Mass distribution in the most X-ray-luminous galaxy cluster RX J1347.5-1145 studied with

12 Pages·2007·0.23 MB·English

A&A472,383–394(2007) Astronomy
DOI:10.1051/0004-6361:20077580 &
(cid:1)c ESO2007 Astrophysics
Mass distribution in the most X-ray-luminous galaxy cluster
−
RX J1347.5 1145 studied with XMM-Newton
M.Gitti1,R.Piffaretti2,andS.Schindler3
1 INAF–OsservatorioAstronomicodiBologna,viaRanzani1,40127Bologna,Italy
e-mail:[email protected]
2 SISSA/ISAS,viaBeirut4,34014Trieste,Italy
3 InstitutfürAstro-undTeilchenPhysik,Leopold-FranzensUniversitätInnsbruck,Technikerstraße25,6020Innsbruck,Austria
Received1April2007/Accepted18June2007
ABSTRACT
Context.WereportontheanalysisofXMM-NewtonobservationsofRXJ1347.5−1145(z=0.451),themostX-ray-luminousgalaxy
cluster.
Aims.Wepresentadetailedtotalandgasmassdeterminationuptolargedistances(∼1.7Mpc),studythescalingpropertiesofthe
cluster,andexploretheroleofAGNheatingintheclustercoolcore.
Methods.Bymeansofspatiallyresolvedspectroscopywederivedensity,temperature,entropy,andcoolingtimeprofilesoftheintra-
clustermedium.Wecomputethetotalmassprofileoftheclusterintheassumptionofhydrostaticequilibrium.
Results.Ifthedisturbedsouth-eastregionoftheclusterisexcludedfromtheanalysis,ourresultsonshape,normalization,scaling
properties of density, temperature, entropy, and cooling timeprofilesarefullyconsistent withthose of relaxed, cool coreclusters.
We compare our total and gas mass estimates with previous X-ray, lensing, dynamical, and SZ studies. We find good agreement
withotherX-rayresults,dynamicalmassmeasurements,weaklensingmassesandSZresults.Weconfirmadiscrepancyofafactor
∼2betweenstronglensingandX-raymassdeterminationsandfindagrossmismatchbetweenourtotalmassestimateandthemass
reconstructedthroughthecombinationofbothstrongandweaklensing.Weexploretheeffervescentheatingscenariointhecoreof
RXJ1347.5−1145andfindsupporttothepicturethatAGNoutflowsandheatconductionareabletoquenchradiativecooling.
Keywords.galaxies:clusters:individual:RXJ1347.5−1145–X-rays:galaxies:clusters–galaxies:intergalacticmedium–
galaxies:coolingflows–cosmology:darkmatter–cosmology:observations
1. Introduction cluster is dominated by two cD galaxies which are separated
by about ∼18(cid:4)(cid:4) along the east-west direction, the X-ray emis-
X-ray observations of the diffuse Intra-Cluster Medium (ICM) sion being centered on the western one. Although this is un-
in clusters of galaxies are a particularly rich source of infor- usual for strong cooling flow clusters, the optical spectrum of
mation forunderstandingthe formationof large scale structure the western Brightest Cluster Galaxy (BCG) indicates that it
andthephysicsofclusters.Astheyarethelastmanifestationof hosts an active galactic nucleus (AGN), with typical emission
hierarchicalclustering,whose historydependsstronglyon cos- lines of giant ellipticals at the center of cooling flow clusters
mology,galaxyclustersarekeyobjectsforcosmologicalstudies (Cohen & Kneib 2002). More striking is a recent discovery
(seeVoit2005, forareview).SincetheevolutionoftheICMis made with Chandra (Allen et al. 2002b) and XMM-Newton
mainlydrivenbythegravityoftheunderlyingdarkmatterhalo, (Gitti & Schindler 2004) of a region with hot, bright X-ray
clusters are expected to show similar properties when rescaled emission located at ∼20 arcsec from the central emission peak
with respectto theirtotalmassandformationepoch.However, in south-east direction. Millimeter observations previously de-
deviations from self-similarity are expected under the effect of tectedaverydeepSZdecrementinthesouth-eastregionofthe
morecomplexphysicalprocesses,beyondgravitationaldynam- cluster (Komatsuetal. 2001;Pointecouteauetal.2001).These
icsonly,whichaffectthethermodynamicalpropertiesofthedif- results were interpreted as indications of a subcluster merger
fuse ICM (e.g. Evrard& Henry 1991;Bryan & Norman 1998; in an otherwise relaxed, massive cool core cluster, pointing
Borganiet al. 2002, and referencestherein).It is thereforees- to a complex dynamical evolution of the system. Furthermore,
sentialtoinvestigatewhethergalaxyclustersobeytheexpected RXJ1347.5−1145isapowerfulgravitationallensandmassre-
scalingrelations,whicharethefoundationtousethesevirialized constructions based on weak and strong lensing analyses have
objects as cosmologicalprobes.The first importantstep in this been performed(Schindler et al. 1995; Fischer & Tyson 1997;
context is to find a proxy for an accurate determination of the Sahuetal.1998;Bradacˇetal.2005b).
clustermass. With a detailed study of the properties of the ICM in
Thegalaxycluster RX J1347.5−1145(z = 0.451)is an ex- this cluster it is thus possible to address many key issues
ceptionalobjectinmanyaspects.ItisthemostX-ray-luminous on both dynamical and non-gravitational processes in galaxy
clusterknowntodate(L = 6×1045 ergs−1 inthe[2–10]keV clusters. A great advantage of observing RX J1347.5−1145
X
energyrange)withaverypeakedsurfacebrightnessprofileand with XMM-Newton is that important quantities derived for the
hosts a strongcoolingflow in its centerwith nominalmassac- undisturbedcluster(i.e.,withthesouth-eastquadrantexcluded)
cretion rate of ∼1900 M(cid:3) yr−1 (Gitti & Schindler 2004). The suchasthe azimuthallyaveragedICM densityandtemperature
Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20077580
384 M.Gittietal.:MassdistributioninRXJ1347.5−1145studiedwithXMM-Newton
profilescanbecomputeduptoalargedistancefromthecenter (thechosenthresholdvaluesare0.15cpsforMOSand0.22cps
(∼1730kpc).Themeasurementofclustertemperaturegradients forpn).Theremainingexposuretimesaftercleaningare32.2ks
atlargedistancesisalsocrucialfordeterminingthetotalgravi- forMOS1,32.5ksforMOS2and27.9ksforpn.Startingfrom
tationalmasses andin turnthe gasmassfractionof clusters. A theoutputoftheSASdetectionsourcetask,wemakeavisualse-
precise determinationof the total mass at large radii allows an lectiononawideenergybandMOS&pnimageofpointsources
estimate of thevirialradiusofthe objectwithoutmuchextrap- in thefield ofview(hereafterFOV).Eventsfromthese regions
olationoftheuniversalNFWdarkmatterprofile(Navarroetal. areexcludeddirectlyfromeacheventlist.
1996). The virial radius can then be used to study the scalings The background estimates are obtained using a blank-sky
of the temperature and entropy profiles and a fair comparison observation consisting of several high-latitude pointings with
between predictionsof numericalsimulationsand observations sourcesremoved(Lumbetal.2002).Theblank-skybackground
canbeperformed.Currently,thetwomostpromisingtechniques events are selected using the same selection criteria (such as
for obtaining accurate determinations of cluster masses are PATTERN,FLAG,etc.),intensityfilter(forflarerejection)and
X-rayobservations,bydeprojectionofX-raysurfacebrightness pointsourceremovalusedfortheobservationevents;thisyields
combined with spectroscopic determination of the cluster tem- final exposure times for the blank fields of 365 ks for MOS1,
perature,andgravitationallensing,througheitherstronglensing 350 ks for MOS2 and 294 ks for pn. Since the cosmic ray in-
features or statistical distortions of background objects (weak duced background might slightly change with time, we com-
lensing). The mass estimates inferred with these two methods pute the ratio of the total count rates in the high energy band
canbequiteinconsistent,particularlyinthecaseofstronglens- ([10–12]keV forMOSand [12–14]keV forpn).The obtained
ing (e.g. Wu et al. 1998,and referencestherein). In contrastto normalization factors (0.992, 1.059, 1.273 for MOS1, MOS2
the X-ray technique,the gravitationallensing methodis essen- andpn,respectively)arethenusedtorenormalizetheblankfield
tiallyfreeofassumptionsonthenatureandthedynamicalstate data. Furthermore,the blank-skybackgroundfiles are recast in
of the gravitatingmaterial. In particular,the X-ray method can ordertohavethesameskycoordinatesasRXJ1347.Theback-
beaffectedstronglyduringmergers(Schindler1996)andinthe groundsubtraction(forspectraandsurfacebrightnessprofiles)is
innerclusterregionwhereastronginteractionbetweenthecen- performedasdescribedinfulldetailinArnaudetal.(2002).This
tral AGN and the ICM is present (e.g., Bîrzan et al. 2004), as procedure consists of two steps. In a first step, for each prod-
in these cases deviations from the assumptions of hydrostatic uctextractedfromtheobservationeventlist,anequivalentprod-
equilibrium and spherical symmetry are expected. Since both uctisextractedfromthecorrespondingblank-fieldfileandthen
the total mass profile derived from X-rays and the total mass subtracted from it. This allows us to remove the particle back-
distribution derivedfromgravitationallensing are available for ground.However,ifthebackgroundintheobservationregionis
RXJ1347.5−1145,acomparisonbetweenthemispossiblethus different from the average background in blank field data, this
providingimportantinsightsonthisissue.Furthermore,thepres- stepcouldleavearesidualbackgroundcomponent.Theresidual
enceofgaswithshortcoolingtimeintheclustercoreoffersthe background component is estimated by using blank field sub-
opportunitytoexploregasheatingprocessessuchasAGNheat- tracted data in a region free of cluster emission and then sub-
ing,whichhavebecomeincreasinglypopularsincethefailureof tractedinasecondstepfromeachMOSandpnproduct.
standardcoolingflowsmodels. The source and background events are corrected for vi-
In this paper, by starting from the results of morphological gnetting using the weighted method described in Arnaud et al.
(Sect. 3) and spectral (Sect. 4) analyses of XMM-Newton ob- (2001), the weight coefficients being tabulated in the eventlist
servationsofRXJ1347.5−1145(Sect.2),wepresentadetailed withtheSAStaskevigweight.Thisallowsustousetheon-axis
study of the cluster mass distribution (Sect. 6), and discuss its response matrices and effective areas. Unless otherwise stated,
comparison with the mass profile derived from previous stud- thereportederrorsareat90%confidencelevel.
ies(Sect.7).We alsostudythescalingpropertiesofthecluster
(Sects.5and6)andexploretheroleofAGNheatingintheclus-
ter coolcorein thecontextofthe effervescentheatingscenario 3. Surfacebrightnessprofile
(Sect.8).RXJ1347.5−1145(hereafterRXJ1347)isataredshift
of0.451.WithaHubbleconstantofH =70kms−1Mpc−1,and PreviousChandraandXMM-NewtonobservationsofRXJ1347
0 revealedthepresenceofahotandbrightX-raysubclumpvisible
ΩM = 1−ΩΛ = 0.3,the luminositydistance is 2506Mpc and tothesouth-east(SE)ofthemainX-raysurfacebrightnesspeak
theangularscaleis5.77kpcperarcsec.
(Allenetal.2002b;Gitti&Schindler2004).Ontheotherhand,
thedataexcludingtheSEquadrant(hereafter“undisturbedclus-
2. Observationanddatapreparation ter”)showaregularmorphology,indicatingarelaxedstate.We
areinterestedindeterminingthecharacteristicpropertiesofthe
RX J1347 was observed by XMM-Newton in July 2002 during
cluster in order to performstudiesof mass profilesand scaling
rev. 484 with the MOS and pn detectors in Full Frame Mode
relationsasitisusuallydoneforrelaxedclusters.Thedisturbed
with THINfilter,foran exposuretimeof37.8ksforMOSand
SE quadrant is thus masked in the following morphological
33.2 ks for pn. We use the SASv6.0.0 processing tasks em-
analysis.
chain and epchain to generate calibrated event files from raw
Wecomputeabackground-subtracted,vignetting-corrected,
data.Throughoutthisanalysissinglepixeleventsforthepndata
radialsurfacebrightnessprofileinthe[0.3–2]keVenergyband
(PATTERN 0) are selected, while for the MOS data sets the
for each camera separately. For the pn data, we generate a list
PATTERNs0–12areused.Theremovalofbrightpixelsandhot ofout-of-timeevents1 (hereafterOoT)tobetreatedasanaddi-
columnsisdonein a conservativeway applyingthe expression tionalbackgroundcomponent.TheeffectofOoTinthecurrent
(FLAG==0).Torejectthesoftprotonflaresweaccumulatethe
observingmode(FullFrame)is6.3%.TheOoTlistisprocessed
lightcurveinthe[10–12]keVbandforMOSand[12–14]keV
band for pn, where the emission is dominated by the particle- 1 Out-of-time events are caused by photons which arrive while the
induced background, and exclude all the intervals of exposure CCD is being read out, and are visible in an uncorrected image as a
time having a count rate higher than a certain threshold value brightstreaksmearedoutinRAWY.
M.Gittietal.:MassdistributioninRXJ1347.5−1145studiedwithXMM-Newton 385
10 levelofatleast25countsineachbin.Thedataaremodeledusing
the XSPEC code, version 11.3.0 (Arnaud 1996). Unless other-
(cid:1)(cid:2)2 1 wisestated,therelativenormalizationsoftheMOSandpnspec-
min tra are left free when fitted simultaneously.We use the follow-
arc ing response matrices: m1_439_im_pall_v1.2.rmf(MOS1),
(cid:1)1 0.1 m2_439_im_pall_v1.2.rmf (MOS2), epn_ff20_sY9.rmf
s
cts (pn).
(cid:1)S 0.01
4.1.Globalspectrum
10 20 50 100 200 500 1000
r(cid:1)kpc(cid:2) For each instrument, a global spectrum is extracted from all
events lying within 5 arcmin to the cluster emission peak. We
Fig.1. Background subtracted, azimuthally-averaged radial surface
test in detail the consistency between the three camera by fit-
brightness profile in the [0.3–2] keV range of the data excluding the
tingseparatelythesespectrawithamekalmodel(withthered-
SEquadrant(undisturbedcluster).Thebestfitβ-modelfittedoverthe
∼350–1730 kpc region is over-plotted as a dashed line (model SO in shiftfixedatz = 0.451)absorbedbyacolumndensityincluded
in the tbabs model (fixed at the nominal galactic value N =
Table 1). When extrapolated to the center, this model shows a strong H
deficit ascompared totheobserved surface brightness. Thesolidline 4.85× 1020 cm−2, Dickey & Lockman 1990). Fitting the data
showsthebestfitdoubleβ-modelfittedoverthewholeregion(model from all instruments above 0.3 keV leads to inconsistent val-
DDinTable1). uesforthetemperaturederivedwiththeMOSandpncameras:
kT = 12.2+0.7 keV(MOS1),10.4+0.5 keV(MOS2),9.3+0.3 keV
(pn). We th−0e.n6 perform a systema−t0ic.5study of the effec−t0o.3f im-
in a similar way as done for the pn observationevent file. The
posing various high and low-energy cutoffs, for each instru-
profilesforthethreedetectorsarethenaddedintoasinglepro-
ment. Good agreement between the three cameras is found in
file, binned such that at least a signal-to-noise ratio of 3 is
r(ce∼lua5scthaeerrcd,m.shTionhw)e.ncTliuhnsetFesirugre.fma1c,iseissibofirnitgtiehsdtndieentsestchpteerdoCfiuIlApeOtooftRothooueltS=uhne1dr.i7ps3atuMwrbipethdc s1thp0ee.0c[+−t0r00.a..865l–af1on0ra.l0My]sOkiseSVi2n,et1nh0eisr.2ge+−yn00re..44argnfyogrerap(knnTg).e=.WT1eh1et.h2ce−+or00em..67fobkrieenVepdfeorMfroOMrmSO+Stph1ne,
variousparametricmodels,whichareconvolvedwiththeXMM globaltemperature,in keV, and metallicity, as a fractionof the
point spread function (PSF). The overall PSF is obtained by solarvalue(Anders&Grevesse1989)derivedfromthebestfit
addingthePSFofeachcamera(Ghizzardi2001),estimatedatan (χ2/d.o.f. = 2717/1697) are respectively: kT = 10.4+−00..33 keV,
energyof1.5keVandweightedbytherespectiveclustercount Z = 0.25+−00..0033 Z(cid:3). The unabsorbed luminosities in this model
rateinthe[0.3–2]keVenergyband.Asingleβ-model(Cavaliere (estimatedfromtheaverageofthefluxesmeasuredbythethree
&Fusco-Femiano1976): camerasafterfixingN = 0)intheX-ray([2.0–10.0]keV)and
H
(cid:1) (cid:2) bolometricbandarerespectively:L =6.2±0.2×1045 ergs−1,
S(r)=S 1+ r2 −3β+0.5 (1) Lbol = 13.5 ± 0.4 × 1045 ergs−1,Xwhere the errors are given
0 r2 as half the differencebetween the maximumandthe minimum
c
value.
is not a good description of the entire profile (model SG in
Table1)andafittotheouterregions(350kpc(cid:1) r (cid:1)1730kpc)
shows a strong excess in the center as compared to the model 4.2.Spatiallyresolvedspectra
(seeFig.1).Thecentrallypeakedemissionisastrongindication
ofacoolingflowinthiscluster.Wefindthatfor350kpc(cid:1) r (cid:1) As donefor the morphologicalanalysis, forthe spectralanaly-
1730 kpc the data can be described by a β-model with a core sisweseparatetheSEquadrantcontainingtheX-raysubclump
radiusr = 307±9kpcandaslopeparameterβ = 0.86±0.02 fromthe rest of the cluster. Thedata of the undisturbedcluster
(3σ concfidencelevel). The single β-modelfunctionalformis a are divided into the following annular regions: 0–30(cid:4)(cid:4), 30(cid:4)(cid:4)–1(cid:4),
convenientrepresentationofthegasdensityprofileintheouter 1(cid:4)–1.(cid:4)5, 1.(cid:4)5–2.(cid:4), 2.(cid:4)–3.(cid:4), 3.(cid:4)–5.(cid:4). The spectra are modeled using a
regions,whichisusedasatracerforthepotential.Theparame- simple,single-temperaturemodel(mekalplasmaemissioncode
tersofthisbestfitarethususedinthefollowingtoestimatethe inXSPEC)withtheabsorbingcolumndensityfixedatthenomi-
clustergasandtotalmassprofilesintheregionwherethesingle nalGalacticvalue.Thefreeparametersinthismodelarethetem-
β-modelholds(seeSect.6). peraturekT,metallicityZ(measuredrelativetothesolarvalues,
Wealsoconsideradoubleisothermalβ-modelintheform: with the various elements assumed to be present in their solar
⎛ ⎞ ratios, Anders & Grevesse 1989) and normalization (emission
S(r)=(cid:3)S0,i⎜⎜⎜⎜⎜⎝1+ rr22 ⎟⎟⎟⎟⎟⎠−3βi+0.5 (2) mleveealssudree)r.ivTehdefbroemst-tfihtetifintgsptoartahmeaetnenruvlaalrusepseacntrda9a0re%sucmonmfiadreiznecde
i c,i inTable2.
wherei = 1,2,andfindthatitcanaccountfortheentireprofile
(seeFig.1).Thebestfitparametersarer = 39±1kpc,β =
c,1 1 4.3.Deprojectionanalysis
0.62±0.01,r =386±17kpc,β =1.01±0.05.Byassuming
c,2 2
acommonβvaluewefind:rc,1 =241±7kpc,rc,2 =47±2kpc, Becauseofprojectioneffects,thespectralpropertiesatanypoint
β=0.76±0.01(seeTable1). in the cluster are the emission-weighted superposition of radi-
ation originating at all points along the line of sight through
thecluster.Tocorrectforthiseffect,weperformadeprojection
4. Spectralanalysis
analysisbyadoptingthe XSPECprojctmodel.Underthe as-
Throughouttheanalysis,asinglespectrumisextractedforeach sumptionofellipsoidal(inourspecificcase,spherical)shellsof
region of interest and is then regroupedto reach a significance emission, this model calculates the geometric weighting factor
386 M.Gittietal.:MassdistributioninRXJ1347.5−1145studiedwithXMM-Newton
Table1.Resultsfromfittingthesurfacebrightnessprofileoftheundisturbedclusterindifferentradialintervals[R –R ].Thesingleanddouble
in out
β-modelsusedforthefittingaregivenbyEqs.(1)and(2),respectively.Theyareindicatedwith:SG(Singleβ-model,fittedintheGlobalradial
range),SO(Singleβ-model,fittedintheOuterregion),DD(Doubleβ-model,withDifferent βvalues),DE(Doubleβ-model,withEqual βvalues).
Thequotederrorsareat3σconfidencelevel.
Model R –R S β r χ2/d.o.f.(χ2 )
in out 0,i i c,i red
(arcmin) (kpc) (cts/s/arcmin2) (arcmin) (kpc)
SG:singleβ 0.0–5.0 0–1731 14.42+0.50 0.590+0.005 0.1492+0.0029 52+1 1620/129(12.56)
−0.50 −0.005 −0.0030 −1
SO:singleβ 1.0–5.0 346–1731 0.891+0.075 0.861+0.022 0.8876+0.0253 307+9 109/87(1.25)
−0.075 −0.020 −0.0265 −9
DD:doubleβ 0.0-5.0 0–1731 18.94+0.86 0.616+0.009 0.1138+0.0032 40+1 258/111(2.32)
−0.86 −0.008 −0.0033 −1
withβ (cid:1)β 0.42+0.04 1.010+0.051 1.1145+0.0483 386+17
1 2 −0.04 −0.043 −0.0506 −18
DE:doubleβ 0.0–5.0 0–1731 18.12+1.00 0.1360+0.0048 47+2 289/112(2.58)
−1.00 −0.0050 −2
withβ =β 0.96+0.06 0.761+0.012 0.6968+0.0205 241+7
1 2 −0.06 −0.011 −0.0211 −7
Table2.Resultsofthespectralfittinginconcentricannularregionsin
16
the[0.8–10.0]keVenergyrangeobtainedbyfixingtheabsorbingcol-
umndensitytotheGalacticvalue(NH=4.85×1020cm−2).Thetemper- 14
ature(inkeV)andmetallicity(infractionofthesolarvalue,Anders&
Grevesse1989)areleftasfreeparameters.ThedataoftheSEquadrant (cid:2)V 12
areexcluded(undisturbedcluster). ke
(cid:1) 10
T
8
Radius sourcecounts kT Z χ2/d.o.f.
6
(kpc) (MOS+pn) (keV) (Z(cid:3))
0–173 46719 9.3−+00..33 0.31−+00..0055 914/964 250 500 750 1000 1250 1500 1750
173–346 18377 12.5+1.1 0.16+0.01 573/546 r(cid:1)kpc(cid:2)
−0.9 −0.01
346–519 8733 11.8+1.5 0.22+0.14 288/295 Fig.2.Deprojected(triangles)andprojected(stars)X-raygastemper-
−1.2 −0.15
519–692 4331 9.4+1.7 0.13+0.18 201/178 ature profilesmeasured inthe [0.8–10.0] keV energy range. Thedata
−1.3 −0.13 pointsoftheprojectedprofileareslightlyshiftedtotherighttoimprove
692–1038 4092 9.8+2.5 0.18+0.25 315/229
−1.7 −0.18 theclarityoftheplot.Thesolidlineshowsthebestfitfunctionusedin
1038–1731 2742 7.3+4.2 0.40+0.64 572/383 thetotalgravitationalmassestimationpresentedinSect.6.1below.
−2.3 −0.40
temperature is maximal, then r = 433 ± 87 kpc for the de-
according to which the emission is redistributed amongst the br
projectedprofile andr = 260±87 kpcfor the projectedpro-
projectedannuli. br
file,respectively.Thisdistancecorrespondsto∼0.1−0.2r (see
The deprojection analysis is performed by fitting simulta- vir
Sect. 6.2), in agreement with works on the scaling properties
neously the spectra of the three cameras. The results are re-
oflargesamplesofclustersofgalaxies(Markevitchetal.1998;
portedinTable3.Wealsocalculatetheelectr(cid:10)ondensitynefrom DeGrandi&Molendi2002;Piffarettietal.2005;Vikhlininetal.
the estimate of the Emission Integral EI = n n dV given by
e p 2005; Pratt et al. 2007). The temperature decrease observed in
tnhee=me1k.2a0l2n3onrpminaltihzeatiioonni:z1e0d−i1n4tEraI-/c(l4uπst[eDrAp(l1as+mza).]2).Weassume wthiethotuhteerfirnedgiinognsso(f∼t4h0es%esftruodmiesr.brTthoe0te.5mrpveirr)aitsuraelsdoercivoendsifsrtoenmt
the deprojected spectral analysis drops from the peak value of
13.6keVtothecentralminimumvalueof9.1keV.Thisisfully
5. Radialprofiles
consistentwiththetypical30%dropseenintemperatureprofiles
5.1.Temperature ofcoolcoreclusters(e.g.seeKaastraetal.2004).
ThedeprojectedtemperatureprofilederivedinSect.4.3isshown
inFig.2,wherewealsoshowtheprojectedprofileforcompar- 5.2.Coolingtime
ison. As expected,the deprojectedcentraltemperatureis lower
The cluster RX J1347 is known to host a cool core (Schindler
than the projected one, since in the projected fits the spectrum
etal.1997;Allenetal.2002b;Gitti&Schindler2004).Thecen-
ofthecentralannulusiscontaminatedbyhotteremissionalong
trallypeakedsurfacebrightnessprofileandthecentraltempera-
the line of sight. We also note that the projected temperature
turedropdiscussedinSects.3and5.1,respectively,areindeed
profile measured by Chandra (Allen et al. 2002b) is system-
signaturesofthepresenceofacentralregionwheretheplasma
atically slightly higher than that measured by XMM-Newton,
cooling time is short.In the followingwe computethe cooling
althoughthegeneraltrendobservedbythetwosatellitesiscon-
timeprofileandthecoolingradiusofthecluster.
sistent(Gitti&Schindler2004).
Thecoolingtimeiscalculatedasthecharacteristictimethat
ThetemperatureprofileofRXJ1347exhibitstheshapechar-
it takes a plasma to cool isobarically through an increment of
acteristic for cool core clusters: the temperature declines from
temperatureδT:
the maximum cluster temperature at a break radius r moving
br
outwards and drops towards the cluster center. If r is sim- 5 kδT
br t = (3)
ply defined as the distance from the cluster center where the cool 2n Λ(T)
e
M.Gittietal.:MassdistributioninRXJ1347.5−1145studiedwithXMM-Newton 387
Table 3. Results of the deprojection analysis on annular MOS+pn where T and ne are the deprojected electron temperature and
spectra using the XSPEC projct model. The column density is density,respectively.
fixed to the Galactic value and the normalizations are in units of In cooling core clusters the radial entropy profiles are ex-
10−14nenpV/4π[DA(1+z)]2. The fit gives χ2/d.o.f. = 3007/2557. The pectedtoincreasemonotonicallymovingoutwards,andtoshow
dataoftheSEquadrantareexcluded(undisturbedcluster).
noisentropiccores(e.g.,McCarthyetal.2004).Thisbehavioris
indeedobservedinnearbycoolingcoreclusters(Piffarettietal.
2005;Prattetal.2006).Entropyprofilesareingeneralwellde-
Radius kT Z norm n
(kpc) (keV) (Z(cid:3)) (×10−3) (×10−3ecm−3) scribedbyapowerlaw.Thevalueofthepowerlawindexscatters
around unity, depending on the cluster or cluster sample used
0–173 9.1+0.4 0.32+0.05 6.02+0.08 23.22+0.16
−0.4 −0.05 −0.08 −0.16 to derive it: for example, Ettori et al. (2002a)found 0.97 from
173–346 12.6−+11..22 0.16−+00..1152 2.73−+00..0079 5.91−+00..0089 ChandradataofA1795,Pratt&Arnaud(2005)derivedaslope
346–519 13.6+3.4 0.22+0.30 1.51+0.07 2.66+0.06 of 0.94±0.14 from scalings of the entropy profiles of 5 clus-
−2.7 −0.21 −0.09 −0.08
519–692 8.6+3.4 0.18+0.25 0.88+0.06 1.46+0.05 ters observed with XMM-Newton, Piffaretti et al. (2005) found
692–1038 11.1−+14.8.9 0.08−+00..1389 0.81−+00..0064 0.69−+00..0052 0.95 ± 0.02 using scaled profiles of 13 cool core clusters ob-
−3.0 −0.08 −0.07 −0.03 servedwithXMM-Newton,andPrattetal.(2006)derivedaslope
1038–1731 7.1−+24..42 0.39−+00..3599 0.54−+00..0078 0.25−+00..0022 of1.08±0.04(extendingthesamplestudiedinPratt&Arnaud
(2005)to10objects).
In Fig. 4 we show the gas entropy profile of RX J1347
200
computed from the deprojected temperature and electron den-
100 sity derived in Sect. 4.3. We fit the profile with a line in log-
log space (with errors in both coordinates) and find: log[S] =
(cid:2)yrs 50 (1.053±0.005)×log[r]+(0.011±0.010)(entropyinkeVcm2
G
(cid:1) 20 and radius in kpc), which is consistent with previous results.
tcool 10 Donahue et al. (2006) recently found that the entropy profiles
theyderivedfromChandraobservationsof9coolcoreclusters
5
arebetterfittedbyapowerlawplusaconstantentropypedestal
of≈10keVcm2thanbyapurepowerlaw.Weperformedsimilar
2
100 150 200 300 500 700 1000 1500 fitsandfindanentropypedestalconsistentwithzero.However,
r(cid:1)kpc(cid:2) we notice that this result might be due to the lack of adequate
spatialresolutionoftheentropyprofileinthecentralregion.
Fig.3.Coolingtimeasafunctionofradius.
Recentresultssuggestthattheentropyscaleswiththe tem-
peratureasS ∝ (cid:7)T (cid:8)0.65, the so-called“entropyramp”,instead
X
oftheself-similarscalingS ∝(cid:7)T (cid:8)(Ponmanetal.2003;Pratt&
where Λ(T) is the total emissivity of the plasma (the cooling Arnaud2005;Piffarettietal.200X5;Prattetal.2006).Here(cid:7)T (cid:8)
X
function) and k is Boltzmann’s constant. Utilizing the depro- isthemeancluster/grouptemperaturecorrectedforthecoolcore
jectedtemperatureprofileandthedensityprofilefromSect.4.3, effectandS istheentropymeasuredatsomefractionofhevirial
wecancalculatethecoolingtimeasafunctionofradius,which radius(usually0.1×r ,seeSect.6.2belowforthedefinition
200
isshowninFig.3.Thecoolingtimeshowsapowerlawbehavior
andcomputationofr ).Inorderto verifyifthe entropymea-
asafunctionofradius.Wefindt ∝r1.46±0.01whenall6radial 200
cool suredinRX J1347followsthisrelation,wethereforeadoptthe
bins are used in the fit and tcool ∝ r1.72±0.21 if only the 4 radial scaling S ∝ h−4/3(z)((cid:7)T (cid:8)/10 keV)0.65, with a mean tempera-
binsbeyond0.2r500 ≈280kpcareconsidered(seeSect.6.2be- tureforRXJ1347equalXto10.1±0.7keV(seeSect.5.2).Here
lowforthedefinitionandcomputationofr500).Thelattervalue h2(z) = Ωm(1+z)3 +ΩΛ and the factor h−4/3 comes from the
agrees with recent results from the analysis in the same radial scaling of the density.At0.1×r the scaled entropyis equal
rangeofa sampleofluminousclustersatz = 0.2(Zhangetal. to382±32,349±54,and437±25010 keVcm2forr computed
200
2007).FollowingBîrzanetal.(2004),wedefinethecoolingra-
fromthetotalmassprofilesderivedfrommodelSO,DDg1,and
dius as the radius within which the gas has a coolingtime less NFW,respectively(seeSect.6.1belowforthedifferentmodels
than 7.7×109 yr, the look-backtime to z = 1 for our adopted
usedinthetotalmassdeterminationfromtheX-raydata).Ifin-
cosmology. With this definition, we find rcool ∼ 210±10 kpc stead thevaluerSim isused(i.e.,we adoptthe size-temperature
whichcorrespondstothecentral36arcsec. 200
relationcalibratedthroughnumericalsimulations,see Sect. 6.2
In the following analysis it is important to correct for the below), the normalization is 567±70 keVcm2. The errors on
effects of the central cooling flow when measuring the char- thesenormalizationsalsotakeintoaccounttheuncertaintyinthe
acteristic temperature of the undisturbed cluster. The average estimateofr .Thenormalizationderivedbyadoptingthesize-
200
emission-weighted cluster temperature is calculated by fitting temperaturerelationisingoodagreementwiththeentropynor-
with a mekal modelthe spectrum extracted up to the outer ra- malizationoftheS(0.1×r )–(cid:7)T (cid:8)relationat(cid:7)T (cid:8)=10keV
200 X X
diusdetectedbyourX-rayobservation(5arcmin),afterexcising byPonmanetal.(2003,seetheirFig.4).Thevaluescomputed
the coolingregion(central35 arcsec)andthe SE quadrant.We using r derived from the total mass profiles are smaller, but
findavalue(cid:7)TX(cid:8)=10.1±0.7keV. stillcon2s00istentwithintheuncertainties,thanthevaluesfoundby
Ponmanetal.(2003).
5.3.Entropy
6. Massdetermination
Thegasentropyingroupsandclustersofgalaxieshasrecently
receivedparticularattentionsinceitresultedtobeaveryuseful In Gitti& Schindler(2004)wepresentedthetotalmassprofile
quantity to probe the thermodynamic history of the hot gas in estimatedfromthesingleβ-model.Herewe performadetailed
these systems. The entropy is usually defined as S = kT/n2/3, study of the radial profiles of total gravitational mass and gas
e
388 M.Gittietal.:MassdistributioninRXJ1347.5−1145studiedwithXMM-Newton
3000
computetheelectronnumberdensitiesforthe two components
2000
n (r)andthetotalelectronnumberdensity,n (r)using:
1500 e,i e
1000 ⎡ ⎤
(cid:3)(cid:2)2cm 570000 ne(r)=(cid:3)ne,i(r)=⎢⎢⎢⎢⎢⎣ne(0)(cid:3)n˜e,i(r)⎥⎥⎥⎥⎥⎦1/2, (5)
V
e 300 i i
k
(cid:1) (cid:11) (cid:12)
S 200
150 n (r)= ne(0) n˜ (r), (6)
100 e,i n (r) e,i
e
⎛ ⎞
100 150200 r(cid:1)3k0p0c(cid:2) 500 700 1000 1500 n˜ (r)=n (0)⎜⎜⎜⎜⎜⎝1+ r2 ⎟⎟⎟⎟⎟⎠−3βi, (7)
e,i e,i r2
Fig.4. Entropy as a function of radius and the best fit power law c,i
log[S]=(1.053±0.005)×log[r]+(0.011±0.010)(entropyinkeVcm2
andradiusinkpc). wherei=1,2andne(0)isthecentral,totalelectrondensity.The
centralnumberdensitiesforthetwocomponentsaregivenby
(cid:11) (cid:12) (cid:11) (cid:12) (cid:1) (cid:2)
4π1/2 Γ(3β) S
n2 (0)= i 0,i A (8)
massreconstructedbyusingdifferentmethods.Thenewvalues e,i α(T)gµ Γ(3β −1/2) r ij
i i e i c,i
donotchangethemainconclusionsinGitti&Schindler(2004)
inwhich
but are moreaccurate.In this section we also presentthe com-
(cid:1) (cid:2)(cid:1) (cid:2)(cid:1) (cid:2) (cid:11) (cid:12)
putationofthecharacteristicradiir∆quotedabove. 1 =1+ gi rc,iS0,j Ti 1/2 Γ(3βj)Γ(3βi−1/2) , (9)
A g r S T Γ(3β)Γ(3β −1/2)
ij j c,j 0,i j i j
6.1.Totalgravitationalmass
where j = 1, 2 and j (cid:1) i. Here g is the Gaunt factor for
i
TheanalysistoestimatethetotalgravitationalmassofRXJ1347 the component i and α(T) is the emissivity due to thermal
i
is not limited to only one specific method, but is instead car- bremsstrahlung. The Gaunt factors are computed using the re-
riedoutbyadoptingdifferentapproaches.Thisenablesustoin- sults of Sutherland (1998). Note that in the derivation of the
vestigatetheeffectsintroducedbydifferentfittingfunctionsfor equations given above it is assumed that each component has
thegasdensityandtemperature,anddifferentmethodstoderive a constant electron temperature T throughout the cluster. As
i
thetotalmassfromtheobservedgasdistribution. shown in Sect. 5 the gas is not isothermal hence this assump-
Thetotalgravitatingmassdistributioniscalculatedunderthe tion is not strictly valid. Nevertheless the temperature depen-
usualassumptionsofhydrostaticequilibriumandsphericalsym- dence of the aboveequationis fairly weak andwe set T1or2 =
metrybyusing Tmax = 13.6keV(themaximumofthetemperatureprofile)and
= T = T = 7.1keV (the minimum of the temperature
(cid:11) (cid:12) 2or1 min
profile)toquantifythemaximumvariationofthetotalmasses-
M (<r)=−kT(r)r dlnρg(r) + dlnTg(r) (4) timatewithtemperature.UsingtheaboveequationsandEq.(4)
tot Gµm dlnr dlnr
p wecomputethemassprofilefor4cases:DDg1(modelDDand
T = T ,T = T ),DDg2(modelDD andT = T ,T =
1 max 2 min 1 min 2
whereG andmp arethegravitationalconstantandprotonmass Tmax), DEg1(modelDE andT1 = Tmax,T2 = Tmin), andDEg2
and µ = 0.62. A welcome property of Eq. (4) is that the total (model DE and T = T ,T = T ). While the assump-
1 min 2 max
gravitationalmasswithinasphereofradiusrisdeterminedfrom tionofisothermalityisjustifiedintheevaluationofthedensity-
the gas density ρg and temperature Tg measured at the cluster- dependent term of Eq. (4) from the observed surface bright-
centric distance r. This implies that when the gas density and nessprofile,theradialdependenceofthegastemperaturemust
temperatureare well modeledonly in the radialrangeRin–Rout be carefully modeled, since the total gravitational mass varies
butnotwithinRin,themassdeterminationisstillreliableinthe stronglywithtemperature.Thetemperatureprofileinthewhole
rangeRin–Rout. Asshownin Sect. 3, a single β-modelprovides observedrangeisclearlynotwelldescribedbyapolytropicre-
a good fit to the surface brightness profile in the radial range lation and it is not possible to model it using a single analyti-
350kpc(cid:1) r (cid:1) 1730kpc(modelSOinTable1).Inthiscasethe cal function due to the central temperature drop. We therefore
deprojected gas density profile is easily computed and the to- model the profile using two functionsjoined smoothly at a cut
talclustermassisindependentofthegasdensitycentralvalue. radiusR ,i.e.wetakecarethatthetemperatureprofileandits
cut
Sincebeyond350kpcthetemperatureprofileisdeclining,itcan gradient are continuous across R . Since the polytropic rela-
cut
bewellmodeledthroughthepolytropicrelationT ∝ ργ−1,with tion provides a good description in the outer region, we adopt
g
1 ≤ γ ≤ 5/3.Thepolytropicfitto the deprojectedtemperature T ∝ ργ−1 asfittingfunctionforr ≥ R ,withρcomputedfrom
profilesgivesinthiscaseγ = 1.23±0.02(1σerrorononepa- the dogubleβ-model fits. The valuesocbuttained for the parameter
rameter). The total mass profile computed using this model is γ are very similar to those obtained when using the single β-
discussedbelowtogetherwiththeresultsfromthemoresophis- model.WithinR wechoosetofitthetemperatureprofileusing
cut
ticateddoubleβ-model. a 5thorderpolynomialwithzeroderivativeatthecenter.Ifthe
In order to obtain a total mass estimate for the whole ob- latter conditionisnotsatisfied the derivedtotalmassdensityis
served radial range we use the double β-model fits discussed found to be negative in the cluster core. We vary R and find
cut
in Sect. 3 (model DD and DE in Table 1). The gas density is thatR = 520kpcprovidesthebestmodel.Theresultingbest
cut
computed from the double β-model surface brightness fits us- fitfunctionisshowninFig.2.Thetotalmassprofilescomputed
ing the formulasderivedin Xue & Wu (2000):we assume that from the surface brightness fits presented in the following are
each componentcorrespondsto a gasphase, invertEq. (2) and computed using this temperature profile modeling and will be
M.Gittietal.:MassdistributioninRXJ1347.5−1145studiedwithXMM-Newton 389
indicatedbythenameofthemodelusedtodescribethesurface
brightness(seeTable1). 1.(cid:2)1015
Therelativedifferencebetweenthemassprofilesformodel
DDg1 and DDg2 (DEg1 and DEg2) is less than 4% (6%) in
5.(cid:2)1014
the whole observed radial range (0–1731 kpc). Models DDg1
andDDg2,andDEg1andDEg2givenearlyidenticalresultsfor
r > 500 kpc. The largest difference is found between models
DDg1andDEg2,butitislessthat15%inthewholeradialrange 2.(cid:2)1014
and less than 5% for r > 250. These small differences show
(cid:2)
thatthetemperaturedoesnotsignificantlyaffectthegasdensity (cid:1)
M 1.(cid:2)1014
determinationfor this massive andhotcluster, and thatmodels (cid:1)
s
s
DEanDDprovidethesamemassestimateforthewholeradial a
M
rangeofinterest.GiventheseresultsandthefactthatmodelDD 5.(cid:2)1013
gives a smaller χ2 than model DE for the surface brightness
red
modeling,wewilldiscuss,inthefollowing,onlythemasspro-
file derived using model DDg1. We compare the mass profiles 2.(cid:2)1013
derivedfromthedoubleβ-modelwiththeonefromthesingleβ-
modelintheradialrange350–1731kpc.Inthisrangetherelative
difference of the mass profiles is at most 13% (close to the in- 1.(cid:2)1013
nermostandoutermostradii),butsmallerthan10%intherange
380–1500kpcforthefourdoubleβ-modelswederived.Hence,
the doubleβ-modelprovidesestimatesin goodagreementwith 250 500 750 1000 1250 1500
the single β-model, and is of course preferred since it allows r(cid:1)kpc(cid:2)
usto estimate the massin the wholeobservedradialrange,i.e.
Fig.5.Integratedthreedimensionaltotalmassprofiles,witherrors,de-
0–1731 kpc. The mass profiles from the double β-model
rived from the double β-model (model DDg1, solid), single β-model
(model DDg1) and the single β-model (model SO) are plotted
(modelSO,dashed),andtheNFWmodel(dot-dashed).Thedottedline
inFig.5.Errorsonthetotalgravitationalmassesarecomputed showsthecumulativegasmassprofile.Seetextfordetails.
bypropagatingthe1σerrorsonthesurfacebrightnessandtem-
peratureprofilesbestfitparameters,andareoftheorderof10%
and minimum value of the total mass and hence its upper and
and 20% for the values derived from the single and double β-
lower errors. These are of the order of 10%. From a visual in-
model,respectively.Theprofilederivedusingthesingleβ-model
spection of Fig. 5 one can note that the NFW mass profile is
is shown only in the region where it is valid, i.e. for r > 350.
lowerthanthedoubleβestimateforr <1150kpcandhigherat
The mild depression visible around ∼250 kpc in the mass pro-
largerradii.Thediscrepancywithin1150kpcisduetothefact
file derivedfromthe doubleβ-modelisdue to theshape ofthe
thatourbest-fitNFWprofiletendstounderestimatethetemper-
temperatureprofileintheinnerregion. atureinthisrange.TherelativedifferencebetweentheNFWand
Theclustergravitationalmasscanalsobecomputedbymak- the doubleβ mass profilesis –38%(underestimate)at r = 500
ingdirectuseofthegastemperatureandgasdensityprofilesde-
butdecreasingtowardsthecenter,andincreasesalmostlinearly
rivedfromthe deprojectionanalysispresentedin Sect. 4.3.We to 30%(overestimate)atr = 1731kpc.Thefairlylowconcen-
inverttheequationofhydrostaticequilibrium(Eq.(4))and,us-
tration parameter c, compared to the predictions of numerical
ingthethree-dimensionalgasdensity,weselectthedarkmatter
simulations(e.g.,Macciò et al. 2006),and the goodnessof our
mass modelthat reproducesbetter the deprojectedtemperature
NFWfitmightindicatethatourtemperatureprofileisnotenough
profile.Intheminimizationthe1σerrorsononesingleparam-
spatiallyresolvedinthecentralregionoftheclusterforthiskind
eterfromthespectralfitsareused.Fordarkmattermassmodel,
of mass determination method. While the mass determination
weconsidertheintegratedNFW(Navarroetal.1996)darkmat-
fromthedoubleβ-modelmaythereforebepreferred,wepresent
terprofile:
valuesalsofromtheNFWfittingforcompleteness.
(cid:19) (cid:20)
c3 ln(1+r/r )− r/rs
M (<r)=4πr3ρ 200 s (1+r/rs) , (10) 6.2.Virialradiusandscalingrelations
DM s c,z 3 ln(1+c)−c/(1+c)
In this section we determine the characteristic radii r∆ used in
where ρc,z = (3Hz2)/(8πG) is the critical density at the clus- Sects. 5 and 5.3. For the variousmass profiles we computer∆,
ter’s redshift. The scale radius rs and the concentration pa- theradiuswithinwhichthemeaninteriordensityis∆timesthe
rameter c are the free parameters. The total gravitational mass criticalvalue,byusing
within a sphere of radius r is given by gas plus dark matter
massandtherefore Mtot(<r) = Mgas(<r)+ MDM(<r)inEq.(4). ∆= 3Mtot(<r∆)· (11)
Nevertheless,inmostofthework Mtot(<r) = MDM(<r)isused, 4πρc,zr∆3
i.e. the NFW profile is used to fit dark matter plus gas mass.
We also computedthetotalmassprofilebytakingintoaccount For the cosmology adopted here the virial radius is given by
the gas mass, i.e. by addingthe cumulativegas mass profile to r =r ,with∆˜ =178+82x−39x2andwherex=Ω(z)−1and
vir ∆˜
thebest-fittingNFWprofile,andfoundlittledifferencebetween Ω(z)=0.3(1+z)3/(0.3(1+z)3+0.7)(Bryan&Norman1998).
thetwoprofiles.Thebest-fitparametersarers = 722±112kpc ThusforRX J1347∆˜ = 135.We also compute Mtot(< r∆) and
and c = 3.20±0.30(errorsare rms of the 1σ jointconfidence Mgas(<r∆) for variousoverdensities:∆ = 2500,1000,500,200.
limits), with χ2 = 6.7 for 4 degrees of freedom. Our best-fit The results obtained from the overdensity profiles calculated
min
NFWprofileisshowninFig.5.Fromthesetof(c,r )parame- from the double β-model (DDg1) and NFW fit are reported in
s
tersacceptableat1σwecompute,foreachradius,themaximum Table4.
390 M.Gittietal.:MassdistributioninRXJ1347.5−1145studiedwithXMM-Newton
Table4.Characteristicradiir∆,totalmassMtotandgasmassMgasforvariousoverdensities∆derivedfromthedoubleβ-model(DDg1)andNFW
fits(1σerrorsinparentheses).Themassesareestimatedwithinr∆.AsdiscussedinSect.6.1,resultsfromthedoubleβ-modelaregenerallymore
reliable.
∆ r∆,DDg1 Mtot,DDg1 Mgas,DDg1 r∆,NFW Mtot,NFW Mgas,NFW
(kpc) (1014 M(cid:3)) (1014 M(cid:3)) (kpc) (1014 M(cid:3)) (1014 M(cid:3))
200 1957.2(183.2) 11.00(2.78) 3.34(0.11) 2286.7(110.8) 17.86(2.07) 3.82(0.18)
500 1387.2(123.9) 9.77(2.30) 2.39(0.05) 1479.2(71.23) 11.85(1.13) 2.55(0.06)
1000 1063.3(91.00) 8.80(1.91) 1.79(0.03) 1029.3(43.08) 7.99(0.62) 1.73(0.03)
2500 729.3(63.2) 7.10(1.40) 1.15(0.02) 608.1(19.8) 4.12(0.22) 0.91(0.01)
√
Thesize-temperaturerelationr∆ ∝ (cid:7)TX(cid:8)predictedbyself- (Arnaudet al. 2005)indicatinga breakingof self-similarity.In
similarity allows an estimate of r∆ from the mean cluster tem- thiscaseweestimateM2500,DDg1 =(4.39±0.35)×1014 M(cid:3).The
perature alone, provided that its normalization is known from massestimatethatwederiveattheoverdensity∆=2500differs
numerical simulations. We compute the normalization for the strongly depending on the model adopted (see Table 4). From
cosmology adopted here by interpolating the values given in modelDDg1weestimateM2500,DDg1 =(7.10±1.40)×1014 M(cid:3),
Evrard et al. (1996). For the mean cluster temperature (cid:7)T (cid:8) = which is much higher than the prediction of the M-T relation.
X
10.1 ± 0.7 keV we derive the characteristic radii r∆Sim, finding ThemassestimateofM2500,NFW =(4.12±0.22)×1014M(cid:3)asde-
rSim = 886 ± 30 kpc and rSim = 3197± 107 kpc. From our rivedfromthebest-fittingNFWprofileisinsteadingoodagree-
2500 vir
X-rayanalysiswefindr =(734±34,729±63,608±20)kpc mentwiththeM-T relation,althoughthelargeerrorbarsprevent
2500
and r = (2378±76,2241±189,2639±108) kpc when us- usfromdistinguishingbetweenaself-similarorsteeperrelation.
vir
inginEq.(11)themassprofilederivedfrommodel(SO,DDg1,
NFW), respectively. These values are consistent with the size- 6.3.Gasmassandgasmassfraction
temperaturerelationderivedfromobservationsofnearbyrelaxed
Fromtheresultsofthedeprojectedspectralanalysiswecompute
clusters (Arnaud et al. 2005). By comparing the above values
thecumulativegasmassprofile M (<r),thusobtainingvalues
we note that the estimates from the X-ray analysis are system- gas
forthe6binsusedininthespectralanalysis.Inordertoderive
aticallylowerthantheonespredictedfromthesize-temperature
better estimates when an extrapolationof the gas mass beyond
relation calibratedbymeansof numericalsimulations.It is not
R isneeded,wecomputethegasmassprofileusingtheradial
surprisingthatwe finda smallerdiscrepancyforr thanr , out
2500 vir gas density profile derived from the best fit parameters of the
as its determination does not require extrapolation of the ob-
doubleβ-model(modelDDg1)ofthesurfacebrightnessprofile.
served mass profile.This is in agreementwith results forother
Thenormalizationofthelatterisfixedusingthegasdensitypro-
individualclusters (e.g., Gitti et al. 2007a)and studies of clus-
ter samples (Sanderson et al. 2003; Piffaretti et al. 2005). The file fromthespectralanalysis.Theresultinggasmassprofileis
showninFig.5.WhenM (<r)isevaluatedwithinR weuse
largestdiscrepancyisfoundforr andinpoor,coolclusters.In gas out
vir the binnedprofile and spline interpolation,which in this radial
thesesystemstheimpactofadditional,non-gravitationalheating
rangeprovidesvaluesconsistentwith theonescomputedusing
ismostpronounced,astheextraenergyrequiredtoaccountfor
theresultsfromthedoubleβ-model.
their observedpropertiesis comparableto theirthermalenergy
Thegasmassfraction f isdefinedastheratioofthetotal
(Ponmanetal.1996;Tozzi&Norman2001).Theobserveddis- gas
gasmasstothetotalgravitatingmasswithinafixedvolume.We
crepancyis also relatedto thecluster totalmassdetermination.
measure f =0.162±0.036fromthemassprofilesderived
In this context it is interesting to note that recent results from gas,2500
fromthedoubleβ-modelfit(modelDDg1).Thisvalueiscloseto
numericalsimulations indicate that the total mass of simulated
theglobalbaryonfractionintheUniverse,constrainedbyCMB
clustersestimatedthroughtheX-rayapproachis lowerthatthe
observations to be Ω /Ω = 0.175 ± 0.023 (Readhead et al.
trueoneduetogasbulkmotions(i.e.deviationfromthehydro- b m
2004;Spergeletal.2003),andishigherthantheaveragevalue
staticequilibrium)andthecomplexthermalstructureofthegas
derived in a number of previous measurements with Chandra
(Rasiaetal.2006;Nagaietal.2007).
A self-similar scaling relation between M and (cid:7)T (cid:8) at (e.g.,Allenetal.2002a;Vikhlininetal.2006).However,wenote
a given overdensity is predicted in the form Mtot ∝ (cid:7)TX(cid:8)3/2. that a general trend of increasing fgas with cluster temperature
Various observational studies have found differetontt and sXome- (hencemass)hasbeenobserved(Vikhlininetal.2006).Thehigh
central gas mass fraction measured here is consistent with this
time conflicting results regarding the slope and normalization
tendency,asRXJ1347isahot,massivecluster.
of the M-T relation (e.g., Allen et al. 2001; Finoguenov et al.
2001; Ettori et al. 2002b;Sanderson et al. 2003; Arnaud et al.
2005, and referencestherein).The relation derivedby Arnaud 7. Comparisonwithpreviouswork
etal.(2005)forasub-sampleofsixrelaxedclustershotterthan
Inthissectionwecomparethemostrelevanttotalandgasmass
3.5keVobservedwithXMM-Newtonisconsistentwiththestan-
estimatesforRXJ1347foundinliteraturewithourresults.The
dardself-similarexpectation,followingtherelation:
valuesinliteratureareconvertedtothecosmologyadoptedhere
(cid:1) (cid:2)
(cid:7)T (cid:8) 1.51±0.11 beforethecomparison.
h(z)M2500 =(1.79±0.06)×1014 M(cid:3) X · (12)
5keV
7.1.ComparisonwithX-raystudies
This result is in agreement with Chandra observations (Allen
et al. 2001). In the case of RXJ1347, Eq. (12) turns into an Using combined ROSAT and ASCA observations Schindler
estimate of M2500 = (4.07±0.46)×1014 M(cid:3). By considering et al. (1997) derived Mtot = 1.11 × 1014 M(cid:3), Mtot = 4.93 ×
the whole XMM-Newton sample (ten clusters in the tempera- 1014 M(cid:3),andMtot =1.45×1015 M(cid:3) within204,850,2550kpc,
ture range[2–9]keV),therelationsteepenswith a slope∼1.70 respectively.Thesevalueswerederivedassumingisothermality
M.Gittietal.:MassdistributioninRXJ1347.5−1145studiedwithXMM-Newton 391
andtheerrorcomingfromtheuncertaintyontheglobaltemper- to only ∼0.4 times the radius where the X-ray emission is de-
atureisoftheorderof10%–15%,asweestimatedfromtheplot tectableintheChandradata.
showing the profile of the integrated total mass (see Schindler
et al. 1997, Fig. 6). We find, for model (SO, DDg1), M =
tot
(1.14±0.14,0.93±0.17)×1014 M(cid:3),Mtot =(8.10±0.84,7.85± 7.2.Comparisonwithdynamicalestimates
1.60)×1014 M(cid:3),andMtot =(1.47±0.15,1.22±0.32)×1015M(cid:3) Usingthevirialapproach,Cohen&Kneib(2002)deriveMtot =
wiciatnhtinm2i0sm4,a8tc5h0,a2t585500kkppcc,,retshpeercetisvuelltys.aWrehiinlerweaesfionndabalysiggonoifd- p(6e.r9s2io−+n12..82m90)e×as1u0r1e4mMen(cid:3)tsw.iWthiinth5in97thkipscrafrdoiumsgwaleaxcioenssvisetleonctiltyyfidinsd-
aegrrroeresmaenndttahtesmdiafflelraenndtalasrsguemrpatdiioin,sinapdaorpttiecdulianrcthoensmidaesrsindgettehre- DMDtotg1=).(6.06 ± 0.61,6.05 ± 1.14)×1014 M(cid:3) formodel(SO,
mination. For the cumulative gas mass Schindler et al. (1997)
found Mgas = 1.33 × 1014 M(cid:3) and Mgas = 5.93 × 1014 M(cid:3) 7.3.Comparisonwithgravitationallensing
within850,2550kpcrespectively,whileourvaluesare M =
gas
(1.39±0.02)×1014 M(cid:3) and Mgas = (4.32±0.17)×1014 M(cid:3) Stoitnaclemthasesgdriasvtritiabtuiotinoanl,liennosirndgeratnoalcyosmispmareeacsournessisttheentplyrotjheectreed-
within850,2550kpc,respectively.Whilethevaluesat850kpc
sultsfromtheX-rayandlensingtechniquesweprojectalongthe
areconsistent,thelargevaluefoundat2550bySchindleretal.
lineofsightthecumulative3DmassprofilesM (<r)derivedin
(1997)isverylikelyduetothenarrowerradialrangeprobedby tot
theirobservation.AsshowninSect.3(seeTable1),thegasden- Sect.6,thusobtainingMtportoj(<r).
sitysteepensintheouterregion.Asaresult,thegasmassderived Fromaweaklensinginvestigation,Fischer&Tyson(1997)
fromasingleβ-modelfittoanarrowcentralregionandextrap- derive Mtportoj = (9.35 ± 2.55)×1014 M(cid:3) within 850 kpc. We
olatedtolargeradiiisbiasedhigh.Incomparingtheresults,we find,ingoodagreement,Mproj =(9.95±1.03,9.17±2.13.79)×
tot
sehtoaul.ld(1a9ls9o7b)eisarpienrmfoirnmdetdhaotnthteheanfaullyls3is6p0r◦edseantate,dasbythSechhointdelne-r 1(1091947M) c(cid:3)omfopramreotdheelir(SmOa,ssDmDega1s)u.reNmoetentthMatproFjiswcihtheirn&85T0yksopnc
hancement in the SE quadrant has been discovered only sub- tot
with the M valuequotedinSchindleretal.(1997)andfinda
sequentlywithChandraandXMM-Newtonobservations(Allen tot
largediscrepancy.AspointedoutbySahuetal.(1998),thetwo
etal.2002b;Gitti&Schindler2004).
mass determinations are in agreement if the correct quantities
arecompared.
We compare our best-fitting NFW profile with the one de-
rivedby Allenet al. (2002b)fromChandradata. Thetwo pro- InthestronglensinganalysisbySahuetal.(1998),Mtportoj =
filesareconsistent,witharelativedifferencerangingfrom15% 5.36×1014 M(cid:3) ismeasuredwithin204kpc,thecluster-centric
to 30% depending on the radial range considered. As a gen- distance of the arcs. Within this projected distance we find
e∼r6a0l0trkenpdc), oanudr phriogfihleerriensuthltesolouwteerrreingiothne(ionuntesirdreeg∼i1o0n0(0inkspidce) DMDtportgoj1)=.A(l2t.h3o8u±gh0t.h2i7s,d2i.s0c5re±pa0n.3cy7)m×ig1h0t1b4eMd(cid:3)uefotortmheodfaeclt(SthOat,
than the one derived by Allen et al. (2002b). In particular, weexcisetheperturbedregionofthecluster,wenotethatsucha
Allenetal.(2002b)findanintegratedmasswithinthevirialra- largemismatchbetweenthemassesdeterminedfromX-raysand
dius of their best-fitting NFW mass profile of Mtot(<2 Mpc) = stronglensingiscommonlyfound(seeWuetal.1998,andrefer-
(1.95+−10..4780)×1015 M(cid:3),whichisinfairlygoodagreementwiththe encestherein).Intheinnercoreofclusters,wherestronglensing
valuethatwemeasure: Mtot(<2 Mpc) = (1.59+−00..1186)×1015 M(cid:3). occurs,thephysicsoftheICMmaybecomplicatedbytheinter-
When considering the mass profile derived from the double β- action with the centralAGN. The central cluster regionis thus
model (DDg1), which at large distances is lower than the one poorlydescribedby the usualsimple modelsused in the X-ray
derivedfromtheNFWfit(seeFig.5),wefind M (<2Mpc) = methods which rely on the assumptionsof spherical symmetry
tot
(1.11+−00..2287)×1015 M(cid:3). Thisvalueis fairlylow comparedto the andhydrostaticequilibrium.
valuefoundbyAllenetal.(2002b),butstillconsistentconsider- We compare our total mass determination with the lensing
ingtheerrorsonthemassestimatesatthislargedistance. results of Bradacˇ et al. (2005b). The results of Bradacˇ et al.
(2005b)areobtainedusingamassreconstructionmethodwhich
Ettori et al. (2004) derive from Chandra data estimates of combinesstrongandweakgravitationallensingdataandeffec-
Mtot = (8.94 ± 0.80)×1014 M(cid:3) and Mgas = (1.81 ± 0.08)× tivelybreaksthemass-sheetdegeneracy(Bradacˇetal.2005a).In
1014 M(cid:3) within 1368 kpc, which corresponds to r500 in their Fig. 6 we showthe X-rayto lensing massratio Mlensing/MX−ray
work.WhileourvalueM (<1368 kpc)=(10.84±1.11,9.72± as a function of radius up to ∼670 kpc, the limiting radius of
tot
2.27)×1014M(cid:3) (formodelSOandDDg1,respectively)agrees the lensing study. From a visual inspection of this figure it is
with the Chandra estimate, we find a larger value for the clearthatthereislackofagreementbetweentheX-rayandlens-
gas mass: Mgas(<1368 kpc) = (2.35 ± 0.05) × 1014 M(cid:3). ingmassestimates.OnlyinthecentralregiontheX-raymassis
The discrepancy might be related to the different approaches marginallyconsistentwiththelensingmass.Themassratiosin-
adopted for the calculation. We estimate the gas mass directly creasewithradiusandtendtoapproachaconstantvalueatlarge
from the density profile derived from the deprojected spec- radii.At600kpctheratiois 2.07,2.17,and2.45fortheX-ray
tral analysis (Sect. 4.3). The gas mass computed by Ettori massestimatedusingthesingleβ-model(SO),doubleβ-model
et al. (2004) is derived by estimating the central electron (DDg1),andNFWmodel,respectively.Westressthatthesame
density from the combination of the best-fit results of the discrepancyisfoundwhenwecompareourmassprofileswitha
spectral and imaging analyses (namely the normalization of corrected mass profile computed from the lensing map where
thethermalspectrumandtheparametersofthesingleβ-model). the SE quadrant, which contains the hot X-ray subclump, is
In particular, the low value measured by Ettori et al. (2004) excluded.
mightbebiasedbyanunderestimateofthecentraldensitydueto Asaprivatecommunicationafterthisworkwasacceptedfor
apossibleundersamplingoftheclusterluminositywithinthera- publication,MarusaBradacpointedoutthatthelensingmasses
diuswherethethermalspectrumisextracted,whichcorresponds reconstructed outside ∼510 kpc are not very reliable because
392 M.Gittietal.:MassdistributioninRXJ1347.5−1145studiedwithXMM-Newton
to inject buoyant bubbles into the ICM, which heat the am-
2.5 bient medium by doing PdV work as they rise and expand
adiabatically. In addition, besides being essential in stabilizing
(cid:1)ray 2 themodel,thermalconductiontransportsenergyfromthehotter,
X
M outerregiontothecentralregion.Unfortunatelyitsefficiencyis
(cid:3)
Mlensing 1.5 pwoitohrlydiffkneorewnnt fsrianccteiointsdefcpeonfdsthoenSmpiatzgenretriactefiealrdessatunddiemdo.dFeolsr
1 a fixed fc between 0 and 1/3 (the maximum for magnetized a
plasma)thecontributionofheatconductionasafunctionofra-
0.5 diusis knownsince the temperaturegradientis estimated from
100 200 300 400 500 600 thedeprojectedtemperatureprofile.Wenotethatifoneassumes
r(cid:1)kpc(cid:2) thatheatconductionalonebalancesradiativelosses,thenitsef-
Fig.6. Ratio of the lensing to the (projected) X-ray mass profile for ficiency would be much larger that 1/3 of the Spitzer rate and
different X-ray mass estimates. The line styles are the same as in therefore unrealistic. The raising entropy profile (in Sect. 5.3)
Fig. 5. The reported errors are those coming from the X-ray mass indicates that convectionis not operatingon the scales that we
determinations. areabletoresolveandisthereforenotincludedinthemodel.The
extraheatingprofileresultingfromsubtractingtheheatconduc-
of the large error bars, and also very small radii have a signif-
tion yield from the ICM emissivity is then assumed to be bal-
icanterror.This,however,doesnotchangethemainconclusion ancedbytheAGNheatingfunction:
derivedfromthecomparisonwithX-raymasses,sinceageneral (cid:1) (cid:2)
largediscrepancyisfoundatallradii. L (cid:21) (cid:22) p (γb−1)/γb 1dlnp
HAGN ∝ 1−e−r/r0 (13)
4πr2 p r dlnr
0
7.4.ComparisonwiththeSunyaev-Zel’dovich(SZ)effect
where p is the ICM pressure (p some referencevalue) and γ
0 b
Throughthe SZ effect,Pointecouteauetal. (2001)measurethe theadiabaticindexofthebuoyantbubbles,whichisfixedto4/3
gas mass of RX J1347. They compare their results with the (i.e., relativistic bubbles). Fitting Eq. (13) to the extra heating
X-ray results of Schindler et al. (1997), finding good agree- profile provides the AGN parameters L (the time-averaged lu-
ment. Within 74 arcsec = 427 kpc the SZ estimate is Mgas = minosity) and r0 (the scale radius where the bubbles start ris-
(4.7 ± 0.4) × 1013 M(cid:3) in agreement with our value, Mgas = ing in the ICM). Only if 0.10 ≤ fc ≤ 0.27 the fitting pro-
(5.5±0.1)×1014 M(cid:3). videsmeaningfulresults.For fc =0.27theAGNparametersare
L = 7.45×1045ergs−1 andr = 4kpc.Aswedecrease f both
0 c
8. Thecoolcore AGN parameters increase monotonically and reach the maxi-
mum at f = 0.10, for which we find L = 10.11×1045ergs−1
c
AsshowninSect.5,thereisnoevidenceforverylowtempera- andr =29kpc.ThetrendoftheAGNparameterswith f indi-
0 c
turegasinthecoreofRXJ1347,suggestingthatthedescription catesthat,intheframeworkoftheeffervescentheatingscenario,
oftheinnerregionofthisclusterbymeansofastandardcooling heatconductionandAGNheatingcooperateinquenchingradia-
flow model is not appropriate.The spectral analysis in Gitti & tive cooling. The inferred AGN time-averaged luminosity lies
Schindler(2004)showsthatifthecoolcorein RXJ1347isfit- thereforeinaquitesmallrange(7.45–10.11×1045ergs−1),and
tedwithanempiricalcoolingflowmodelwherethelowesttem- is largerbutcomparableto thecluster luminosityin theenergy
peratureisleftasafreeparameter,verytightconstraintsonthe range[2.0–10.0]keV(L =6.2±0.2×1045ergs−1).Themodel
existence of a minimum temperature(∼2 keV) are found.This with f =0.22istheoneXwiththesmallestreducedχ2andinthis
c
situation is common for cool core clusters and it has become caseL=8.32×1045ergs−1andr =13kpc.
0
clear thatthe gaswith shortcoolingtime at the center of these TheeffervescentheatingmodelappliedtoRXJ1347predicts
objectsmustbepreventedfromcoolingbelowtheobservedcen- thatthescalewherethebubblesstartrisingintheICMisinthe
tral temperature minimum. The most appealing mechanism is
range4–29kpc.TheobservedextensionoftheAGNjetsshould
heating by AGN because it is strongly motivated by observa- be of the same orderof magnitude(Piffaretti& Kaastra 2006).
tions. CentralAGNswith strongradioactivity arefoundin the Interestingly,thefirstresultsfrom1.4GHzVLAobservationsof
majorityofcoolcoreclusters(e.g.,Burns1990;Balletal.1993)
thecentralregionofRXJ1347showhintsoffaintstructuresem-
andpowerfulinteractionsoftheradiosourceswiththeICMare anatingfromthe discrete radiosource outto ∼20kpcfromthe
observed(e.g.,Bîrzanetal.2004;Raffertyetal.2006,andref- center(Gittietal.2007b).Acomparisonbetweenthederivedlu-
erencestherein).ThepresenceofacentralAGNinRXJ1347is minosity L with the observedAGNluminosityis unfortunately
indicatedbytheNRAOVLASkySurvey(NVSS),thatshowsa notpossible.Infact,in theframeworkoftheeffervescentheat-
strongcentralsourcealongwithsomehintofapossibleextended ingmodel,thederivedAGNluminosityisatime-averagedtotal
emission. However, the resolution and sensitivity of the NVSS AGN power and a fair comparison is possible only if the total
arenotsufficienttostudythecharacteristicsofthecentralsource jetpowerisestimated(X-rayandradiopowersareknowntobe
andestablishtheexistenceofdiffuseemission.Weobtainednew poortracersofthetotalAGNpower).Atpresent,thiswasdone
VLAdatainordertofurtherinvestigatethenatureandproperties onlyforM87intheVirgocluster(Owenetal.2000).
oftheradiosourceinRXJ1347(Gittietal.2007b).
InordertoexploretheheatingbyAGN,weadoptthemodel
9. Summary
developed by Ruszkowski & Begelman (2002, hereafter effer-
vescent heating). The details of the model and the procedure As indicated by previous studies (Allen et al. 2002b;
adoptedtoestimatetheAGNparametersfromtheobservedtem- Pointecouteau et al. 2001; Gitti & Schindler 2004), the clus-
perature and density profiles are given in Piffaretti & Kaastra ter RXJ1347 shows both the signatures of strong cooling flow
(2006). Here we simply summarize the essential elements. In and subcluster merger, that are rarely observed in the same
the effervescent heating scenario the central AGN is assumed system.