations (see Hasinger et al. 2007), the wouldbeapproximatelygivenbythenumberofindepen-
samesourcecouldbe detectedin upto 4 differentpoint- dent source detection cells across the field of view. For
ings. Forthisreasonbotheboxdetect andemldetect were the complex multi-stage source detection algorithm, like
runinrastermode. Thesourceparameters(positionand the one applied here, N cannot be calculated ana-
trial
flux) were fitted simultaneously on all the observations lytically, but has to be estimated through Monte Carlo
where the source is observable, taking into account the simulations. These simulations, which are discussed in
PSF at the source position in each pointing. As likeli- Section 4, return a number of spurious sources of ∼2%
hood threshold for the detection, we adopted the value at the likelihood level chosen. All the sources were fit-
det ml=6. This parameter is related to the probability ted with a PSF template convolved with a beta model
of a random Poissonian fluctuation having caused the (Cavaliere & Fusco-Femiano 1976). Sources which have
observed source counts: acoreradiussignificantlylargerthanthePSFareflagged
as extended (ext parameter >0).
det ml=−lnP (3)
random A total of 1307, 735 and 187 X-ray sources were de-
In principle, the expected number of spurious sources tected in the three bands. Of these sources, twenty-six
could be estimated as the product of the probability for wereclassifiedasextended. TheanalysisoftheX-rayex-
a random Poisson fluctuation exceeding the likelihood tendedsourcesintheCOSMOSfieldisbeyondthescope
threshold times the number of statistically independent of this work; these sources are extensively discussed by
XMM-COSMOS survey II: the X-ray data and the logN-logS 5
TABLE 1
Summaryof sourcedetection
EnergyBand Γa ECFb Slimc Nsourcesd Singledetectionse
keV cts s−1/10−11 ergcm−2 s−1 ergcm−2 s−1 All Point-like
0.5–2 2.0 10.45 7.2×10−16 1307 1281 661
2–4.5 1.7 1.52 4.0×10−15 735 724 89
4.5–10 1.7 1.21 9.7×10−15 187 186 3
a Γistheaveragespectralindexassumedineachband.
bTheenergyconversionfactor.NotethattheECFvaluesinthesecondandthirdrowsaretheconversionfactors
fromfluxinthe2–10keVand5–10keVbandstocountrateinthe2–4.5keVand4.5–10keVbands,respectively.
TheECFsarecomputed byassumingas ameanspectrum anabsorbedpower-lawwithNH=2.6×1020 cm−2
andspectralindexΓ=2.0inthe0.5–2keVbandandΓ=1.7inthe2–4.5keVand4.5–10keVbands.
c Thefluxofthefaintestsource.
d Thetotal numberofsourcesdetected fortheentiresampleandthepoint-likesampleonly.
e thenumberofsourcesdetected onlyinoneband.
Finoguenov et al. (2007). A total of 1281, 724 and 186
point-likesourcesweredetectedinthe threebandsdown
to limiting fluxes of7.2×10−16 ergcm−2 s−1, 4.7×10−15
erg cm−2 s−1 and 9.7×10−15 erg cm−2 s−1 respectively.
The minimum number of net counts for the detected
sourcesis∼21,17and27inthethreebands,respectively.
Atotalof1390independentpoint-likesourceshavebeen
detected by summing the number of sources detected in
each band but not in any softer energy band. The num-
berofsourcesdetectedonlyinthe 0.5–2keV,2–4.5keV,
4.5–10 keV bands are 661, 89 and 3, respectively.
From the count rates in the 0.5–2 keV, 2–4.5 keV and
4.5–10 keV bands the fluxes were obtained in the 0.5–
2 keV, 2–10 keV and 5–10 keV bands respectively using
theenergyconversionfactors(ECF)listedinTable1,to-
getherwithasummaryofthesourcedetection. TheECF
values have been computed using the most recent EPIC Fig. 4.— The cumulative probability to detect a true
response matrices in the corresponding energy ranges. source with det ml>6 in a circle of a given radius in the 0.5–2
As a model, we assumed power-law spectra with N (continuousline),2–4.5(dashedline)and4.5–10keV (dashed−
=2.6×1020 cm−2, (correspondingto the averagevalue oHf dottedline)energybands. The68%,90%and99%levelsareplot-
tedashorizontallines.
N over the whole COSMOS field (Dickey & Lockman
H
1990))andthesamespectralindicesusedtocomputethe
exposuremapswithoutconsideringanyintrinsic absorp- (Hasinger et al. 2005). This was then converted to a
tion (see Table 1). It is worth noting that the spectral 2–4.5 keV and 4.5–10 keV logN-logS assuming that all
indicesandthe absorptionsofthe individualsourcescan the sources have the same intrinsic spectrum (a power-
besignificantlydifferentfromtheaveragevaluesassumed law with spectral index Γ = 1.7). We then applied, to
here. In particular Mainieri et al. (2007) found that the the simulated fields, the same source detection proce-
spectral indices Γ of the XMM-COSMOS sources are in dure usedin the realdata. Schmitt & Maccacaro(1986)
the range1.5÷2.5,inthe CDFS Tozzi et al. (2006) mea- showed that with the threshold adopted here for source
sured an average photon index < Γ >∼1.75 and sim- detection, which corresponds roughly to the Gaussian
ilar values were obtained by Kim et al. (2004) in the 4.5-5σ, the distortion of the slope of the logN-logS due
CHAMP survey. The mean spectrum assumed here is to Poissonian noise is <3% for a wide range of slopes.
thereforeconsistentwiththevaluesmeasureduptonow. Therefore,the uncertaintiesintroducedbyusing asingle
Bychangingthespectralindexof±0.3theECFschange logN-logS as base for the simulations are negligible. A
of 2%, 12% and 4% in the 0.5–2 keV, 2–4.5 keV and totalof30626,13579and3172simulatedsourceswerede-
4.5–10 keV, respectively. tectedinthe0.5–2keV,2–4.5keVand4.5–10keVbands
4. MONTE CARLO SIMULATIONS downtothesamelimitingfluxesoftheobservations. For
everypossible pairofinput-output sourceswe computed
Inorder to properlyestimate the source detectioneffi-
the quantity
ciencyandbiases,detailedMonteCarlosimulationswere
performed (see, e.g., Hasinger et al. 1993; Loaring et al. x−x 2 y−y 2 S−S 2
2005). Twenty series of 23 XMM–Newton images were R2 = 0 + 0 + 0 , (4)
(cid:18) σ (cid:19) (cid:18) σ (cid:19) (cid:18) σ (cid:19)
createdwiththesamepattern,exposuremapsandback- x y S
ground levels as the real data. The PSF of the simu- wherex,y andS arethepositionandfluxofthedetected
lated sources was constructed from the templates avail- sourceandx ,y andS arethecorrespondingvaluesfor
0 0 0
able in the XMM–Newton calibration database. The allthe simulated sources We then flag as the most likely
sources were randomly placed in the field of view ac- associations those with the minimum value of R2. The
cording to a standard 0.5-2 keV logN-logS distribution distribution of the positional offsets is plotted in Fig. 4
6 N. Cappelluti et al.
for each energy band analyzed. from their input counterpart are classified as spurious.
These account for 2.7%, 0.5%, 0.6% of the total num-
ber of sources in the 0.5–2 keV, 2–4.5 keV and 4.5–10
keV bands, respectively. Source confusion occurs when
two or more sources fall in a single resolutionelement of
the detector and result as a single detected source with
an amplified flux. In order to determine the influence of
thesourceconfusionweadoptedthemethoddescribedin
Hasinger et al.(1998). We define as ”confused”sources
those for which S /(S +3∗σ ) > 1.5 (where σ
out in out out
is the 1σ error on the output flux). The fraction of
”confused” sources is 0.8%, 0.15% and <0.1% in the
0.5–2keV,2–4.5keVand4.5–10keVbands,respectively.
The photometry was also tested; the ratio of output to
input fluxes in the simulation is plotted in Fig.5.
Atbrightfluxes this ratioisconsistentwith one,while
at fainter fluxes the distribution of S /S becomes
out in
wider, mainly because of increasing errors, and skewed
toward values greater than one. This skewness of the
distribution can be explained mainly by two effects:
a) source confusion and b) Eddington Bias (Eddington
1940). While source confusion, as defined above, affects
only a small fraction of the sources, the Eddington bias
resultsinasystematicupwardoffsetofthedetectedflux.
Themagnitudeofthiseffectdependsontheshapeofthe
logN-logS distribution and the statistical error on the
measured flux. Since there are many more faint than
bright sources, uncertainties in the measured flux will
result in more sources being up-scattered than down-
scattered. Togetherwiththis,thefactthatinthe4.5–10
keV band we are sampling a flux region in which the
logN-logSis steeperthaninthe otherbands (seeSection
5), explains why such an effect is more evident in the
4.5–10 keV band.
Besides assessing the reliability of our source detec-
tion procedure, one of the aims of these simulations is
toprovideapreciseestimationofthecompletenessfunc-
tion of our survey, known also as sky coverage. We con-
structed our sky-coverage (Ω) vs. flux relation by di-
viding the number of detected sources by the number of
input sources as a function of the flux and rescaling it
to the sky simulated area. Having analyzed the simula-
tionswiththesameprocedureadoptedfortheanalysisof
the data, this method ensures that when computing the
source counts distribution (see next section) all the ob-
servational biases are taken into account and corrected.
The Ω vs. flux relation relative to the 0.5–2 keV, 2–10
keV and 5–10 keV bands is plotted in fig. 5. The total
skyareais2.03deg2anditiscompletelyobservabledown
to fluxes of ∼0.3, 1.3 and 2×10−14 erg cm−2 s−1 in the
threebands,respectively. Theskycoveragedropsto0at
Fig. 5.— The ratio Sout/Sin as a function of the output de- limitingfluxesof∼7×10−16ergcm−2s−1,∼4×10−15erg
treecspteedctiflvuexlyTinopthmeid0d.5l–e2ankedVb,ot2t–o4m.5pkaenVel.and 4.5–10 keV bands, cm−2 s−1and∼9×10−15 ergcm−2 s−1,inthe 0.5–2keV,
2–10 keV and 5–10 keV bands, respectively.
We find that 68% of the sources are detected within
5. SOURCE COUNTS
2.1”, 1.3” and 0.8” in the 0.5–2 keV, 2–4.5 keV and
4.5–10keV bands, respectively. Since the detectionsoft- Oncetheskycoverageisknown,thecumulativesource
warefits thepositionofthesourceusingthe information number counts can be easily computed using the follow-
available for the three bands together, we expect to be ing equation:
able to detect sources with an accuracy of the order of,
or somewhat better than, that shown in Fig. 4. As NS 1
in Loaring et al. (2005), we then define a cut-off radius N(>S)= deg−2, (5)
rcut of 6”. Sources with a displacement larger than rcut Xi=1 Ωi
XMM-COSMOS survey II: the X-ray data and the logN-logS 7
Fig. 6.— The sky coverage vs. flux relation in the 0.5-2, 2-10
and 5-10 keV energy bands (respectively continuous, dashed and
dash-dotted line), resulting from the simulations described in the
text.
TABLE 2 Fig. 7.— The 0.5-2 keV logN-logS of the XMM-COSMOS
Cumulativenumbercounts (red dots) sources compared with the ROSAT medium sensitiv-
ity survey (Hasingeretal. 1993) (blue dot dashed line), com-
log(S)a Ωb N(>S)c bined ROSAT, XMM–Newton , Chandra (Hasingeretal. 2005)
ergcm−2 s−1 deg2 deg−2 t(igere(eRnosdaatishetedal.lin20e0),2)th(me aCghenantadracondteienpuofiuesldlinsoeu),thth1eσCehrarnor-
dra deep field north 1σ error tie (Baueretal. 2004) (pink dot−
0.5–2keV dashed line), the 100 ks of the XMM–Newton Lockman
-13.0 2.03 4.5±1.5 hole (Hasingeretal. 2001) (cyan circles), the HELLAS2XMM
-13.5 2.03 18.8±3.1 (Baldietal. 2002) (black pentagons) and the extended CDFS
-14.0 2.03 105.2±7.0 (Lehmeretal. 2005) (black continuous line) surveys. The over-
-14.5 2.03 327.0±12.7 layed black-dashed line represents the logN-logS predicted by the
-15.0 0.58 790±23.3 model of Gilli,Comastri&Hasinger (2006). The source number
-15.1 0.12 931±53.0 countsareplottedscaledbyS1.5inordertohighlightthedeviation
2–10keV fromtheEuclideanbehavior.
-13.0 2.03 8.6±2.0
-13.5 2.03 57.0±5.3
-14.0 1.40 258.9±11.6
-14.3 0.13 600.1±34.2 in the previous section, the sky coverage Ω was derived
5–10keV from realistic Monte Carlo simulations and therefore no
-13.5 2.03 21.3±3.2 further correction for the Eddington Bias is required.
-14.0 0.35 111±11.0 In order to parameterize our relations, we performed
abFSkluyxcoverage a maximum likelihood fit to the unbinned differential
b Cumulativesourcecounts counts. We assumed a broken power-law model for the
0.5–2 keV and 2–10 keV bands:
where N is the total number of detected sources in the
fiasesldocwiaittehSdflwuxitehsgthreeatfleurxthoafnthSeainthdsΩoiuirscteh.eTskhyecvoavreiarnagcee n(S)= ddNs =(cid:26)ABSS−−αα12 SS >≤SSbb, (7)
of the source number counts is therefore defined as:
where A = BSα1−α2 is the normalization, α is
NS 1 2 the bright end slopbe, α the faint end slope, S 1the
σi2 = (cid:18)Ω (cid:19) . (6) break flux, and S the flu2x in units of 10−14 erg cbm−2
Xi=1 i s−1 . Noticethatusingthemaximumlikelihoodmethod,
Source number counts are reported in Table 2. The the fit is not dependent on the data binning and
cumulative number counts, normalized to the Euclidean therefore we can make full use of the whole dataset.
slope (multiplied by S1.5), are shownin Figures 7, 8 and Moreover, the normalization A is not a parameter of
9, the fit, but it is obtained by imposing the condition
for the 0.5–2 keV, 2–10 keV and 5–10 keV energy that the number of expected sources from the best
ranges,respectively. With sucha representation,the de- fit model is equal to the total observed number. In
viations from the Euclidean slope are clearly evident as the 0.5–2 keV energy band the best fit parameters are
well as the flattening of the counts towards faint fluxes. α1=2.60+−00..1158, α2=1.65±0.05, Sb=1.55+−00..2284 ×10−14 erg
Source counts are compared with the findings of other cm−2 s−1 and A=123. Translating this value of the
deep and shallow surveys collected from the literature. normalization to that for the cumulative distribution
The plotted reference results were selected in order to at 2×10−15 erg cm−2 s−1 , which is usually used in
sample a flux range as wide as possible and at the same the literature for Chandra surveys, we obtain A ∼450
15
time to keep the plots as clear as possible. As discussed which is fully consistent with most of previous works
8 N. Cappelluti et al.
Fig. 8.— The 2-10 keV logN-logS of the XMM-COSMOS Fig. 9.— The 5-10 keV logN-logS of the XMM-COSMOS
(red dots) sources compared with Chandra, XMM–Newton and (reddots)sourcescomparedwiththeHELLAS2XMM(Baldietal.
ASCA (blue dashed line) (Morettietal. 2003), HEL- 2002) (green pentagons), the Chandra deep field south 1σ error
LAS BeppoSAX (Giommietal. 2000) (black hexagons) tie(Rosati etal.2002)(magentacontinuousline),theHELLAS-
the Chandra deep field south 1σ error tie (Rosatietal. BeppoSAX data from Fioreetal. (2001) (black hexagons), the
2002) (magenta continuous line), the HELLAS2XMM ELAIS S1 (blue stars) (Puccetti etal. 2006) and the 100 ks of
(greenpentagons)(Baldietal.2002), the ELAISS1(blue stars) theLockmanHole(cyanopencircles)(Hasingeretal.2001). The
(Puccetti etal. 2006), the extended CDFS (Lehmer etal. 2005) overlayed black-dashed linerepresents the logN-logS predicted by
1σerrortie(blackcontinuousline)andthe100ksoftheLockman themodelofGilli,Comastri&Hasinger (2006). Thesourcenum-
hole (cian open circles) (Hasingeretal. 2001). The overlayed bercountsareplottedscaledbyS1.5inordertohighlightdeviation
black-dashedlinerepresentsthelogN-logSpredictedbythemodel fromtheEuclideanbehavior.
of Gilli,Comastri&Hasinger (2006). The source number counts
areplottedscaledbyS1.5 inordertohighlightthedeviationfrom
theEuclideanbehavior.
In the 2–10 keV band the XMM-COSMOS counts
where a fit result is presented (Hasinger et al. 1993;
bridge the gap between deep field observations
Mushotzky et al. 2000; Hasinger et al. 2001; Baldi et al.
(Rosati et al. 2002) and shallower large area Bep-
2002; Rosati et al. 2002; Bauer et al. 2004; Kim et al.
poSAX (Giommi et al. 2000) and XMM–Newton sur-
2004; Hasinger et al. 2005; Kenter et al. 2005), but sig-
veys (Baldi et al. 2002). At relatively bright fluxes
nificantly lower than that found in the CLASXS sur-
(>10−14 erg cm−2 s−1) the XMM-COSMOS logN–logS
vey (Yang et al. 2004). In the 2–10 keV band the
nicely matches previous measurements, though provid-
best fit parameters are α =2.43±0.10, α =1.59±0.33,
S =1.02+0.25 ×10−14 erg c1m−2 s−1 and 2A=266. The ing a much more robust estimate of the source counts
b −0.19 thanks to the much smaller statistical errors.
latestvaluetranslatesintoA ∼1250. Alsointhisband,
15 A major step forward in the determination of X–ray
ourresultsareinagreementwithprevioussurveyswithin
source counts is achieved in the 5–10 keV band, where
1σ, with the exception of the CLASXS survey which is
the previously existing data from different surveys show
∼30%higherinthisband(Yang et al.2004). Inthe5–10
verysignificantdifferences. ThankstoXMM–COSMOS,
keV energy bands, where the differential counts do not
a solid measure of the hard-X logN–logS in the flux in-
showanyevidenceforabreakinthesampledfluxrange,
terval 10−14 – 10−13 erg cm−2 s−1 is obtained for the
we assumed a single power-law model of the form:
first time. From Fig. 9 we notice that the normaliza-
dN tion of the XMM–COSMOS logN–logSis slightly higher
n(S)= =AS−α1, (8) than (∼10%), although consistentat 1σ with, that mea-
ds
suredbyChandrawhile,ELAISS1(Puccetti et al.2006)
for which the best fit parameters are found to be sourcecountsare30%lower. However,intheoverlapping
A=102 and α1=2.36±0.1. flux range the latter is characterizedby large errors due
In the soft 0.5-2 keV (Fig. 8) energy range a visual to the small number of relatively bright sources in the
inspection of the various datasets suggests a remarkably Chandra deep fields. Interestingly enough, the XMM–
goodagreementbetweenXMM-COSMOSandliterature COSMOScountsmatchnicely,withsmallererrors,those
data7. of the wide area HELLAS2XMM survey (Baldi et al.
2002),while the pioneering measurements ofBeppoSAX
7 In particular, it is worthwhile to notice the good agreement
(Fiore et al. 2001) are systematically higher than the
betweentheXMM-COSMOSandtheHasingeretal.(2005)logN-
logS, whichhas been usedas input inour simulations. Thisgood counts from XMM-COSMOS.
agreement can be considered as an a posteriori support of the re-
liabilityofthoseresultsfromthesimulationswhichdependonthe assumedinputlogN-logS.
XMM-COSMOS survey II: the X-ray data and the logN-logS 9
5.1. Resolved fraction of the X-ray background tween infinite and zero, and assuming that the slope
of the ”real” logN-logS remains constant down to low
OneofthemainaimsofXMM-COSMOSwithitslarge
fluxes, we estimated the total contribution of AGNs to
and medium–deep coverage, is to provide a solid census
the XRB. We predict a total flux of AGNs in the XRB
of the X-ray source population to be compared with ob-
of 1.25×10−11 erg cm−2 s−1 deg−2. This value is ∼40%
servations and models of AGN evolution. According to
lowerthanthatmeasuredbyDe Luca & Molendi(2004),
recent synthesis models (see e.g.; Comastri et al. 1995;
and ∼ 25% smaller than those obtained by integra-
Gilli, Comastri & Hasinger 2006; Worsley et al.2005) a
tion the model logN-logS of Gilli, Comastri & Hasinger
high fraction of heavily obscured AGN is necessary to
(2006) which predicts a flux of ∼1.66×10−11 erg cm−2
explainthe spectralshapeandthe intensityofthe X-ray
s−1 deg−2. This discrepancy between our predicted flux
background(XRB).Weexaminethereforewhichfraction
and that of Gilli, Comastri & Hasinger (2006), could
of XRB is resolved into discrete sources in our survey.
arise by the fact that, in our measurement, we consider
As a first test, we computed the flux which XMM-
that all the sources have the same spectrum and from
COSMOS itself resolves into discrete sources by sum-
statistical uncertainty of the logN-logS parameters. By
ming their fluxes weighted on the sky coverage in the
assuminganaveragespectralindex<Γ>=1.4forallour
0.5–2 keV, 2–10 keV and 5-10 keV energy bands. As
sources,weobtaina value forthe totalflux ofthe AGNs
in Worsley et al. (2005) we used as reference value of
of∼1.48×10−11ergcm−2 s−1 deg−2 whichisconsistent,
the normalizationat1keVofthe XRB spectrumthatof
withinthestatisticaluncertanties,withthepredictionof
De Luca & Molendi(2004)whichassumesthatthespec-
the model. Considering the total flux of the XRB pre-
tralshapeinthe1-10keVbandisapower-lawwithspec-
dictedbythemodelandourestimatefromthelogN-logS
tralindexΓ=1.4andanormalizationat1keVof11.6keV
cm−2 s−1 keV−1. The latter value corresponds to a flux distributions,inthe2–10keVband,XMM-COSMOSre-
of0.80,2.31and1.27×10−11 ergcm−2 s−1 deg−2 inthe solves the ∼55–65% of the total flux of the XRB into
discrete sources.
0.5–2keV,2–10keVand5-10keVenergybands,respec-
It is interesting to observe how in the 5–10 keV band
tively. In the 0.5–2keVband we measure a contribution
our data are in good agreement with the prediction of
ofthesourcestotheXRBwhichcorrespondstoanormal-
izationat1keVof0.49±0.08×10−11ergcm−2s−1deg−2. the model. This result is particularly important since in
this bandit is expectedthe majorcontributionofhighly
The correspondingvalues in the 2–10keV and 5–10keV
bands are 0.92±0.22×10−11 erg cm−2 s−1 deg−2 and absorbedAGN,whichareanimportantingredientofthe
0.28±0.15×10−11ergcm−2 s−1deg−2. ThereforeXMM- XRB models. A detailedanalysisof the spectralproper-
COSMOS resolves by itself ∼65%, ∼40% and ∼22% of ties of the brightest X-ray sources in XMM-COSMOS is
presented by Mainieri et al. (2007).
theXRBintodiscretesourcesinthe0.5–2keV,2–10keV
and 5–10 keV energy bands, respectively. It is worth
6. SAMPLE VARIANCE
noticing that the flux measured by De Luca & Molendi
(2004) is the highest measured in literature in the 1–10 Theamplitudeofsourcecountsdistributionsvariessig-
keV energy range (see e.g. Gilli, Comastri & Hasinger nificantly among different surveys (see e.g. Yang et al.
2006, for a complete collection). It is also worth notic- 2003; Cappelluti et al. 2005, and references therein).
ing that we computed the fraction of resolved XRB by This ”sample variance”, can be explained as a combi-
assuming that all the sources have the same spectrum. nation of Poissonian variations and effects due to the
Therefore, in our estimate, effects due to the broad ab- clustering of sources (Peebles 1980; Yang et al. 2003).
sorption and spectral index distributions of AGNs are The variance of counts in cells for sources which are an-
not included. gularly correlated can be obtained with:
In Figs. 7, 8 and 9 we compared our logN-
logS to those predicted by the recent XRB model of <(N −NΩ)2 >=NΩ+N2 dΩ1dΩ2w(θ1,2) (9)
Z
Gilli, Comastri & Hasinger (2006). This model makes
where N is the mean density of objects in the sky, Ω is
use of the most recent observational constraints on the
the cell size, and w(θ ) is the angular two–point corre-
AGN populations and includes a conspicuous fraction 1,2
lationfunction. ThefirsttermofEq. 9isthePoissonian
of Compton thick AGN which, however, are not ex-
variance and the second term is introduced by the large
pectedtosignificantlycontributetotheXMM-COSMOS
scalestructure. Inordertodeterminewhetherthediffer-
counts. In the 0.5–2 keV band a direct comparison
ences observed in the source counts of different surveys
of our data with the model shows a 1σ agreement at
could arise from the clustering of X-ray sources,we esti-
the bright end. At the faint end the model predicts
mated the amplitude of the fluctuations from our data,
a slightly higher normalization when compared to most
by producing subsamples of our survey with areas com-
of the plotted data, including ours. A similar behavior
parable to those of. e.g., Chandra surveys.
is observed in the 2–10 keV band. It is worth notic-
The XMM-COSMOS field and the Monte Carlo sample
ing that in the model the average unabsorbed power-
law spectral index of the sources is < Γ >∼1.8 in the fields of Section 4 were divided in 4,9,16 and 25 square
boxes. Making use of the 0.5–2 keV energy band data,
flux intervalsampledby XMM-COSMOS(see Fig. 19in
we computed for each subfield, the ratio of the number
Gilli, Comastri & Hasinger (2006)). Since in our data
of real sources to the number of random sources. In
analysis we assumed < Γ >=1.7 we expect in this band
aslight(∼10%)underestimationofthefluxeswhencom- order to prevent incompleteness artifacts, we conserva-
tively cut the limiting flux of the randomand data sam-
pared to those of the model. This effect is almost negli-
ple to 5×10−15 erg cm−2 s−1. At this flux our survey is
gible (i.e. <5%) in the other bands investigated here.
complete overthe entirearea. Inorderto avoidartifacts
By integrating our best fit 2–10 keV logN-logS be-
introduced by the missing pointings in the external part
10 N. Cappelluti et al.
TABLE 3
Summaryof the0.5–2 keVsamplevarianceinthe
COSMOS field. Prediction andobservationata flux
limit S =5×10 15 ergcm 2 s 1
lim − − −
Areaa σobsb σpc σcld σexpe χ2/d.o.f.f
arcmin2
40′×40′ 0.09±0.04 0.10 0.09 0.13 4.21/3
26′×26′ 0.20±0.05 0.15 0.10 0.19 8.93/8
20′×20′ 0.21±0.04 0.20 0.11 0.23 16.63/15
16′×16.′ 0.24±0.02 0.25 0.12 0.28 25.15/24
a Sizeoftheindependent cells.
b Theobservedstandarddeviation.
c ThepredictedPoissonianstandarddeviation σp.
d Thepredictedstandarddeviationduetoclusteringσcl.
e Thetotal predictedstandarddeviations.
f Valueofthefittedχ2/d.o.f.
counts fluctuations on this area (σ ) comes from the
exp
large scale structure, therefore the contribution of sta-
tistical fluctuations becomes less important. With the
sameprocedure,wecanestimatethetotalexpectedfluc-
Fig. 10.— The counts in cell fluctuations within the XMM- tuations(σ )andtherelativeimportanceofσ andσ
exp p cl
COSMOSfield. Thedataarenormalizedtoarandomdistributed
also for the hard band (5-10 keV), even if in this band
fieldinboxesof40’,26’,20’and16’ofside,respectively. Thedashed
linesrepresentthe1σ expected fluctuation. we do not have enough statistics to divide our field in
sub-samples. Usingtheformalbestfitforθ inthisband
0
foundbyMiyajietal. (2007)(θ =6”),wefindthatatthe
0
of the field of view, we concentrated our analysis to the faintest 5-10 keV flux (S∼10−14 erg cm−2 s−1) sampled
central80′×80′. InFig.10weplottheratioofthedatato bytheXMM-COSMOSsurvey(N ∼110deg−2 )thera-
the random sample as a function of the size of the cells tio σ /σ is smaller than one on all the four scales here
cl p
under investigation. The measured fractional standard analyzed,withatotalexpectedstandarddeviationofthe
deviations of the sample is reported in Table 3. Using fluctuations ranging from ∼0.20 on the largest scale to
Eq. 9 we computed the expected amplitude of source ∼0.40 on the smallest scale. These values for σ are
exp
countsfluctuationswithw(θ1,2)takenfromMiyaji et al. significantly larger than those shown in Table 3 for the
(2007). They computed the X-ray two–point correlation soft band, because in the hard band the surface density
function in the XMM-COSMOS field and detected clus- of sources is lower and the angular correlation length is
tering signal with angular correlation length θ0 ∼1.9” higher than in the soft band.
∼0.8” and ∼6” in the 0.5–2 keV, 2–4.5 keV and 4.5–10 This analysis is at least qualitatively consistent with
keV band, respectively. The observed slope is γ=1.8 in Figures 8 and 10, which show a significantly larger dis-
all the energy bands. persion in the data from different surveys in the hard
Thepredictedfractionalstandarddeviationsarethere- band than in the soft band. Moreover, the results here
fore 0.13,0.19,0.23 and 0.28 on scales of 0.44 deg2, 0.19 discussed are also consistent with the observed fluctua-
deg2, 0.11 deg2 and 0.07 deg2, respectively. These val- tionsinthedeepChandrafields(see,forexample,Bauer
ues are in good agreement with those observed in the et al. 2004). Large area, moderately deep surveys like
sub-samples of our dataset as shown by the value of the XMM-COSMOS are needed to overcome the problem of
fitted χ2 to the counts in cell fluctuations (see Table 3). low counting statistics, typical of deep pencil beam sur-
As shown in Table 3, at this limiting flux and on the ar- veys,and,atthesametime,toprovidearobustestimate
eas considered here the main contribution to the source of the effect of large scale structure on observed source
counts fluctuations is from the Poissonian noise. At the counts.
flux limit assumed here, the ratio σcl/σp increases from As a final consideration, we tried to compute the ex-
∼0.5 on the smallest scale (16 x 16 arcmin) to ∼0.85 on pected intrinsic variance of XMM-COSMOS. This esti-
the largest scale (40 x 40 arcmin). This ratio scales as: mate must be made with care since we have only one
σ /σ ∝N0.5θ(γ−1)/2a(3−γ)/2, (10) sample on this scale. Assuming that the angular corre-
cl p 0 lation function of Miyaji et al. (2007) was universal, the
where N deg−2 is the surface density of the sources, θ residualuncertaintiesonthesourcecountsareestimated
0
(deg) is the angular correlation length and a (deg) is to be <5-6% in the 0.5–2 keV and 2–10 keV bands, and
the size of the cell. In order to estimate at which flux of the order of the 10% in the 5–10 keV band.
limit fluctuationsintroducedby the largescalestructure
are predominant, we estimate that σ /σ would be ∼1 7. SUMMARY
cl p
on the smallest scale, corresponding to a Chandra ACIS The data analysis of the first run of observations of
field of view (16 x 16 arcmin) at a surface density of the XMM-Newton COSMOS wide field survey has been
the order of ∼900 deg−2, corresponding to a 0.5-2 keV presented. A total of 1390 point-like sources are de-
flux S∼ 8×10−16 erg cm−2 s−1. At even fainter fluxes tected on a contiguous area of about 2 deg2 down to
the dominant contribution to the total expected source fluxes of 7.2×10−16 erg cm−2 s−1, 4.0×10−15 erg cm−2