X-ray observations of the galaxy cluster PKS 0745-191: To the virial radius, and beyond

0.78 MB·English

by  Matthew R. George

Mon.Not.R.Astron.Soc.000,000–000(0000) Printed22January2009 (MNLATEXstylefilev2.2)
X-ray observations of the galaxy cluster PKS 0745-191: To the virial
radius, and beyond
M. R. George,1⋆ A. C. Fabian,1 J. S. Sanders,1 A. J. Young2 and H. R. Russell1
1InstituteofAstronomy,MadingleyRoad,CambridgeCB30HA
2H.H.WillsPhysicsLaboratory,UniversityofBristol,TyndallAvenue,BristolBS81TL
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2 Accepted22January2009

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ABSTRACT
J
WemeasureX-rayemissionfromtheoutskirtsoftheclusterofgalaxiesPKS0745-191with
2
Suzaku,determiningradialprofiles of density,temperature,entropy,gasfraction,and mass.
2
These measurementsextendbeyondthe virialradiusfor the firsttime, providingnew infor-

] mationaboutclusterassemblyandthediffuseintraclustermediumoutto∼ 1.5r200(r200 ≃
h 1.7Mpc≃15′).Thetemperatureisfoundtodecreasebyroughly70percentfrom0.3−1r200.
p We also see a flattening of the entropyprofile near the virialradius and considerthe impli-
- cationsthishasfortheassumptionofhydrostaticequilibriumwhenderivingmassestimates.
o
Weplacetheseobservationsinthecontextofsimulationsandanalyticalmodelstodevelopa
r
t betterunderstandingofnon-gravitationalphysicsintheoutskirtsofthecluster.
s
a
Keywords: galaxies:clusters:individual:PKS0745-191–X-rays:galaxies:clusters–galax-
[
ies:clusters:general

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v
0
3
1 1 INTRODUCTION symmetry and hydrostatic equililbrium between the gas pres-
1 sure and gravitational potential. Though numerical simulations
Theoutskirtsofgalaxyclusterspresentanopportunitytostudythe
. predict a decline in temperature towards the virial radius (e.g.,
7 formation of largescale structure as it happens. Beyond the core
0 Evrardetal.1996;Frenketal.1999;Lokenetal.2002),observa-
wherenon-gravitationalprocessessuchascoolingflowsandfeed-
8 tionsatsmallerradiihaveproducedinconsistentresults.Someanal-
backfromactivegalacticnucleicandominateactivity,clustersare
0 yses have found declining profiles (e.g., Markevitchetal. 1998;
expectedtobemorerelaxedandtofollowself-similarscalingrela-
: DeGrandi&Molendi 2002; Vikhlininetal. 2005; Prattetal.
v tions(Kaiser1986).Thevirialradiuscanbethoughtofasaborder
2007),whileothershaveseenascatteringofslopesconsistentwith
i betweenregionsofequilibrationandinfall,somergeractivityfrom
X flatorevenincreasingprofiles(e.g., Irwinetal.1999;Zhangetal.
accretingmaterialmayplayanimportantroleintheouterdynam-
r 2004;Arnaudetal.2005).Thesestudiestypicallydonotmeasure
ics.
a thetemperatureprofilesmuchfurtheroutthanhalfthevirialradius,
As the largest virialized systems in the universe, clusters of
evenwithChandraandXMM.Differentmethodsofestimatingthe
galaxies can be useful in constraining cosmological models. The
virialradius,usingeitherscalingrelationsordirectdetermination
positionofclustersatthehighendofthemassspectrumandtheir
from the mass profile, make comparisons difficult, but very few
evolutionfromtheinitialdensityperturbationsmakesthemsensi-
measurements havebeen made of cluster gastemperatures out to
tive probes of the scale of these fluctuations, σ8, and the density thevirialradius(e.g., Solovyevaetal.2007;Reiprichetal.2008),
ofmatterintheuniverse,Ωm (Whiteetal.1993;Ekeetal.1996). andtoourknowledgenonehavebeenreportedbeyondit.
Additionally,theevolutionwithredshiftofclusterpropertiessuch
Until recently, X-raydetectors have been unable tomeasure
asthegasmassfractioncanbeusedtostudyotherportionsofthe
thetemperatureoftheintraclustermedium(ICM)outtothevirial
cosmicenergydensitybudget(e.g., Allenetal.2008).Forareview
radius due to its low surface brightness in the outskirts relative
ofthecosmologicalimportanceofgalaxyclusters,seeVoit(2005).
to background noise. Typically a mass profile such as that of
To understand cluster properties, it is important that the re-
Navarro,Frenk&White(1997, NFW)isusedtoextrapolatemass
lationships between observables and derived quantities are well-
estimatestodistancesgreaterthanthoseobserved.Oneaimofour
calibrated. A common example is that temperature and den-
work istomeasure properties of theICM out to the virial radius
sity profiles can be measured from X-ray spectra and used to
inordertocheckthereliabilityofsuchextrapolations.Forourpur-
determine a cluster’s mass under the assumptions of spherical
poses,weequatethevirialradiuswithr200,theradiuswithinwhich
themeantotaldensityis200timesthecriticaldensityoftheuni-
verseattheredshiftofthecluster.
⋆ Email: [email protected] - Current address: Department of
Astronomy,UniversityofCalifornia,Berkeley,CA94720,USA The low orbit of Suzaku places it within Earth’s mag-
(cid:13)c 0000RAS
2 M. R. Georgeet al.
netopause, giving it a significantly lower and more stable
Table1.Observationalparametersofthefivepointings
particle background compared to Chandra and XMM-Newton.
Reiprichetal. (2008) have recently leveraged this ability for low
surfacebrightnessobservationsintheoutskirtsofA2204,measur- Obs.ID Position Exposure(ks) RA Dec(J2000)
ingthetemperaturenearlytor200.Otherclusterobservationswith
Suzaku havedemonstrated itscapacity for temperature and abun- 802062010 Center 32.0 116.8852 -19.2901
802062020 NW 32.2 116.6543 -19.2063
dancemeasurements(e.g., Satoetal.2007),providinganoutline
802062030 NE 30.8 116.9737 -19.0727
forsomeofthemethodsusedhere.
802062040 SE 32.9 117.1155 -19.3739
In this work, we present Suzaku observations of PKS 0745-
802062050 SW 33.4 116.7966 -19.5079
191,arelaxed,coolcoreclusterthatisthebrightestinX-raysbe-
yond z = 0.1 (Fabianetal. 1985; Edgeetal. 1990; Allenetal.
1996).Previousmeasurementshavefoundameangastemperature
intherangeof6.4−8.5keV,dependingonthemodelsusedand
regions studied (Chen,Ikebe&Bo¨hringer 2003, and references
therein).Allenetal.(1996)findgoodagreementbetweenthecen-
tralmassfromX-raysandthatdeterminedfromastronglylensed
arc,buttheresultsofChenetal.(2003)disagree,findingafactor
NE NW
of2smallermassfromXMMdata(seealso Snowdenetal.2008,
forareanalysisoftheXMMdata).Wedescribeourobservationsin
thenextsection,followedbydetailsofthespectralanalysisinSec-
tion3,andtheresultingprofilesinSection4.InSection5weplace
ourfindingsinthecontextofotherclusterstudies,andweconclude
thepaperinSection6.Fordistancescales,weusethecosmological
parametersH0 = 70kms−1Mpc−1 andΩm = 1−ΩΛ = 0.3,
giving an angular scale of 113kpcper arcminute at the cluster’s
redshift,z = 0.1028.Theplottedandquotederrorrangesare1σ
statisticaluncertaintiesexceptwhereotherwisestated.
2 OBSERVATIONSANDDATAREDUCTION
SE SW
Suzaku observations of PKS 0745-191 were taken between 2007
May 11-14 in five separate fields of roughly 32ks each. Details
of these pointings are listed in Table 1. The central pointing is
aimed toward thepeak of the cluster emission and the others are
Figure1.Exposure-corrected mosaicofPKS0745-191,smoothedwitha
positioned adjacently, with 4’ overlap at each chip edge, as in
Gaussian of radius 1’. Background subtraction and vignetting correction
Fig. 1. We use only data from the X-ray Imaging Spectrometer
havebeenomitted,andcalibrationregionsandpointsourceshavenotyet
(XIS: Koyamaetal. 2007). We exclude the back-illuminated de-
beenexcised.Ringradiiare2.5’,6’,9.5’,13.5’,18.5’,and24’.
tector,XIS1,despiteitshighersensitivityatlowenergies,because
italsohasasignificantlyhigherparticlebackgroundlevelthanthe
twofront-illuminatedsensors,XIS0andXIS3,whichhavesimilar
responses.Thereisanoffsetbetweenthemeasuredtemperaturesof
theBIandFIchips,andwediscussthiscontributiontooursystem-
atic uncertainties in Section 4.3. We simultaneously analyze data excised with circular regions of radius 2.5′ to remove more than
from the two FI sensors to effectively double the exposure time 99per cent of thefluxspreadbythePSF.Detector response ma-
while keeping the noise low. Observations were taken in normal tricesandeffectiveareafunctions areconstructedwithxisrmfgen
clocking andeditingmodes withspaced-row chargeinjectionon, andxissimarfgen(Ishisakietal.2007),respectively.Thelattertool
andthedatahavebeenprocessedwiththeenergyscalecalibration generatesthespectralresponseforagivenskybrightness,account-
ofv2.1.6.16.Thedatapreparationdescribedbelowwascarriedout ingfor theknown issueof contamination on theoptical blocking
usingXSELECT2.4.1andFTOOLSversion6.5.1fromHEASARC, filter.Uncertaintiesinthiscontaminationshouldnotaffectourre-
withinstrumentalparametersfromCALDBupdated2008Septem- sultssignificantly,aswedonotconsiderenergiesbelow1keV.Vi-
ber 5. Updates to the calibration parameters released during the gnettingeffectswillbedifferentforclusterandbackgroundemis-
preparationofthispaperdonotaffecttheresultsbeyondthestatis- sion components, so we use a uniform surface brightness out to
ticaluncertainties. a radius of 20′ when modeling the background emission and in-
We performed the standard screening of events files to re- put a β-model surface brightness profile using the parameters of
move time intervals during satellite manoeuvres, telemetry satu- Chenetal.(2003)fortheauxiliaryresponsefileappliedtotheclus-
ration,andpassagethroughtheSouthAtlanticAnomaly,aswellas teremissionmodel.Wefindthatmodifyingtheparametersofthe
elevationangleslessthan5◦ and20◦ fromthenighttimeandday- surface brightness profile used to determine the “effective area”
timeEarth.Thelightcurvefortheremainingtimeintervalsissta- withxissimarfgen does not significantlyimpact the output. Thus,
ble,showingnosignofflaringorexcessparticlebackground. We wedonotexpectanunresolvedcentralcusporuncertaintiesfrom
excludethecornersofthedetectorswhere55Fecalibrationsources theoutwardextrapolationofthesurfacebrightnessprofiletoinflu-
lie,andobviouspointsourcesseeninSuzakuorXMMimageswere enceourresults.
(cid:13)c 0000RAS,MNRAS000,000–000
PKS 0745-191atthevirialradius 3
2.1 BackgroundSubtractionandModelling outerregionsofPKS0745-191isimprovedwithahighertempera-
turecomponent(& 1.5keV),indicativeofclusteremissioncover-
Accountingforbackgroundemissioniscriticalwhenobservingre-
ingtheentirefield.
gions of low surface brightness, and it consists of multiple com-
ponents.WesubtractthenonX-raybackground(NXB)ofcharged
particlesandgammarayswithxisnxbgen(Tawaetal.2008),which
modelsthetrendoftheseeventsfromnightEarthdata,weightedby
themagneticcutoffrigidity.TheX-raybackgroundconsistsofsolar
windchargeexchange,thermalemissionmainlyfromthehotlocal
bubble and the Galactichalo, and the cosmic background (CXB)
duetounresolvedpointsources.Chargeexchangecontaminatesthe
lowenergyspectrumwithemissionlinesthatcanvaryonatime-
scaleof10minutes(Fujimotoetal.2007),whilethediffusether- 3 SPECTRALANALYSIS
malemissionandCXBareexpectedtobemorestableandeasily Spectrawereextractedinannularregionsofradii0′−2.5′,2.5′−
modeled.AtthelowGalacticlatitudeofthissource(b = 3◦),the 6′,6′ −9.5′,9.5′ −13.5′,13.5′ −18.5′, and > 18.5′, with the
softthermalbackgroundcouldvarysignificantlywithposition.We outermostregionreachingtonearly24′.Foreachannuluswede-
opttoexcludethehighenergyendofthespectrumwheretheNXB
fineaneffectiveradiusthatisapproximatelyanemission-weighted
component dominateswithseveral emissionlines,andtoalsoig-
mean (McLaughlin 1999), r = [0.5(r3/2 +r3/2)]2/3. These re-
norethelowenergyendwherechargeexchangeandlocalthermal in out
gionsarecenteredatrightascensionanddeclination07:47:31.325,
emissionmuddlethedata,leavingthe1−5keVbandforconsid-
-19:17:39.95(J2000),whichiscoincidentwiththecDgalaxyand
eration.Sincethecentralregionshavetemperatureshigherthanthe
boththepeakandcentroidofX-rayemission.Duetothelowcount
upper limitoftheenergyband used, wetestthattheyareconsis-
ratesinsomechannels,weusetheCash(1979)Cstatistic.
tentwithtemperaturesmeasuredina1−8keVband.Systematic
We used XSPEC v12.5.0 to simultaneously fit models of the
uncertaintiesdue toparticlebackground subtractionat highener-
spectra, with data from each pointing grouped by annulus unless
gies and Galactic and other low energy background components
specifiedotherwise.WefirstsubtracttheNXBspectrafromiden-
arediscussedinSection4.3.Weoptforthenarrowerenergyrange
ticalregions onthedetector, scaled bytherelativeexposure time
tooptimizethesignaltonoiseforwholecluster.
ofthenightEarthobservations.Next,wemodelthelocalthermal
Sinceclusteremissionfillstheobservedfield,wecannotuse
emissionandCXBcomponents,fixedtothebest-fittingvaluesfrom
detector regions from these pointings to subtract the remaining
theLockmanHoleobservations. Finally,wemodeltheremaining
background. Instead, we analyze Suzaku data from the Lockman
emission,thatfromthecluster,withanotherMEKALcomponentat
Hole (observation ID 102018010) taken only 8 days prior to the
thecluster’sredshift,z = 0.1028. Wefixthecolumndensityab-
startofourobservations.Despitethelargedifferenceinabsorbing
fcoorluthmenLdoecnksmityanmHeoasleurveedrsfurosm4.2H×Im10ap21sc(NmH−3=fo5r.7PK×S10071495c-m19−13; saotrtbhiengcetnhteerc,luNstHer=and3.C6X×B1c0o2m1pcomn−en3t,swtohitchheibselsot-wfietrtinthgavnaltuhee
HI measurement butconsistent withthevaluefromXMM’sEPN
Kalberlaetal. 2005), ROSAT observations (Snowdenetal. 1997)
detectsimilarbackground levelsfrom1−2keVatthetwoposi- (Chenetal.2003).Weallowthemetallicitytovaryinthecenterbut
tions. We find that the Lockman Hole data from 0.5−8keV is fixitto0.3Z⊙atlargerradii.Oftheremainingparameters,onlythe
temperatureandnormalizationofthethermalICMcomponentare
well-modeled by a power law of photon index 1.4, absorbed by
allowedtovary.
the column density measured by the HI maps, added to an un-
Thebroadpoint-spreadfunction(PSF)ofSuzaku,withahalf-
absorbed MEKALthermalplasmamodel(Meweetal.1985,1986;
powerdiameterof∼2′,willcausesomeemissionfromeachannu-
Liedahletal. 1995) at 0.1keV with solar metallicity using the
lusontheskytobedistributedintoothersonthedetector.Wecor-
relative abundances of Anders&Grevesse (1989), allowing only
rectforthiseffectfollowingthemethodofSatoetal.(2007),who
the normalizations to vary. The best fitting normalizations in the
1 − 5keV range are 7.26 × 10−4photonskeV−1cm−2s−1 at importantlyshowthatSuzaku’sPSFisnearlyenergy-independent.
1keVfortheCXBand0.78cm−5arcmin−2 forthesoftthermal Weuseacircularlysymmetricβ-modelwiththebest-fittingparam-
component.1Wedonotfindanimprovementinthefitwithanother etersof Chenetal. (2003), consistent with the surface brightness
profileobservedhere,andamonochromaticenergyof1.5keVto
low-temperaturecomponent,asisoftenused(e.g., Vikhlininetal.
2005). We note that in the 1− 5keV band used here, the fit is generate aphoton list that ispropagated witharay-tracing simu-
lator(xissim)throughthedetectoroptics.Foreachannulusonthe
notevenparticularlysensitivetothenormalizationoftheremain-
sky,weusetheratiooffluxlandinginthecorrespondingdetector
ingsoftthermalcomponent,butweincludeitasanempiricalde-
annulustothefluxineachotherannulustocalculatecross-annuli
scriptionofthebackgroundmodeltobeappliedtothePKS0745-
normalizationfactors.Inthespectralmodel,weaddathermalcom-
191data.Weattemptedtofittheoutermost regionsofthecluster
ponentfromeachannulustoeveryotherannuluswiththetemper-
observations witha similar model and an added low-temperature
(∼ 0.25keV) Galactic component. The normalizations required ature tied to the original region and the normalization scaled by
thesefactors.Therelativecontributionstoeachannulusfromother
aremuchhigherthanfortheLockmanHoleandwouldbeincon-
annuli, asderived from these PSFcorrection factors and the best
sistentwiththeROSAT observationsforthissource.Thefittothe
fittingnormalizations, aregiven inTable2.Themodel wasfitted
simultaneouslyoverallannuliandresultedinanexcellentfit;theC
statistic,thoughnotadirectmeasureofgoodnessoffit,was65413
1 We follow Satoetal. (2007) in dividing the surface brightness nor-
using98640binsand98627degreesoffreedom.Thespectraand
malization of the thermal component by the solid angle used in the
ancillary response file generation, Ω = 20′, so that Norm = models are shown in Figs. 2 and 3. We note that the individual
10−20R nenHdV/{4π(1 + z)2DA2}/Ω in cm−5arcmin−2, where spectraarefittedsimultaneously,andareonlycombinedbyannu-
DAistheangulardiameterdistancetothecluster. larregionsinthesefiguresforvisualclarity.
(cid:13)c 0000RAS,MNRAS000,000–000
4 M. R. Georgeet al.
0’-2.5’ 2.5’-6’ 6’-9.5’ 9.5’-13.5’ 13.5’-18.5’ 18.5’-24’
0’-2.5’ 89.9 19.3 2.6 0.4 <0.05 0.1
2.5’-6’ 9.7 66.8 5.7 0.6 0.1 0.1
6’-9.5’ 0.3 13.1 84.4 7.8 0.6 0.1
9.5’-13.5’ 0.1 0.5 6.5 78.5 7.3 0.8
13.5’-18.5’ <0.05 0.1 0.5 11.9 84.1 10.9
18.5’-24’ <0.05 0.1 0.3 0.7 7.8 88.1
Table2.RelativefluxcontributionsduetoPSFspreading.Valuescorrespondtothefractionoffluxmeasuredinthedetectorregion(columns)originatingfrom
theclusterregion(rows),i.e.,ofthefluxmeasuredintheoutermostannulus,weexpect88.1%tocomefromthecorrespondingregioninthesky,andonly
0.1%tohaveoriginatedinthecentralprojectedregion.
profilecansimilarlybefitwithapowerlaw,excludingthecentral
regionagainforuniformity,withindexα =−2.23±0.01.Ifwe
n
assumeapolytropic distributionfor anideal gas, P ∝ nHkT ∝
nΓ,thenwefindΓ=1+(α /α )=1.42±0.03.Thisvalueis
H T n
higherthanthatfoundforcoolingflowclustersdeterminedbye.g.,
DeGrandi&Molendi(2002),whomeasuredΓ≃1.2intheradial
range0.2r180 <r.0.6r180.
Gaswithhighentropyrises,sotheradialentropyprofileisex-
pectedtoincrease.Puzzlingly,theentropyprofileweobserverises
fromthecenterandthenappearstoleveloffbeyond∼10′,putting
itontheborderofconvectiveinstability.Wewilldiscusspossible
explanationsforthisbehaviorinlatersections.
4.2 Massprofiles
To derive a mass profile, we assume that the gas properties are
spherically symmetric and that the cluster is in hydrostatic equi-
librium.Balancingthethermalpressuregradientagainstthegravi-
tationalpotential,weobtainanexpressionforthetotalgravitating
Figure2.DataandspectralfitsincludingPSF-correctionforeachannular
massintermsoftemperatureanddensity:
region,illustratingthesofteningofthespectrawithincreasingradius.The
r9e.g5i′o−ns1p3lo.5tt′ed(baluree)0,′1−3.52′.5−′ (1b8l.a5c′k)(,cy2a.n5)′,−an6d′>(re1d8),.56′′(−ma9g.e5n′ta()g.reDeant)a, M(<r)= −kr2 TdnH +nHdT . (1)
havebeenrebinnedtoaminimumsignificance of5σ foreachpoint,and GµmHnH „ dr dr«
eachspectrumhasbeenarbitrarilyrenormalizedforvisualclarity. Weassumethat thetotaldensitydistributioncanbedescribed by
anNFWprofile,
ρ(r)= ρ0 , (2)
4 RESULTS r/rs(1+(r/rs))2
4.1 Temperature,density,andentropyprofiles whereρ0isadensitynormalizationandrsisascaleradiusrelated
tothecluster’sconcentration,c200 ≡r200/rs.
Temperatureanddensityprofilesaretheprimarydataproductsof Following an approach similar to that of Schmidt&Allen
X-rayobservationsofclusters,fromwhichotherpropertiesinclud- (2007),weuseanNFWmodel andtheobserved gasdensitydis-
ing entropy, mass, and gas fraction profiles can be derived. We tributiontopredictatemperatureineachannulus,beginningwith
obtain the density fromthe normalization of the best-fittingther- theoutermostbin.Densitygradientsaretakenlinearlybetweenthe
malplasmamodelwhichisproportionaltotheemissionmeasure, radialbins,whichreducesthecorrelationinuncertaintiesbetween
nenHdV, where ne ≈ 1.2nH for typical abundances. We use non-adjacent datapointsthatarecreatedwithotherinterpolations
Rthe simpifying assumption of constant density within each annu- such as cubic splines, as some authors use (see Voigt&Fabian
lus, and estimate the volume as that of the intersection between 2006, for a discussion). This approach could be improved with
cylindical and spherical shells with shared inner and outer radii, more radial bins, but the wide PSF of Suzaku and the low count
V =(4π/3)(ro2ut−ri2n)3/2,scaledbythefractionoftheprojected rateintheclusteroutskirtslimitusfromusingthinnerannularre-
annulus observed. With the density and temperature determined, gions. Toensure that theoutermost temperature value isrobustly
wecancalculatetheentropyprofile,K =kT/n2/3.Eachofthese estimated,wetakethemedianoutervalueoftheprofilesthatbest
e
profilesisshowninFig.4. fit100MonteCarlorealizationsoftheobservedtemperaturepro-
The cool core, though blurred by thewide PSF,isseen asa file,normallydistributedwithinitserrorbars.Themodeltempera-
decrease intemperature near the center. The more novel result is tureprofilesaresimilarifwebeginattheinnermostregion,sothe
theclearly-observeddeclineintemperatureintheoutskirtsofthe resultisnotparticularlysensitivetotheboundaryvalues.Iterating
cluster.Excludingthecore,thisdeclinecanbefitwithapowerlaw over a range of NFW parameters, we select the mass model that
T(r) = T0rαT withindexαT = −0.94±0.06.Thegasdensity producesthetemperaturesthatbestfittheobservedprofile.
(cid:13)c 0000RAS,MNRAS000,000–000
PKS 0745-191atthevirialradius 5
Figure4.Projectedtemperature,density,andentropyprofiles.Thevertical
dashedlineshowsourestimateofr200,derivedinSection4.2.
InordertoresolvetheregionwithintheNFWscaleradius,we
supplementtheSuzakudatawithanarchival20ksChandraobser-
vation(ID2427)takenwiththeACIS-SdetectorinVFAINTmode.
ThesedatawerereducedfollowingthedescriptionofO’Deaetal.
(2008), with spectra extracted in circular annuli and deprojected
usingthemethodofSanders&Fabian(2007).Afterusingtheout-
ermost Chandra annulus to subtract contaminating flux from in-
nerregionsitisomittedfromfurtheranalysissinceitmaycontain
externalclusteremission,leavingsixregionstoreplacetheinner-
mostSuzaku bin,wherethetemperatureanddensityisinreason-
ableagreement withtheChandra data. Weuse Chandra data for
itssharperPSF,buttheXMMtemperatureprofileinSnowdenetal.
(2008)isalsoconsistentatthesmallerradiiofthatobservation.
Themodel temperature profile,shown inFig. 5, does not fit
thedataverywelloverallannuli,andthebestfittotheobserved
temperatures(χ2 ≈39for7degreesoffreedom)isobtainedafter
ignoring the outermost Suzaku bin which is beyond the virial ra-
diuswheretheassumptionofhydrostaticequilibiriumisexpected
tofail,andtheChandraregionsinthecoolcorewithin∼70kpcof
thecenterwherethegasislikelytobemultiply-phased.Themain
deviation in our data from this acceptable temperature fit arises
fromthe2.5′ −6′ Suzakuannulus.Possibleexplanationsinclude
aPSF-correctionthatcouldbetoolarge,across-calibrationissue
betweenChandraandSuzaku,orevennon-gravitationalheatingin
thatregion.
Theresultingmassprofilehasbest-fittingNFWparametersof
c200 = 7.5+−10..19 and rs = 230+−4400kpc, producing a virial radius
r200 = c200rs = 1.72±0.06Mpc,or 15.2′ andmassM200 =
200ρc(z)(4π/3)(r200)3 = 6.4±0.6×1014M⊙ . We estimate
Figure 3. Same as Fig. 2, but with residuals to show the quality of the the total uncertainty on the virial mass, including systematics, of
spectralfits,andwiththeLockmanHolebackgroundspectrumincludedfor
30%, which isdescribed further inthenext section. Wecompare
comparison.Countlevelshavenotbeenrenormalizedandwenotethatthe
thesevalueswithprevious determinationsinTable3andplot the
regionshavedifferentareasandexposuretimes.Dottedanddashedcurves
representthebackground(CXB+thermal)andclusteremissionmodels,re-
s(cid:13)cpe0ct0iv0e0lyR.AS,MNRAS000,000–000
6 M. R. Georgeet al.
Figure5.Chandra(redtriangles)andSuzaku(blackcrosses)temperature Figure7.GasfractionprofileforPKS0745-191,theratioofthedottedto
valuesusedinmassfittinganalysis,alongwithmatchingtemperaturesfor solidcurvesinFig.6,with1σstatisticalerrorrangeingray.Dottedlines
bestfittingNFWprofile(bluecircles). showthe1σrangearoundthevalueofΩb/ΩmfromKomatsuetal.(2008).
Theverticaldashedlineshowsourestimateofr200,derivedinSection4.2.
adopt.Schmidt&Allen(2007)foundanevenlargervalueforthe
virialradius,fittinganNFWprofiletoChandradatainthecentral
region to obtain r200 ≈ 2.2Mpc. One issue withpast NFW fits
usedtocalculatethevirialradiusisthatthedataoftendonotextend
eventotheNFWscaleradius,letalonethevirialradius.
Wecancompareourmassprofilewiththeprojectedmassde-
termined from a strong lensing arc of radius 34.5kpc seen with
Hubble imagery by Allenetal. (1996). Updating their mass esti-
mateforthecircularlensmodeltoaccountforthecurrentcosmo-
logicalparameters,weexpectamassof6.4×1012M⊙ projected
withinacylinderalongthelineofsightofthecenterofthecluster
witharadius of thelensing arc, which isconsistent withthesta-
tisticalandsystematicuncertaintiesofourbest-fittingNFWmodel
whenintegratingthemassinthecylinderouttor200.Wenotethat
this includes an extrapolation of our profile into the core region
Figure6.Cumulative profilesofgasmass(dottedlowercurve)andtotal
wherewehaveexcluded datafromour fitbecause of nonthermal
gravitational mass (solid upper curve) with 1σ statistical error ranges in
gray.Thesingleerrorbarshowsthe30%systematicuncertaintyonM200 processes. Whileitisreassuringtoseethisreasonableagreement
andthe vertical dashedline showsourestimate ofr200,derived inSec- betweenseparatemassestimates,wecautionthatcomparisons of
tion4.2. thistypeofwide-fieldX-rayanalysiswithstronglensingdataonly
involveasmallfractionofthetotalclustermass.Weaklensinganal-
yses,whichcanprovidemassprojectionsoveramuchbroaderarea,
massprofileinFig.6,alongwiththecumulativegasmassprofile willprovideimportantcomparisonsforvirialmassestimates.
obtainedfromthepower-lawfittotheSuzakugasdensityprofile. InFig.7,weplotthegasfractionprofile,definedasthefrac-
TheNFWconcentrationishigherthanpreviousestimates,and tionofmasswithinagivenradiuscomposedofX-rayemittinggas.
the virial mass we determine is lower, due in part to the smaller Thegasfractionappearstoriseslightlyattheouterradii,consis-
virialradiusfoundinthiswork.Reiprich&Bo¨hringer(2002),who tentwiththeprofileobservedforPKS0745-191inROSATdataby
usedanisothermalfittoROSAT andASCAdataandfoundavalue Allenetal.(1996).Thevaluesofthefgasprofileintheoutskirtsof
of 1.95±0.03Mpc updated to the cosmological parameters we thisclusteraresimilartorecentmeasurementsofthemeancosmic
baryonfraction(Komatsuetal.2008).
c200 M200(1014M⊙) Reference
4.3 Uncertainties
3.83+0.52 18.6+3.5 Allenetal.(2003)
−0.27 −4.0
5.12+0.40 10.0+1.2 Pointecouteauetal.(2005) A number of systematic uncertainties could add contributions to
−0.40 −1.2
5.46+3.22 9.7+52.2 Voigt&Fabian(2006) our error budget beyond the statistical ranges plotted. We sum-
−2.88 −8.5
5.86+1.56 11.82+4.70 Schmidt&Allen(2007) marize our estimates of several of these systematic uncertainties
−1.07 −3.55
7.5+1.1 6.4+0.6 Thiswork tothetemperatureprofile,includingtheeffectsofPSF-correction
−0.9 −0.6
and renormalization of background components, in Table 4. The
Table 3. Concentration and virial mass determinations for PKS 0745- changesduetothePSF-correctionaremostlysmall,withthemain
191,compiledbyComerford&Natarajan(2007)withvaluesforthiswork effectbeinga∼ 12percentincreaseintemperatureinthesecond
added. innermostannulusafteraccountingforemissionfromthecoolgas
in the core that has scattered outward. There is a significant un-
(cid:13)c 0000RAS,MNRAS000,000–000
PKS 0745-191atthevirialradius 7
Radius kT Stat. NoPSF NXB CXB Gal. NH Z
(’) (keV) ±3% ±10% ±50% ±10% 0.2−0.4Z⊙
0–2.5 6.92 +0.12 +0.08 <0.005 <0.005 <0.005 0.68 <0.005
−0.12
2.5–6.0 7.85 +0.45 −0.82 <0.005 <0.005 0.01 0.90 0.02
−0.39
6.0–9.5 4.90 +0.30 −0.01 0.02 0.04 0.03 0.41 0.05
−0.27
9.5–13.5 3.22 +0.47 −0.05 0.14 0.14 0.06 0.28 0.07
−0.36
13.5–18.5 2.15 +0.19 +0.09 0.06 0.17 0.06 0.15 0.11
−0.18
>18.5 2.07 +0.25 +0.02 0.10 0.21 0.06 0.13 0.12
−0.23
Table4.EstimateduncertaintiesintheradialtemperatureprofileduetoremovingPSF-correctionsorchangingnormalizationsofbackgroundcomponentsand
spectralmodelparameterswithintherangesgiven.Eachparameterisvariedindependentlyandwepresentonlythemaximumoftheupwardanddownward
temperatureshifts(in keV)forclarity.Best-fittingPSF-correctedtemperaturesandtheirstatisticaluncertaintiesareincludedforcomparison.
certaintyinthetemperatureofthecentralregionbecauseSuzaku’s
PSF blurs the steep gradient of the cool core. As Reiprichetal.
(2008)pointsout,theapproachtoPSF-correctionsdescribedinthe
previoussectiondoesnotfullyaccountforthisblurringwithinthe
centralregion,howeverourmethodprovidesareasonableapprox-
imationtothecorrectionsneeded.
To ensure that the background models used do not signifi-
cantlyimpacttheresults,wevarythenormalizationsofthesecom-
ponentsandmeasurethedeviationsproducedintemperature.The
uncertaintyintheNXBis∼3percent(Tawaetal.2008),andfrom
ananalysis of ROSAT databy Carrera,Fabian&Barcons (1997),
weestimatethatthecosmicvarianceduetopointsourceclustering
intheCXBis∼ 10per centover thisfieldof view.Wealsotest
theeffectofmetallicityfrom0.2−0.4Z⊙intheouterannuliand
arangeof±10percentinthecolumndensity.Eachofthesevari-
ationsresultsinachange intemperatureof. 10per cent forall Figure8.ComparisonbetweenChandra(redtriangles)andSuzaku(black
annuli,andtheindividualsystematicuncertaintiesaresmallerthan crosses)densityprofiles.Errorbarsaresmallerthantheplotsymbols.
thePoissonuncertaintiesforallbutthecolumndensity’seffecton
thecentralregionswherethecountrateishigh.Finally,thenormal-
izationofthelocalthermalcomponent,whichcouldvarythemost
direction is consistently above or below the average temperature
acrosstheclusterfieldofviewbecauseofthelowGalacticlatitude,
ordensityforeveryannulus.Scatterthatislargerthanthestatisti-
actuallyhasaverysmalleffectontemperaturefitsabove1keV.
caluncertaintiescouldbeattributedtoremainingpointsourcesor
Without spectral deprojection, the data from each annulus
minorasymmetryinthecluster.
will be contaminated by emission from regions at larger radii.
TheentropyseenintheoutermostradialbinoftheNWpoint-
But because the density profile falls so steeply and the ther-
ing is significantly lower than nearby regions, mainly due to the
mal bremsstrahlung emission scales as the square of the density,
temperature drop seen there. However, scatter between pointings
the only noticeable effect is in the cluster core (e.g., Fig. 3 of
orindividualoutliersareunabletoexplaintheobservedflattening
Sanders&Fabian2007).Thisregioniswellwithinourinnermost
oftheentropyprofileinthesummedannuli.Weplotapowerlaw
radialbin,sowedonotexpectsignificanterrorsduetothelackof
risingasr1.1tocomparewiththeentropyprofilepredictedbyan-
deprojectionoftheSuzakudata.
alyticalmodelsofaccretionshockheatingandseeninsomeobser-
As an additional check on the reliability of our temperature vations as well as numerical simulations (Tozzi&Norman 2001;
anddensityprofiles,wecomparethevaluesfromSuzakuwiththe Ponmanetal.2003;Voitetal.2005).Asmallnumberofobjectsin
Chandra observations used in the mass estimate. The high spa- thesampleofPonmanetal.(2003)haveentropycurvesthatdonot
tial resolution of Chandra allows for our central region to be di- risewithradius.Theobservedandexpectedprofilesagreeatsmall
vided into several annuli, with the average temperature in agree- radii,risingoutofthecore,butthereisaclearentropydeficitinthe
mentwiththeSuzakuvalue.AsshowninFig.8,thedensityprofiles outskirtsofthecluster,perhapsindicativeofinfallinggaswhichis
arealsoreasonablyconsistentbetweenthetwoobservatories,with not dynamically stable. Our background model would haveto be
aslightlysteepeningslopeatthelargerradiiseenbySuzaku. offbyanorderofmagnitude,orthecolumndensitychangedbya
We can check the assumption of spherical symmetry used factorof2,toincreasetheentropyintheoutskirtstothepredicted
when deriving the mass profile, seeing if the emission is at least values.
circularlysymmetricbyconsideringtheprojectedprofilesineach For the estimates of the virial radius and mass, the method
ofthepointingsseparately.Fig.9showsthetemperature,density, offittinganNFWmodeltoourtemperatureprofileisanadditional
andentropyprofilesforeachpointing.HerewedonotincludePSF- sourceofuncertainty.Wehaveexcludedtheinnerandouterregions
correctionsinordertokeepeachsetofobservationsindependent. wheretheassumptionofhydrostaticequilibriumislikelytobreak
Theuncertaintiesarelargerwhensplittingupthedata,butthere- down, but several variations of thetemperatureprofilewiththese
sults from the separate pointings broadly overlap, and no single pointsincludedor excludedproduce valuesfor r200 consistent to
(cid:13)c 0000RAS,MNRAS000,000–000
8 M. R. Georgeet al.
400
350
c)300
p
k
s (
u
di250
a
R
e
al
Sc200
150
100
5 6 7 8 9 10 11
Concentration
Figure10.Likelihoodcontoursfortheconcentrationandscaleradiuspa-
rametersoftheNFWfits,drawnat∆χ2 = 2.30,6.17,and11.80,corre-
spondingtothe1σ,2σ,and3σ confidence intervals, respectively. Thick
redcontours show theconstraints fromthe combination ofChandraand
Suzakudata,excludingtheclustercoreandtheoutermostannuluswhichis
beyondthevirialradius.Thinbluecontoursshowtheconstraintswithout
theSuzakudataforcomparison.
5 DISCUSSION
Figure9.Comparisonoftemperature,density,andentropyprofilesineach
direction.ThetemperatureintheNEdirectionisnotwell-constrainedfrom Thesearethefirstwell-constrainedmeasurementsofthegastem-
9.5′ − 13.5′ due to a large amount of area excluded because of point peratureprofilebeyond r200 forarichandrelaxedcluster, which
sources, sothetemperature andentropy points arenotplotted inthis re-
wecannowcomparewithmodelpredictionsandsimulations.We
gion.Slightoffsetsareaddedtobinradiiforclarity.Thedottedcurveinthe see that there is a clear decline in temperature between 0.3 −
bottompanelshowsK∝r1.1.Theverticaldashedlineshowsourestimate
ofr200,derivedinSection4.2. 1.5r200, consistent with recent observational trends at growing
radii(Vikhlininetal.2005;Prattetal.2007;Reiprichetal.2008)
andsuggestingthatconductiondoesnotplayasignificantroleon
typical cluster time-scales. Roncarellietal. (2006) measured the
∼ 10 per cent. Similarvalues arealso obtained when using only magnitudeofthetemperaturedropinhydrodynamicalsimulations,
theSuzakudata,whichhasalargeuncertaintyinthecentraltem- findinga40percentdeclinefrom0.3−1r200,thesamesizefound
peratureduetoPSF-blurring.Thewideradialspanofthisdataset intheanalyticaltreatmentofOstriker,Bode&Babul(2005).The
provides significantly tighter constraints on the NFW parameters dropobservedinPKS0745-191overthisradialrangeiscloserto
thancouldbeobtainedwiththeChandradataalone,asshownin 70percent,butthegeneralshapesoftheprofilesaresimilar.
Fig. 10. Data from the cluster core are still excluded in the con- Theobservedentropyprofiledeviatesfromexpectationsnear
tours plotted, though they might be used in a typical analysis. In the virial radius. Tozzi&Norman (2001) describe the effects on
either case withonly Chandra data, the NFW scale radius is not entropy of the accretion phases, including adiabatic infall, shock
well-constrainedsincethedatadonotextendoutthatfar,andthe heating,andadiabaticcompressionfollowedbycoolingwithinthe
resultingestimateforr200,andthusM200,wouldbesignificantly halo.Interestingly,weseeevidenceforanaccretionshockbeyond
largerthanthevaluesweobtain.Wecanalsoincludethesystematic thevirialradiusinonedirection(NWpointinginFig.9),sugges-
uncertaintiesinthetemperatureprofilewithinthisprocessoffitting tiveofcoolmaterialfallinginwardalongafilament.Thechangein
overNFWparameterspace.Evenwithdifferencesof0.5−1keV entropyintheouterannulusofthisregionisnotseenintheother
betweentheFIandBIsensorswhichhavesimilarlyshapedbutoff- directions, though the values there are still lower than would be
settemperature profiles,changes inthebest fittingvalueof R200 expectedfromthetypicalincreaseofK ∝r1.1.
areof order 10%,giving asystematicuncertaintyof 30% forthe Thesharperdeclineintemperaturethanpredictedandtheflat-
determinationofM200. tening of the entropy profile in the outskirts suggest a need for
We can also estimate the cluster mass independently of any nonthermalpressuresupportinordertomaintaindynamicstability.
model parametrization by plugging our density and temperature ThenumericalsimulationsofEke,Navarro&Frenk(1998)showa
profilesdirectlyintoEquation1andcalculatinggradientsfromthe significantriseintheratioofbulkkineticenergytothermalenergy
finitedifferencequotientsofadjacentpoints.Atlargeradii,thecu- beginningwithinthevirialradius.Mergeractivityincreasesthetur-
mulativemassestimateusingthismethodactuallydecreases,indi- bulent pressure, and even though PKS 0745-191 appears relaxed
cating that the hydrostatic assumption fails, and the uncertainties morphologically,itshouldstillbeaccretingmatterintheoutskirts.
arelargebecausespatialgradientsaretakenbetweenpointssepa- Wenotethattheinfalltime-scale,t ∼ (r3/GM)1/2,isoforder
f
ratedbythewidethicknessofannularbins.However,atthevirial 1Gyr at the virial radius, and the time-scale set by the speed of
radiusnear15′,themassestimateagreeswiththatderivedfromthe sound,ts∼(r2mH/ΓkT)1/2,isseveraltimeslarger.
NFWmodeltowithin∼30percent. Neumann(2005),studyingthesummedprofilesof14nearby
(cid:13)c 0000RAS,MNRAS000,000–000
PKS 0745-191atthevirialradius 9
Abell clusters beyond r200, argues that the ICM at large radii
maynotbeinhydrostaticequilibrium,andthatcool gasnot seen
in X-rays could increasingly dominate the baryon content in the
outskirts.Afshordietal.(2007)stackedWMAPobservationsofa
largesampleofmassiveclustersandfoundadeficitinthermalen-
ergyintheoutskirtsfromtheSunyaev-Zel’dovichprofile,alsoar-
guingforcoolphaseoftheICM.Itisnotwellunderstoodhowthese
different phases would mix, and complicated gas physics would
likely result. The assumption of hydrostatic equilibrium fails be-
yondthevirialradius,asseenbythepoorertemperaturefitsfrom
massmodelingwhentheoutermosttemperaturevalueisincluded.
ItisnotobvioustowhatextenttheICMwithinthevirialradiusis
not in equilibrium, but the entropy and temperature profiles sug-
gestthatnonthermal physicsmaybeimportantintheoutskirtsof
thiscluster.
In Fig. 11, we plot the observed temperature profile against Figure 11. Suzaku temperature profile, normalized by the emission-
twomodels.Thefirstistheexpectedtemperatureifthegascontent weightedmeanandcomparedwithmodelprofiles.Thesolidcurveshows
tracedtheNFWdistributionofdarkmatter,withaKeplerianveloc- theparametrizationofEquation3,alsorescaledbytheemission-weighted
ityprofile,i.e.,T(r)∝v(r)2 ∝M(<r)/r.Thesecondandmore meantemperature thatweobserve.Thedotted curveshowsthetempera-
realisticcaseisfortheprojectedX-raytemperatureofgasarranged tureforgastracinganNFWdistribution,whilethedashedcurveshowsa
polytropicallyandinhydrostaticequilibriumwithanNFWgravita- polytropicprofileinhydrostaticequilibriumwithanNFWpotential.Both
modelsarenormalizedtomatchthemaximumobservedtemperature.
tionalpotential,asderivedbySuto,Sasaki&Makino(1998).The
outertemperatureswehaveobservedarelowerthanthoseexpected
for reasonable valuesof themodel parameters2.Additionally, we
canfittheobservedtemperatureprofileusingasimpleparametriza- (Chenetal.2003),but similar tothe ROSAT value of Allenetal.
tion (1996). The trend of fgas rising with radius is also seen in other
clusters and in simulations (e.g., Vikhlininetal. 2006; Ekeetal.
r α r β
T(r)=T1 1+ keV (3) 1998), since the gas density distribution is less centrally concen-
„r « „ r «
s s tratedthanthat for collisionlessdarkmatter.Theoutermost mea-
withbest-fittingparametersT1 =135,α=2.4,β =−4.1,where suredvalueoffgas isconsistentwiththemeancosmicbaryonra-
rs is the scale radius from the best-fitting NFW profile. We note tioderivedfromWMAPdataandothercosmologicalobservations,
thatthenormalizationisrelatedtothevalueofthetemperatureat Ωb/Ωm =0.165±0.006(Komatsuetal.2008).
thisradius,T1=T(rs)/2β.
Apossibleexplanationforthedeficitofthermalenergyseen
atlargeradiiisthatinfallingmatterhasretainedsomeofitskinetic
6 SUMMARY
energyinbulkmotion.Ifthereisincreasingpressuresupportfrom
bulkmotion,turbulence,orothernonthermalprocessesintheouter We have presented the first measurements of the gas beyond the
regionsofthecluster,thenthegravitationalpotentialandthustotal virialradiusfromarichandapparentlyrelaxedgalaxycluster.The
mass would be incorrectly estimated when assuming hydrostatic temperatureprofileshowsasignificantdeclineatouterradii,while
equilibrium.Thiseffectwoulddependonthechangesinboththe the entropy profile levels off. The spatially resolved temperature
temperature and its gradient, making estimation of the true mass anddensitymeasurementsouttoandbeyondthevirialradiuspro-
difficult. duce improved constraints on the mass and gas fraction profiles,
Alternatively, the peak temperature, seen in the second- thoughtheobservedtemperatureprofiledoesshowdeviationsfrom
innermostannulus, couldbeinflatedduetononthermal processes that expected from cluster gas in hydrostatic equilibrium with an
such as shock heating during infall. AGN heating is thought to NFWmassprofile.
playanimportant roleincool coreclusters,andsome excessen- Observations of the outskirts of clusters offer a direct probe
ergy could also heat the gas beyond the core. More observations oftheirassemblyhistory.Theapparentshockfrontinonedirection
are needed of this cluster and others to determine how well the makesitclearthatthisclusterisstillaccretingmaterial,likelyalong
self-similar scaling relations, which depend on the dominance of afilament.Evidencefornonthermalpressuresupportsuggeststhat
gravitationalprocessincreatingequilibrium,applyouttothevirial bulk motions from merger activity could be making a significant
radius. contributiontothegasenergyintheoutskirtsofthiscluster.
The gas fraction we obtain is more consistent withprevious PKS 0745-191 is an ideal candidate for such observations,
results. At r200, fgas = 0.13, lower than that found with XMM givenitsdistanceandluminosity.Theangularsizefitsreasonably
withinafewpointingsandthecountrateishighenoughforgood
spectral statistics. The low and well-constrained background lev-
2 WesettheparameterBp,definedbySutoetal.(1998),equaltounity, elsofSuzakuarecrucialforlowsurfacebrightnessmeasurements
andusethepolytropicindexderivedfromthebest-fittingpowerlawstoour
likethosepresentedhereandbyReiprichetal.(2008).Weexpect
dataexcluding thecentral region, Γ = 1.5.Itispossibletoobtain tem-
that as the number of cluster observations in the Suzaku archive
peratureprofilesthatdeclineassteeplyastheobservedonebyincreasing
increases, these types of analyses will be able to probe the self-
thevalueofBp,thoughthiswouldrequiretruncatingthegasdistribution
shortlybeyondtheregionswehavemeasured.FortherangeΓ=1.1−2, similarityoftheoutskirtsofclusters.Morestudiesatthevirialra-
thepolytropicindexuseddoesnothaveasignificanteffectontheshapeof dius, including X-ray observations, gravitational lensing, the SZ
thescaledprofile. effect,andnumericalsimulations,willprovideabetterunderstand-
(cid:13)c 0000RAS,MNRAS000,000–000
10 M. R.Georgeet al.
ingoftheregimewherehydrostaticequilibriumbreaksdownand PointecouteauE.,ArnaudM.,PrattG.W.,2005,A&A,435,1
clustersarestillbeingassembled. PonmanT.J.,SandersonA.J.R.,FinoguenovA.,2003,MNRAS,
343,331
PrattG.W.,Bo¨hringerH.,CrostonJ.H.,ArnaudM.,BorganiS.,
FinoguenovA.,TempleR.F.,2007,A&A,461,71
ACKNOWLEDGMENTS
ReiprichT.H.,Bo¨hringerH.,2002,ApJ,567,716
WethankJamesGraham,ThomasReiprich,SteveAllen,Richard ReiprichT.H.,etal.,2008,preprint(arxiv:0806.2920)
Mushotzky, and Mark Bautz for helpful discussions and Roder- RoncarelliM.,EttoriS.,DolagK.,MoscardiniL.,BorganiS.,Mu-
ickJohnstoneformuchassistance.MRGacknowledgesaHerschel ranteG.,2006,MNRAS,373,1339
SmithScholarship, HRR issupported by STFC,and ACFthanks SandersJ.S.,FabianA.C.,2007,MNRAS,381,1381
theRoyalSocietyforsupport.Thisresearchhasmadeuseofdata SatoK.,etal.,2007,PASJ,59,299
obtainedfromtheSuzakusatellite,acollaborativemissionbetween SchmidtR.W.,AllenS.W.,2007,MNRAS,379,209
thespaceagenciesofJapan(JAXA)andtheUSA(NASA). SnowdenS.L.,etal.,1997,ApJ,485,125
SnowdenS.L.,MushotzkyR.F.,KuntzK.D.,DavisD.S.,2008,
A&A,478,615
SolovyevaL.,AnokhinS.,SauvageotJ.L.,TeyssierR.,Neumann
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