Table Of ContentA&A manuscript no.
(will be inserted by hand later) ASTRONOMY
AND
Your thesaurus codes are:
ASTROPHYSICS
02 (11.01.2 11.03.1 12.04.2 13.25.2 13.25.3) 1.2.2008
A Large-Area Cross-Correlation Study of High Galactic
Latitude Soft and Hard X-ray Skies
6 Takamitsu Miyaji1, Gu¨nther Hasinger2, Roland Egger1, Joachim Tru¨mper1, and Michael J. Freyberg1
9 1 Max-Planck-Institut fu¨r extraterrestrische Physik,D–85740 Garching b. Mu¨nchen, Germany
9
2 Astrophysikalisches Institut,An derSternwarte 16, D–14482 Potsdam, Germany
1
n Received date; accepted date
a
J
0 Abstract. We havemade cross-correlationanalysesof(2 1. Introduction
3
– 15 keV) HEAO-1 A2 and 1 keV ROSAT PSPC All-
Sky Survey maps overa selected area (∼ 4000deg2) with With deep ROSAT observations of blank fields, up to ∼
v1 high galactic latitude (b >∼ 40◦). We have calculated the 60%ofthesoft(<∼2keV)cosmicX-raybackground(XRB)
has been resolved into individual sources (e.g. Hasinger
3 correlations for the bright ROSAT sources and residual
7 backgroundseparatelywiththeHEAO-1A2TOT(2–10 etal.1993). A number of groups have worked/are cur-
1 rentlyworkingonidentificationprogramsoftheseROSAT
keV)andHRD(5–15keV)maps.Inanycase,theangular
1 sources and we can expect that we will have the over-
dependence of the cross–correlation function (CCF) was
0
all picture of the origin of most of the soft (∼ 1 keV)
6 consistent with expected from the HEAO-1 A2 collima-
X-ray background including contributing source popula-
9 tor response function and the smoothing function of the
/ ROSAT 1 keV map. The amplitude of the brightROSAT tions and their cosmological evolution. With ASCA ob-
h
servationsofblankfields,theXRB athigherenergies(2 –
p source – A2 CCFs are consistent with expectations from
10keV)havealsobeenresolvedintosources,althoughthe
- modelpopulationsofAGNsandclustersofgalaxies,which
o resolvedfractionofthetotalXRBfluxissmallerthanthat
emit in both bands. However, the residual ROSAT back-
r
t ground – A2 CCFs amplitude at zero degree are about a ofROSATbecauseofthelimitedspatialresolution.While
s
theseobservationaleffortsarerapidlyinprogress,theuni-
a factor of three larger than that expected from the model
: populations. fiedtheoryofAGNsandsupportingX-rayobservationsof
v
AGNs for the basic frameworkof the unified scheme have
i Our soft-hard zero-lag and angular CCF results have
X provided insights to the origin of the bulk properties of
been compared with the 1 keV auto-correlation function
r the XRB. In particular,intrinsic photoelectric absorption
(ACF) foundby Soltanetal.(1995)for the sameROSAT
a
data.TheirsignificantangularCCFatascaleofθ <∼5◦ is observed in the X-ray spectra of Seyfert 2 galaxies (e.g.
Awaki etal.1991; Mulchaey etal.1992), consistent with
ofanunknownoriginanditcouldrepresentanewclassof
the view ofthe unifiedschemethataSeyfert2galaxyis a
cosmicX-raysources.Ifthis 1keVACFhasahotplasma
Seyfert 1 seen at an angle where a torus surrounding the
spectrum with kT ∼ 2 keV, contribution of this compo-
centralengineblocksthelineofsight.Awiderangeofab-
nentisconsistentwithbothourzero-lagCCFinexcessof
sorptioncolumndensities havebeenobserved(Schartelet
the populationsynthesis model predictionandthe upper-
◦ al.1995)forahardX-rayflux-limitedsampleofAGNsby
limit to the angular CCF at θ ∼2.5 . On the other hand,
Piccinotti et al. (1982).Models of the XRB with evolving
if this component has a lower temperature or a steeper
populationsofunabsorbedandinternally-absorbedAGNs
spectrum,amajormodificationtothe populationsynthe-
with various absorption column densities, based on the
sis model and/or an introduction of new classes would be
unifiedschemeofAGNshavebeensuccessfullymadecon-
needed.
sistent with many observational properties of the XRB
(Madau etal.1994; Comastri etal.1995). In particular,
Key words: Galaxies:active–Galaxies:clusters:general
they explained the global spectral shape of the XRB, es-
— (Cosmology): Diffuse Radiation — X-rays: galaxies –
pecially the characteristic break at 30 keV and source
X-rays: general
counts in soft and hard X-rays. While these models are
basicallysuccessful,thereisstillroomformajormodifica-
tions,givencurrentobservations.ArecentASCAobserva-
tionofNGC3628byYaqoobetal.(1995)showedthatthe
Send offprint requests to: T. Miyaji X-ray (E <∼ 10 keV) spectrum of this spiralgalaxy,which
2 Miyaji et al. Cross-Correlation of Soft and Hard X-ray Skies
hadpreviouslybeenclassifiedasastarburst,isratherflat. ACF component. Thus the main portion of the extended
Based on this observation, they argued that the contri- ACF could represent still a new population of cosmic X-
bution of low-luminosity extragalactic X-ray sources, like rayemissionandinvestigatingtheirnatureisonlypossible
NGC 3628, to the E >∼ 2 keV XRB could be significant. by statistical analyses over a large region of the sky.
Such a low X-rayluminosity populationhas been deliber- In this paper, we present the results and possible in-
ately neglected in the Madau etal.(1994) and Comastri terpretations of a cross-correlation analysis between the
etal.(1995) models. Also these models assumed a sim- soft (∼1 keV) X-ray sky observed with ROSAT PSPC
ple version of the AGN unified scheme where the ratio All-Sky Survey and the hard (2 – 15 keV) X-ray sky ob-
of the numbers of absorbed and unabsorbed objects does served with the HEAO-1 A2 experiment. The purpose of
not depend on their intrinsic X-ray luminosity. However, the correlationbetweensoft-hardX-rayspresentedinthis
Barcons etal.(1995) argued that this is not likely to be paperistwo-folded.Zero-lagandangularcross-correlation
the case but rather the fraction of the unabsorbed AGNs functions(CCFs)betweensurfacebrightnessescontainin-
(type 1) should increase with the intrinsic luminosity. formation on X-ray sources common to these two bands.
Besides detailed studies of the nature of individual Thus this would give additional constraints to the popu-
X-ray sources which can contribute to the XRB, sta- lation synthesis models. Especially, it would give a check
tistical properties of the spatial fluctuation of the un- to the models based on unabsorbed and absorbed AGNs.
resolved background provide us with other perspectives A large area correlation study also may give a clue to
of cosmic X-ray sources. Fluctuations of the unresolved the nature of the extended ACF component that Soltan
XRB have been used to infer the logN − logS rela- etal.(1995)found.Thescopeofthispaperisasfollows:In
tion below the source detection flux-limit (e.g. Shafer Sect.2,weexplainthedataused.WeexplaintheCCFcal-
1983; Hasinger etal.1993; Barcons et al. 1994). The an- culationandpresentthe resultsofthe calculationinSect.
gular auto-correlation function is often used to describe 3. Sect.4 presents formulations relating observed CCF
spatial structure of the XRB. Many authors discussed withmodelsincludingindividualsourcesinthepopulation
the constraints on the combination of the X-ray volume synthesis models and extended components.In Sect.5, we
emissivity and clustering properties of the X-ray sources use the formulation to compare various models with the
from the ACF (or upper limits of ACF) (e.g. Danese observations. The purpose of the section is to check the
etal.1993; Carrera et al.1991; Soltan & Hasinger 1994). effects of various components on the observed CCF and
While the XRB ACF traces the properties of all the X- we do not intend to construct a complete model consis-
raysourcesalongthelineofsightandthustheinterpreta- tent with all the existing constraints. Such an elaborate
tion is highly model dependent, cross-correlatingcatalogs modeling would be a topic of a future paper. Finally we
of known sources with the XRB gives more concrete in- conclude our discussion in Sect. 6.
formation on the XRB constituents. In particular, cross-
correlation functions (CCF) of unresolved XRB spatial 2. Data
fluctuations with galaxy catalogs give information on the
contribution of these galaxies and objects clustered with 2.1. The ROSAT All-Sky Map
thesesourcestotheXRB(Jahodaetal.1991,1992;Lahav
We have used a clean surface brightness map constructed
etal.1993; Miyaji etal.1994; Roche etal.1994; Barcons
from the ROSAT (Tru¨mper 1983) PSPC (Pfeffermann
etal.1995).
et al. 1986) All-Sky Survey (Snowden & Schmitt 1990;
Auto and cross-correlation function analyses over a
Voges 1992) in the north galactic pole region. In mak-
large region of the sky occasionally discover new compo-
ing the map, the period of Short-Term Enhancements
nents of cosmic X-ray emission. The auto-correlation of
has been excluded and non-cosmic backgrounds (parti-
theHEAO-1A2hardX-raymapnearlyoverthewholesky
cle background, solar scattered X-rays and the Long-
athighgalacticlatitudesrevealedaweaklarge-scalecom-
Term Enhancements) have been subtracted as explained
ponentatθ <∼40◦,whichperhapsisassociatedwithstruc- inSnowdenetal.(1995).Soltanetal.(1995)selectedarel-
tures in the supergalactic plane (Jahoda 1993).Using the
ativelylargeportionofthehighgalacticlatitudeskywhich
ROSAT All-Sky Survey (RASS) data,Soltan etal.(1995)
is free fromcontaminationbygalacticstructurestoinves-
found an extragalactic extended component in the ACF
tigate the extragalactic structures in the soft X-ray sky:
of at 1 keV at a scale of 5 degrees. They also found an
angular correlation at 5 – 10 degree scales in the CCF
between the 1 keV XRB and the positions of the Abell 70◦ < l <250◦, b>40◦. (1)
clusters.They modeledthe lattercomponentasa 10Mpc
scalediffusegassurroundingclustersofgalaxies,whichit- We also use this areafor our correlationwith the hardX-
self had not been recognized in any previous observation. raysky.Wealsoincludeda3.5degreewidestripsurround-
They found, however, that clusters of galaxies, consider- ing this region in our analysis, taking the larger HEAO-1
ingthisputativecircum-clusteremissionandclusteringof A2collimatorresponsefunctionintoaccount.Inthiswork,
clusters,explainonlyaboutathirdoftheirextended1keV we have only used the map in the R6 (PI channel range
Miyaji et al. Cross-Correlation of Soft and Hard X-ray Skies 3
91 – 131, correspondingto 0.9 – 1.3 keV) band (Snowden HRD map. For a power-law spectrum with photon index
etal.1993), which is least contaminated by the galactic α = 1.7, the conversion factor between the TOT count
ph
emission,scatteredsolarX-rays,andparticlebackground. rates and the 2–10 keV flux is 2.2×10−11 erg s−1 cm−2
The energy response curve of the R6 band is shown as a (TOT cts s−1)−1 and the conversion factor between the
solid line in Fig.1. HRD count rates and the 5 – 15 keV flux is 1.8×10−11
The conversion factor between the observed R6 count erg s−1 cm−2 (HRD cts s−1)−1. These conversion factors
rate and the 0.5 – 2 keV flux before the absorption by varyonlyby<∼4%fora40keVbremsstrahlungspectrum,
the Galaxyis 3.24×10−11 ergs−1cm−2/(R6 cts s−1)for a an α = 0.7 power-law, the same power-law with neutral
power-law photon index of (αph =2.0) for the absorption gas absorption up to NH <∼1024cm−2.
column density of N = 1.8 × 1020cm−2, which is the The maps used here have the beam profile (or the
H
average galactic value for the region. The range of the collimator response function) well represented by (Shafer
galactic column in the region is 0.6−4.×1020cm−2 and 1983):
the conversionfactors in that regiondiffer from the mean
valueby<∼5%.ThereforeweusetheaverageNH valuefor B =max(1− |x|,0) max(1− |y|,0) (2)
A2 ◦ ◦
the whole region for the analysis. 3.0 1.5
wherey representsthecoordinatealongthescandirection
of the survey,which is along the greatcircle of a constant
ecliptic longitude,andxisthecoordinatealongthedirec-
tion perpendicular to the scan path.
2.3. Excluded Regions
Regions around conspicuous sources in the R6 band have
been excluded from the analysis in order to avoid the sit-
uationthat afew sourcesdominate the correlationsignal.
Those are the Coma cluster, Abell 1367, Mkn 421 and
NGC 4253(Mkn766).These areallthe sourcesinthe re-
gion with R6 count rates greater than 0.9 counts per sec-
◦
ond. We have excluded 3.4 radius regions (corresponding
to themaximumextentoftheA2 beam)aroundMkn421
andNGC 4253.The exclusionradiusaroundthe twocon-
spicuous galaxy clusters (i.e. the Coma cluster and Abell
◦
1367) was 7 . In addition, we have also excluded the 3.4
Fig.1.EnergyresponsecurvesoftheROSATR6andHEAO-1 degree radius regions around the HEAO-1 A2 sources in
A2TOT/HRDbands,usedinourCCFanalysis,areshownas Piccinotti etal.(1982). The flux cutoff of this complete
labeled. Each curveis normalized at its peak flux-limited catalog is 1.25 counts s−1 in the HEAO-1 A2
R15band,whichissimilarto theTOTAL bandusedhere
but a little harder (Allen etal.1994).
2.2. The HEAO-1 A2 Hard X-ray Map
3. The Soft-Hard Cross-Correlation Function
We have used the all-sky hard X-ray map constructed
3.1. The CCF calculation
from the combination of the HED3 and MED detectors
of the HEAO-1 A2 experiment (Rothschild etal.1979). Wehavecalculatedtheangularcross-correlationfunctions
The combinationofthe detectorsissensitivein2–60keV. between the ROSAT All-Sky Survey R6 and HEAO-1 A2
Conventionallyall-skymapsfromthiscombinationarean- maps in the region defined in Eq.(1). Since the ROSAT
alyzedinanumberofstandardcolorsdefinedasweighted All-Sky map has a much higher spatial resolution and
sums ofcounts from certaincombinationsof detector lay- densersamplings,wehavesmoothedtheROSATdatabe-
ers andpulse heightchannels (discoveryscalers;see Allen fore correlating. As the smoothing function, we took the
etal.1994). In this work, we have used the TOTAL (in- form represented by Eq. (2) but smaller FWHMs in or-
dicated by TOT) and HARD (indicated by HRD) band der to improvethe signal-to-noiseratioofthe correlation.
maps. The energy response curves of the TOT and HRD Amonganumberofsizeswetriedforthesmoothingfunc-
◦
bands are shown as dashed and dotted lines respectively tion,thebestresultscouldbeobtainedwhenwechose1.5
◦
in Fig.1.For the cosmic X-raybackgroundandcanonical and0.75(FWHMs)inthexandydirectionsrespectively.
AGNspectrum,mostofthephotonscomefromthe2–10 As a statistical measure to indicate the degree of cor-
keVrangefor the TOTmap and5 –15 keVrangefor the relation between two maps (here we denote the two maps
4 Miyaji et al. Cross-Correlation of Soft and Hard X-ray Skies
by subscripts s and h, representing soft and hard respec- background from immediate surroundings. Then we slid
tively),wecalculatetheangularcross-correlationfunction the detection cell againto the originalmap to find signif-
(CCF): icant excess counts over the background map created in
the above process (MDETECT).
N−1 [(I −hI i)(I −hI i)]
pair ij si s hj h Thesourcedetectionhavebeenmadeusingprocedures
W (θ)= , (3)
sh P hI ihI i within the EXSAS software package (Zimmermann et al.
s h
1994). The size of the detection cell has been taken to be
where Is and Ih are the ROSAT and HEAO-1 A2 inten- 3×3 cells (36′ ×36′) and the source detection threshold
sities measured at the gridding points which are within
is set at a significance of −logP = 10, where P is the
the region defined above. We have taken pairs along the i i
probabilitythattherandomPoissonfluctuationmakethe
scanpath(eclipticlongitude)tocalculatetheangularcor-
excesscountsinthecell.Thisroughlycorrespondstoa4σ
relation in order to make use of the narrower collimator
excessofa Gaussianfluctuation.Since theROSATPSPC
response.
PSF and extents of clusters of galaxies (except for closest
The uncertainties of the correlationfunctions are esti-
ones, which have been excluded from the analysis (Sect.
matedbycorrelatingtheROSATmapwithdifferentparts
2.3) are much smaller than the size of the detection cell,
of the sky in the HEAO-1 A2 map. We made this by
thesourcelistfromtheMDETECTprocedureisexpected
rotating the ROSAT map around the galactic pole and
to be free from significant biases.
calculating the correlation with the A2 map in the same
Intheleastsensitiveareas,thedetectionlimitwas0.08
way.We have alsotransposedthe ROSAT mapabout the R6ctss−1.IfweassumeaSeyfert1-likebrokenpower-law
galactic equator followed by rotations about the galactic
spectrum with α = 2.3 for E ≤ 1.5 keV, α = 1.7 for
pole to calculate the correlation with the A2 map. Thus ph ph
E > 1.5 keV, and the average galactic N of the region
we produced a number of different artificial null samples H
(=1.8×1020cm−2), 0.08 R6 cts s−1 corresponds to a 0.5
withequivalentstatisticalproperties.RegionsaroundPic-
– 2 keV flux of 2.7×10−12 ergcm−2s−1 and 2 – 10 keV
cinottietal.sourcesareexcludedaswed◦idinthe◦realcor- flux of 3.8×10−12 ergcm−2s−1.
relationcalculation.Wealsoexcluded20 and25 regions
By this procedure, we have obtained a complete flux-
around LMC and SMC respectively. We have rotated the
◦ limited (> 0.08R6ctss−1) sample of 183 sources above
map in steps of 30 on both hemispheres, thus we get 23
this limit over the 4575 deg2 area of the sky (0.04
null-hypothesis CCFs between unrelated parts of the sky.
sources deg−2). The log N – logS function of the de-
These give a fair estimate of the uncertainties of the cor-
tected sources has a Euclidean slope. The number den-
relation function.
sity correspondsto that ofthe Einstein Medium Sensitiv-
ity Survey (EMSS) (Gioia etal.1990) above 4.1×10−12
3.2. CCF of ROSAT bright sources with the HEAO-1 A2 ergcm−2s−1 in 0.3 – 3.5 keV. They are consistent if
Maps
the 0.3 – 3.5 keV flux versus R6 count rate conver-
In order to evaluate the contribution to the CCF from sion factor is ∼ 5 × 10−11 ergs−1cm−2(R6ctss−1)−1.
bright ROSAT sources, we have made a list of bright For a power-law spectrum with αph = 2.0, this factor
sourcesbyperformingasourcedetectionproceduretothe is ∼ 5.7 × 10−11 ergs−1cm−2(R6ctss−1)−1 and for a
R6 map in the region defined in Eq.(1). The source de- kT = 2 keV Raymond-Smith spectrum (heavy element
tection has been made to the map gridded in 12′ × 12′ abundance=0.4 cosmic), this number is ∼ 4.4 × 10−11
pixels, larger than the ROSAT PSPC point spread func- ergs−1cm−2(R6ctss−1)−1.Thusourbrightsourcecounts
tion, and thus is much less sensitive than the source de- are consistent with the EMSS counts considering a possi-
tection procedure directly applied to the full-resolution ble range of the source spectra.
ROSAT All-Sky Survey data. A ROSAT All-Sky Survey We have calculated the CCF between the detected
bright source list using such a procedure (Voges 1995) is sources (R6 count rate weighted) and the HEAO-1 A2
in progress at the time of writing this paper. An analysis maps in the same way as Sect. 3.1. The errors of these
using the source list will be a topic of a future paper. In CCFs have been calculated also in the same manner.
this work, we use the coarsely rebinned map to obtain a Using the detected sources, we have also constructed
complete R6 flux-limited sample of bright sources.As de- a source-removed ROSAT map. This has been made by
scribedbyHasingeretal.(1993),thesourcedetectionhave replacing the 3×3 image pixel regions around the sources
beenmadeintwosteps:thefirststepistoslideadetection with R6 count rate greater than 0.08 cts s−1 by the pixel
cell over the map and find excess over the region imme- values in the same regions of the background map pro-
diately surrounding the cell (LDETECT). A background ducedfortheMDETECTprocedure(seeabove).Wehave
map was created by removing the sources detected in the alsocalculatedtheCCFbetweenthesource-removedmap
LDETECTprocedure,fillingtheholesbythemeancounts and the HEAO-1 A2 maps.The source-removed map still
surrounding them, and making a bi-cubic spline fit to the contains sources below the limit and we expect that such
filled map. This procedure gives a more robust measure fainter sources still contribute to the correlation.
ofthe backgoundfor the sourcedetectionthantaking the
Miyaji et al. Cross-Correlation of Soft and Hard X-ray Skies 5
Table 1. The Zero-lag Correlation Results
Id. R6cr. range HEAO-1 hIsi hIhi Wsh(0)
[cts s−1] A2Band [cts s−1 deg−2]
T1 0 – 0.9 TOT 2.9×10−1 7.2×10−1 (3.2±0.4)×10−3
T2 0 – 0.08 TOT 2.9×10−1 7.2×10−1 (1.7±0.3)×10−3
T3 0.08 – 0.9 TOT 6.1×10−3a 7.2×10−1 (6.6±1.0)×10−2
T4 0.2 – 0.9 TOT 2.6×10−3a 7.2×10−1 (8.3±1.7)×10−2
H1 0 – 0.9 HRD 2.9×10−1 8.6×10−1 (2.4±0.4)×10−3
H2 0 – 0.08 HRD 2.9×10−1 8.6×10−1 (1.0±0.3)×10−3
H3 0.08 – 0.9 HRD 6.1×10−3a 8.6×10−1 (5.4±1.6)×10−2
H4 0.2 – 0.9 HRD 2.6×10−3a 8.6×10−1 (6.6±2.6)×10−2
a Intensity from sources in the quoted fluxrange
3.3. Results of the CCF Calculations The angular correlation functions for selected cases
have been plotted in Fig. 2 along with the angular cor-
Significant zero-lag correlation signals have been de- relation functions between the rotated R6 maps with the
tected inmostofthe caseswe havecalculated(θ =0 case A2 map to show the dispersion of the CCF when no real
of Eq. [3]). Table 1 summarizes the zero-lag correlation sky-correlationexists.Thelabelineachfigurecorresponds
resultsforthecalculationswemadeforvariouscases.The to the correlation ID in Table 1. Also the angular depen-
second column of Table 1 is the R6 count rate range of denceoftheCCFincaseofthepurelyPoissoniancase(see
the sources correlated with the A2 map. A zero value of Sect.4)duetotheA2collimatorreponseandtheROSAT
the lower bound in this column means that the R6 sur- All-Sky Survey map smoothing, normalized at θ =0, has
face brightness map has been used and a non-zero value beenplottedoneachplot.Inanycase,wedidnotfindsig-
represents that the source list in the quoted flux range nificant extended component in the angular CCF beyond
explained in Sect. 3.2 has been used. expected from the Poissoneffect.
4. Basic Formulations
The CCF depends on Poisson and clustering effects. The
Poisson effect is caused by individual sources which emit
both soft and hard X-rays and the angular dependence
of the correlationcoefficient simply reflects the overlapof
the finite-sizedbeamsofsoftandhardX-rayobservations
and smoothings.The clustering effect reflects the realsky
structureoftheX-raysourcescommonto(oratleastcor-
related with) both soft and hard X-rays. This structure
may be due to clustering of sources or a diffuse X-ray
component which extends to a scale comparable or larger
than the size of the beam. If one is concerned with real
extended structure, the distinction between Poisson and
clusteringeffects issomewhatambiguous.Inourcase,the
extent of the X-ray emission from an individual galaxy
cluster is much smaller than the beam size of the HEAO-
1 A2 experiment and thus we treat them in the Poisson
term. On the other hand, we treat the effect of possible
diffuse components with scales of several degrees in the
clustering effect.
The observed angular correlationfunction is then, ex-
Fig. 2. The angular CCF for selected cases as labeled. The
pressed by the sum of two terms (cf. Lahav et al. 1993;
open octagons show the observed correlation and the dotted
Miyaji 1994; Miyaji etal.1994):
lines show the 23 uncorrelated cases. The solid line is the an-
gular dependenceof thePoisson effect caused by theA2 colli-
mator response function and smoothing W (θ)hI ihI i=η (θ)+η (θ), (4)
sh s h p c
6 Miyaji et al. Cross-Correlation of Soft and Hard X-ray Skies
whereI representtheintensitiesofsoftandhardX-rays maps. Thus the bounds of the luminosity integrationsde-
s,h
per beam respectively: pendonredshiftandthespectrumofthepopulation.Now
letthesoftandhardX-rayluminositiesofeachpopulation
I ≡ hI iB (Ωˆ)dΩ≡hI iΩ , (5) be related by Ls = aiLh. Then the double integral over
s,h Z s,h s,h s,h Bs,h hard and soft X-ray luminosities can be reduced to:
whereΩˆ istheunitvectortowardsthesolidangleelement Lmsax LmhaxL L Φˆ (L ,L ,z)dL dL
dΩ. ZLmsin ZLmhin s h i s h h s
As we will see in Sect. 5, the correlationis dominated min(Lmsax ,aiLmhax)
by local sources and cosmological evolution is not impor- = a L2Φˆ (L ,z)dL , (8)
Z i s s s s
tantinourcase,becauseofthelargebeamoftheHEAO-1 max(Lmsin,aiLmsin)
A2 experiment. However,we will developa full cosmolog- ˆ
where Φ (L ,z) is the comoving soft X-ray luminosity
s s
ical formulation below for completeness.
function,whichwecanfindinliteraturebasedonROSAT
surveys (e.g. Boyle et al. 1993, 1994). In the case of the
4.1. Poisson Effect from Common Sources pure-luminosity evolution of the power-law form, L(z) =
L(0)(1+z)p, the evolving luminosity function can be ex-
We can express the Poisson term of the cross-correlation
pressed by the present epoch one:
function as:
Φˆ (L ,z)=Φˆ ([1+z]−pL ,0)(1+z)−p. (9)
si s si s
η (θ)= S S N (S ,S )dS dS ×
p Z Z s h sh s h s h
4.2. Extended Component
h B (Ωˆ)B (Ωˆ −θ)dΩi, (6)
Z s h The underlying angular CCF of the soft and hard X-ray
skies
where N (S ,S )dS ,dS is the bivariate N(S) function
sh s h s h hI (Ωˆ)I (Ωˆ +θ)i
definedasthenumberofsourcespersolidanglewhosesoft w (θ)≡ s h −1, θ >0 (10)
sh
hI ihI i
andhardX-rayfluxesfallin the ranges[S −0.5dS ,S + s h
s s s
0.5dSs]and[Sh−0.5dSh,Sh+0.5dSh]respectively.Alsoθ reflects the extended structure common to soft and hard
is the offset vector between hard and soft X-ray measure- X-rays and clustering of X-ray sources.
ments.Thefluxintegrations(overSsorSh)areoversource The observed angular correlation function (Wsh(θ)) is
fluxesincludedinthecorrespondingmaps.Whenweusea contributed by the underlying angular cross-correlation
surface brightness map where bright sources above a cer- function w (θ) of the real sky. The term η in Eq. 4 re-
sh c
tainlimitareexcluded,thislimitdefinestheupperbound flects this component:
of the integration and the lower bound is zero. When we
η (θ)=hI ihI i×
use a complete flux-limited source list, this flux limit de- c s h
fines the lower bound. w (θ′)B (Ωˆ )B (Ωˆ −θ)dΩ dΩ , (11)
The double integral over the soft and hard fluxes Z Z sh s 1 h 2 1 2
in Eq. (6) can be calculated for given population syn- whereθ′ =|Ωˆ −Ωˆ +θ|.Ineffect,the underlyingangular
1 2
thesis models. Let us suppose we have evolving popula-
correlation function is smoothed with the convolution of
tions of objects with the bivariate soft-hard luminosity
softandhardbeams.Atlargeseparations(θismuchlarger
function (for the i-th population) per comoving volume:
thanthe scalesizeofthe beam),W (θ)≈w (θ) andthe
Φˆ (L ,L ,z)dL dL , where each population is assumed sh sh
i s h s h Poisson term is zero.
to have a universal spectral shape for simplicity. Then,
Theunderlyingw canbeexpressedbythecosmolog-
sh
c zmax ically evolving soft and hard volume emissivities and the
Z SsShN(Ss,Sh)dSsdSh = 16π2H Z × spatialcorrelationfunctionofsoftandhardX-raysources.
0 0 The expression is quite parallel to the case of ACF found
1
[K (z)K (z)× in literature (e.g. Danese etal.1993; Soltan & Hasinger
DL(z)2(1+z)3(1+Ω0z)21 i=Xpop si hi 1994).Let us consider populations of soft and hard X-ray
Lmsax Lmhax emitting sources with redshift dependent comoving vol-
Z Z LsLhΦˆi(Ls,Lh,z)dLhdLs ] dz, (7) ume emissivities of ρˆs(z) and ρˆh(z). Let the spatial cor-
Lmsin Lmhin relation function between these populations be ξsh(r,z).
Then, in the small-angle long-distance approximation,
where D (z) is the luminosity distance as a function of
L
redshift and K is the soft (hard) band K-correction c
s(h)i w (θ)= ρˆ(z)K (z)ρˆ (z)K (z)×
for the i-th population. The luminosity integrations are sh 16π2H Z s s h h
0
overluminositieswheretheobservedfluxfallsintherange
of source fluxes included in the corresponding correlating Z ξsh( (DAθ)2+x2,z)dx(1+z)−4(1+Ω0z)12dz, (12)
p
Miyaji et al. Cross-Correlation of Soft and Hard X-ray Skies 7
where K (z) and K (z) are the K-corrections for the because this quantity is proportional to the contribution
s h
soft and hard X-ray bands respectively and D (z) (= from each of the R6 sources at a certain flux-range and
A
D (z)(1+z)−2) is the angular distance. source-removedbackground.
L
5. Comparison of Models with Observations
Table 2. Comparison of correlation results with models
5.1. AGN and Cluster Contributions
We have calculated the expected contributions from two Wsh(0)hIsihIhi
major classes of extragalactic X-ray sources, i.e. AGNs Id. [10−4 R6cts s−1 A2 cts s−1]
Observed Modelsa
and clusters of galaxies, to the observed zero-lag correla-
P1 P2 P3 E1 E2
tion strengths using the population synthesis technique.
For the following models, the standard cosmology with T2 3.5±0.6 0.9 1.3 0.9 3.1 1.9
Λ=0andq =0hasbeenused.We alsodenotethe Hub- T3 2.9±0.4 2.5 3.6 2.5 ... ...
0
ble constant by H = 50h kms−1Mpc−1. Note that the
0 50
expected correlations from the models do not depend on H2 2.5±0.7 0.7 1.1 0.8 0.8 0.2
H3 2.8±0.8 1.7 2.5 1.7 ... ...
the value of the Hubble constant.
As the first model (Model P1, where P represents a See Sect. 5.1 for theexplanation of model P1, Sect.5.3
the Poisson effect) we have constructed an AGN popu- for P2 & P3, and Sect. 5.5 for E1 & E2
lation synthesis model following the recipe by Comastri
etal.(1995) for their baseline model. Contributions from
X-ray clusters of galaxies have been added. In adding the
Figure 3 shows the cumulative contributions of clus-
cluster contribution, we have used the analytical forms
ters, type 1 AGNs and type 2 AGNs in model P1 to the
of the 2 – 10 keV X-ray luminosity function (XLF) by
W (0)hI ihI i values for selected correlations. The ob-
sh s h
Edge etal.(1990). We have used their volume-limited
servedvaluewith±1σrangeisshownforeachcorrelation.
expression for z < 0.1 and flux-limited expression for
As we see in Table 2 and Fig. 3, model P1 is consistent
0.1 ≤ z < 0.17, taking into account the deficit of most
within2σwiththeobservedcorrelationsbetweenA2maps
luminous clusters at higher redshifts they observed. In
andbrightR6sources(T3andH3).Wealsoseethatthese
the 0.17 ≤ z < 0.6, we have used the power-law forms
correlationsare dominatedby clusters ofgalaxies.Onthe
oftheXLFgivenbyHenryet al.(1992)intheirthreered-
other hand, the observed correlations between the bright
shift bins. They showed the steepening of the XLF for
source removed R6 map and the A2 maps are about a
higherredshiftbins.Thustheirpower-lawformwouldpre-
factor of 3 – 4 larger than the model predictions. In any
dict too large an XLF at low X-ray luminosities (below
case, the correlation is dominated by sources in the local
their sample limit). Thus we take the smaller (in comov- universe (z <∼ 0.2) and the expected correlation does not
ing coordinates) of the Edge et al. analytical form and
depend on the cosmological evolution significantly. The
the Henry et al. power-law form. We have taken the 2–
contribution of galactic stars, effects of minor modifica-
10 keV X-ray luminosity range of 0.01 ≤ L ≤ 120,
x44 tions to the model, and the effects of possible extended
whereL representsX-rayluminositymeasuredinunits
x44 components are discussed in the followings.
of 1044h−2ergs−1. The clusters have been assumed to
50
haveX-rayspectra representedby the Raymond& Smith
5.2. Contribution of Galactic Stars
plasma with a heavy element abundance of 0.4. The tem-
peratures of a cluster have been chosen from kT = 1, Amongthe835serendipitouslyfoundX-raysourcesin780
1.5, 2.5,4, 7, 10 keV, according to its luminosity between deg2ofhighgalacticlatitudeskyintheEinsteinExtended
the minimum and the maximum values given above. The MediumSensitivitySurvey(EMSS),about25%areinden-
dividing luminosities are L = 0.02, 0.1, 0.5, 3.0, and tifiedwithgalacticstars(Stockeetal.1991).Theidentifi-
x44
15.0, which roughly corresponds to the X-ray luminosity cationwas96%completeandtheflux limits ofthesurvey
versus temperature correlation (David et al.1993). There range between0.5 – 34 ×10−13ergs−1cm−2 inthe 0.3–3.5
is a significant scatter in the luminosity – temperature keV band. When converted to the ROSAT R6 band, this
correlation but this has not been taken into account in corresponds to a flux range just below the detection limit
the model. However, the results are insensitive to the de- in our source detection discussed in Sect. 3.2. Based on
tailedassumptiononthisL –T correlation.Forexample, the flux-number (log N – log S) relation for the EMSS
x
assuming a single temperature of kT =4 keV for allclus- sample of stars, we have estimated the contribution of
terschangedthe resultby10%forT2,whichissomewhat Galactic stars to the present correlation signals. Assum-
smaller than the statistical error of the observation. The ing a kT = 2 keV Raymond & Smith plasma spectrum
expected correlation from this model is compared with with cosmic abundances, which is typical of a variable
data in Table 2. We compare the values of W (0)hI ihI i hardcomponentofstellarcoronalemission,theestimated
sh s h
8 Miyaji et al. Cross-Correlation of Soft and Hard X-ray Skies
Fig. 3.Thecumulativecontributionsofclusters,type1and2AGNs,andthetotaloftheseformodelP1totheobservedCCFs
are plotted. Each component is drawn in a different line style as labeled in the lower left panel. The observed values with 1σ
errorbarsarealso shown. Thehorizontal positioning ofthe observeddatadoesnothaveanysignificance butplaced thereonly
for theconvenienceof thedisplay.
contributionto the R6 backgroundversusA2 TOT corre- In model P2, each AGN has an unabsorbed Raymond
lation (T2) is ≈ 3% and R6 source versus A2 TOT cor- & Smith plasma component of kT = 1 keV with a 0.5 -
relation (T3) is ≈10% of the observed. Thus, the contri- 2 keV luminosity of 2×1042h−2ergs−1. This is a typical
50
butionsofgalacticstarstotheobservedcross-correlations value for most luminous groups of galaxies found in the
are within the statistical errors and not significant. ROSAT North Ecliptic Pole Survey (Henry etal.1995).
Thespatialnumberdensityofgroupsofgalaxiesatthislu-
minosity is severaltimes 10−5h3 Mpc−3,whichis compa-
50
rable to the number density of Seyfertgalaxiesandabout
5.3. Unabsorbed Soft Component associated with AGNs
two ordersofmagnitude smaller thanthe number density
In our model P1, we used the AGN population synthe- of bright spiral galaxies. Thus, it is unlikely that every
sis model by Comastrietal.(1995).We here consider two AGN is associated with a group of galaxies at this lumi-
minormodificationstothismodel.Ifasignificantfraction nosity.Thepurposeofthismodelisnottoberealisticbut
of AGNs are embedded in groups of galaxies with X-ray toexaminetheeffectoftheadditionalcomponent.Table2
emittinggaswithkT ∼1keV,thiscouldcontributetothe shows that adding this component has little effect on the
soft-hard correlation. In many type 2 AGNs, there is an correlations T2 and H2, thus fails to explain the excess
unabsorbed X-ray emitting component, which is believed correlation even in this extreme case.
to be electron-scatteredX-rays from the nucleus. Comas- As another model, P3, we put a soft component to
tri et al. (1995) etal.deliberately neglected this compo- AGNs with fluxes proportional to the intrinsic (i.e. un-
nent because its luminosity is much weaker than the soft absorbed) luminosity. The underlying idea of this model,
X-ray luminosity in type 1 AGNs with a comparable op- in terms of the unified scheme of AGNs, is to add an
tical luminosity. We see the impact of these effects to our unbasorbed X-ray component in Seyfert 2, which is gen-
correlation. erally considered as electron-scattered nuclear emission.
Miyaji et al. Cross-Correlation of Soft and Hard X-ray Skies 9
LikeMadauet al.(1994)consideredintheirmodel,weas- ulatedthatthis componentcouldbe due tothe clustering
sume that 2%ofthe nuclear emissionintype 2 AGNs are of groups of galaxies. However, information on statistical
from the scattered component and can reach us without properties of groups of galaxies was very scarce and they
being absorbed. As we see in Table 2, this component is did not make further arguments on this possibility.
◦ ◦
not sufficient to explain the observed excess correlation TheexpectedR6ACFat∼1 –3 fromtheclusterings
over model P1. ofAGNandclustersusedinmodelP1usingEq.12(inthis
case,twobandsintheexpressionarethesame)aretwoor-
dersofmagnitudesmallerthantheactualvaluesobserved
5.4. Low-Luminosity Flat X-ray Spectrum Galaxies
by Soltan et al. (1995). We also checked if the AGN and
The Comastri et al. (1995) model deliberately neglected cluster clusterings can explain the excess correlation in
the contribution of low X-ray luminosity objects (Lx <∼ our zero-lag CCFs (T2 and H2). The expected clustering
1042h−502ergs−1) to the hard X-rays (E >∼ 2 keV), while effects to the ROSAT – HEAO-1 zero-lag CCFs (because
they left some room for these objects to contribute to of the beam smearing, the zero-lag values are mainly due
soft X-rays (E <∼ 2 keV). However, Yaqoob et al. (1995) to the clustering at a scale of 1◦) for the same model are
recently reported that NGC 3628, a low X-ray luminos- also two orders of magnitude smaller than the observed
ity object, which had usually been classified as a star- excesses. For these estimates, we have assumed a form
burst, has a rather flat X-ray spectrum (a photon in- ξ(r,z) = (r/r0)−γ(1+z)−3−ǫ for r < 3r0 and ξ(r,z) = 0
dex of αph = 1.2). Based on this observation, they ar- for r ≥ 3r0. The parameters used for the estimations are
gued that a class of sources represented by this object (r0[kms−1], γ)=(1000,1.8),(2400,1.8)and(880,2.2)for
could contribute significantly to the XRB. Here we esti- the AGN-AGN, cluster-cluster (Bahcall 1988) and AGN-
mate the contributionof the possible low luminosity pop- cluster (Lilje & Efstathiou 1988) correlationfunctions re-
ulation to our correlations. For an estimation, we con- spectively. At the angular scales of degrees, the expected
sider low-luminosity X-ray galaxies of the 2 – 10 keV lu- correlation is insensitive to the cosmological evolution of
minosity range of 1040 − 1042h−2ergs−1 at the present clustering and we have used ǫ = 0. Since the discrepan-
50
epoch. We assumed a power-law differential lumninos- cies are two orders of magnitude, we also expect that the
ity function (dΦ(L )/dL ∝ L−γ) with γ = 1 and to- clustering of low X-ray luminosity objects (galaxies, low-
x x x
tal 2 – 10 keV present-epoch volume emissivity of 2 × luminosity AGNs),whichhavenotbeenconsideredinthe
1038h ergs−1Mpc−3.Thisvolumeemissivityisanupper above calculation, cannot make much contribution, since
50
limit from the low-luminosity source contribution derived their 2 – 10 keV X-ray volume emissivity should be lower
by Miyaji et al. (1994) based on the XRB- IRAS galaxy than that of AGNs (Miyaji et al. 1994). Thus we expect
cross-correlationandhasbeenconsideredintheYaqoobet that the Soltan et al.’s extended ACF component truely
al.baselinemodel.Forthispopulation,wehaveassumeda represents a new population of X-ray structure.
power-lawspectrumwithα =1.2andsimpleluminosity Here we consider a picture that the component re-
ph
evolution of ∝(1+z)3.2 up to z =2. The contribution of sponsible for the Soltan et al.’s ACF component is also
this population to our correlation calculated using above responsible for the excess zero-lag CCF in T2 and H2.
assumptions is only ∼1% for either T2 or T3. Note that, We constrain the nature of this component by compar-
◦
in this model, most contribution to the correlation signal ing the upper-limit to our θ = 2.5 CCF with their ACF
comesfromaroundz ∼0.1,unlikethecontributiontothe and also investigate the contribution of this component
totalsurfacebrightness,whichismostlycontributedfrom to our zero-lag CCF. Since the spatial resolution of their
thehigh-redshiftregiongiventhisevolutionlaw.Thusthis ACFmeasurementismuchhigherthanourCCFmeasure-
estimate is insensitive to the detailed behaviorof the cos- ment, we havesmoothed their ACF with the beam of our
mologicalevolution.Theaboveestimationshowsthat the CCF (see Eq. [11]) and compared it with our CCF. The
lowX-rayluminositygalaxiescannotexplaintheobserved smallest angle where there is no overlap of the beams is
◦
excess correlationin T2 or H2. at θ ∼ 2.5 . At this angle, the smoothed ACF value is
∼ 1×10−3, while the 2σ upper-limit of our CCF (T2) is
3×10−4. Assuming that the detected R6 ACF is domi-
5.5. Extended Emission Component
nated by a single component with a single spectrum, the
We consider here the effect of the clustering term (or ex- hard-to-soft flux ratio Ih/Is of this component is:
tended components) to the observed W (0). In the ex-
sh (I /I )=(W hI i)/(W hI i). (13)
h s sh h ss s
tragalactic component of the R6 (1 keV) map, Soltan
etal.(1995) found a significant extended component in The upper limit to this ratiois 1.3 (TOT cts s−1) (R6 cts
the auto-correlation function (ACF) at a scale of θ <∼ 5◦. s−1)−1. This corresponds to a Raymond & Smith plasma
They arguedthat the ACF signalthey have found should with kT <∼2.5 keV or a power-lawphoton index of αph >∼
bedominatedbyrealextendedstructuresratherthanclus- 2.3foragalacticcolumndensityofN =1.8×1020cm−2.
H
tering of sources, based on comparison with the ACF in Assuming that the structure causing the extragalactic
Soltan and Hasinger (1994) at smaller scales. They spec- 1 keV(R6) ACFin Soltanetal.(1995)inthe (0.1◦ <∼θ <∼
10 Miyaji et al. Cross-Correlation of Soft and Hard X-ray Skies
◦
3 )comesfromasingleextendedcomponent,wehavecal- the zero-lag amplitude of the CCFs. This means that if
culatedtheexpectedzero-lagR6-A2CCF(W (0)).These the extended component in the R6 ACF is a thermal
sh
values are shown under the models E1 (assuming a kT = plasma with kT ∼ 2 keV this would also explain the ex-
2 keV Raymond-Smith spectrum) and E2 (kT = 1 keV) cess zero-lag CCF over the model P1 prediction in our
(E representsthe extended). Aheavymetalabundance of source-removedCCFswithin2σ.ConsideringthattheH2
0.4(cosmic)hasbeenusedinthese estimations.Since the zero-lag correlation still exceeds the model P1+E1, while
ROSAT R6 (1 keV) band is dominated by the Fe L emis- statistical significance is poor, a flatter spectrum in the
sion lines, this estimate is sensitive to the heavy element E >∼ 2 keV range for this component is preferred. It is
abundance and should be taken as a rough measure. possiblethattheR6ACFsignalSoltanetal.(1995)found
is composed of more than one component. For example,
a composite model with a small-scale (θ <∼2◦) hard com-
ponent and a large-scale (2◦ <∼ θ <∼ 5◦) soft component
would better explain the data.
6. Concluding Discussions
As we see from the analysis presented above, AGNs
and clusters account well for the correlation between the
ROSATbrightR6sources(>∼0.08R6ctss−1,corresponds
to 2.5×10−12ergs−1cm−2) and the HEAO-1 A2 surface
brightness. This correlation is dominated by the Pois-
son effect from individual clusters of galaxies in the lo-
cal universe. On the other hand, the correlationsbetween
the residual R6 background and the HEAO-1 1 A2 sur-
face brightnesses are about a factor of 3 – 4 larger than
the Poisson effect expected from the population synthe-
sismodelbyComastrietal.andclustersofgalaxiesbased
on the known X-ray luminosity functions. We have con-
sidered a few possible components which have not been
considered in the population synthesis model, i.e., AGN-
groupassociation,unabsorbed(scattered)softcomponent
in type 2 AGNs, and low-luminosity X-ray galaxies. Any
ofthesethreearenotlikelytoexplaintheobservedexcess
correlation.
Due to the large collimator beam of the HEAO-1 A2
experiment, the zero-lag correlation could also be con-
tributed by the clustering effect or an extended com-
ponent. The extragalactic 1 keV (R6) angular auto-
correlationfunction (ACF) by Soltan et al. (1995)clearly
shows an extended structure up to a separation of sev-
eral degrees. The origin of this component is not clear at
thismoment.Theyshowedthattheeffectsofrichclusters
including the cluster-cluster clustering and the putative
∼ 10 Mpc-scale diffuse gas component in their model to
explaintheAbellcluster–1keVcross-correlationfunction
only amounts to about one third of the R6 ACF signal.
Fig. 4. The observed angular CCFs for the source-removed
They suggested diffuse emission from groups of galaxies
cases are shown with two models as indicated. The 1σ error
could possibly contribute to the R6 ACF. However, sta-
barsarefrom thescatters in the’rotated’ correlations (dotted
tistical properties concerning poor groups, e.g. luminos-
lines in Fig.2). Note that the errors in data points are not
ity/temperature functions and clustering properties with
independentbut highly correlated
richclusters/AGNs,arescarcelyknown.Comparingthe 1
keVACFwiththeupper-limittoourR6–A2(TOT)CCF
◦
Figure 4 shows the comparisons of the observed and atθ =2.5 ,theminimumangularseparationwherebeams
modeled angular CCF for the source-removed cases. The do not overlap, we have constrained the spectrum of the
models shown are E1 and E2 in addition to P1 as la- extended structure causing this R6 ACF signal. This cor-
beled. As we see in Fig. 4, model (P1+E1) could explain responds to a Raymond& Smith plasma of kT <∼2.5 keV
