Physical conditions of Abell 2142 up to the virial radius

22 Pages·2016·3.66 MB·English

A&A595,A42(2016) Astronomy
DOI:10.1051/0004-6361/201628183
&
(cid:13)c ESO2016 Astrophysics
The XMM Cluster Outskirts Project (X-COP):
Physical conditions of Abell 2142 up to the virial radius
C.Tchernin1,2,D.Eckert2,3,S.Ettori4,5,E.Pointecouteau6,11,S.Paltani2,S.Molendi3,G.Hurier7,12,
F.Gastaldello3,8,E.T.Lau9,D.Nagai9,M.Roncarelli4,andM.Rossetti10,3
1 CenterforAstronomy,InstituteforTheoreticalAstrophysics,HeidelbergUniversity,Philosophenweg12,69120Heidelberg,
Germany
e-mail:[email protected]
2 DepartmentofAstronomy,UniversityofGeneva,ch.d’Ecogia16,1290Versoix,Switzerland
3 INAF–IASF-Milano,viaE.Bassini15,20133Milano,Italy
4 INAF–OsservatorioAstronomicodiBologna,viaRanzani1,40127Bologna,Italy
5 INFN,SezionediBologna,vialeBertiPichat6/2,40127Bologna,Italy
6 CNRS,IRAP,9Av.colonelRoche,BP44346,31028ToulouseCedex4,France
7 CentrodeEstudiosdeFisicadelCosmosdeAragon,PlazaSanJuan1,Planta-2,44001Teruel,Spain
8 DepartmentofPhysicsandAstronomy,UniversityofCaliforniaatIrvine,4129FrederickReinesHall,
Irvine,CA92697-4575,USA
9 DepartmentofPhysics,YaleUniversity,NewHaven,CT06520,USA
10 UniversitàdeglistudidiMilano,Dip.diFisica,viaCeloria16,20133Milano,Italy
11 UniversitédeToulouse,UPS-OMP,IRAP,38000Toulouse,France
12 Institutd’AstrophysiqueSpatiale,CNRS,UMR8617,UniversitéParis-Sud11,Batiment121,Orsay,France
Received25January2016/Accepted17June2016
ABSTRACT
Context. Galaxy clusters are continuously growing through the accretion of matter in their outskirts. This process induces inho-
mogeneities in the gas density distribution (clumping) that need to be taken into account to recover the physical properties of the
intraclustermedium(ICM)atlargeradii.
Aims.Westudiedthethermodynamicpropertiesintheoutskirts(R > R )ofthemassivegalaxyclusterAbell2142bycombining
500
theSunyaevZel’dovich(SZ)effectwiththeX-raysignal.
Methods. We combined the SZ pressure profile measured by Planck with the XMM-Newton gas density profile to recover radial
profilesoftemperature,entropy,andhydrostaticmassoutto2×R .Weusedamethodthatisinsensitivetoclumpingtorecoverthe
500
gasdensity,andwecomparedtheresultswithtraditionalX-raymeasurementtechniques.
Results.Whentakingclumpingintoaccount,ourjointX-SZentropyprofileisconsistentwiththepredictionsfrompuregravitational
collapse, whereas a significant entropy flattening is found when the effect of clumping is neglected. The hydrostatic mass profile
recoveredusingjointX-SZdataagreeswiththatobtainedfromspectroscopicX-raymeasurementsandwithmassreconstructions
obtainedthroughweaklensingandgalaxykinematics.
Conclusions.WefoundthatclumpingcanexplaintheentropyflatteningobservedbySuzakuintheoutskirtsofseveralclusters.When
usingamethodthatisinsensitivetoclumpingforthereconstructionofthegasdensity,thethermodynamicpropertiesofAbell2142
arecompatiblewiththeassumptionthatthethermalgaspressuresustainsgravityandthattheentropyisinjectedataccretionshocks,
withnoneedtoevokemoreexoticphysics.OurresultshighlighttheneedforX-rayobservationswithsufficientspatialresolution,
andlargecollectingarea,tounderstandtheprocessesatworkinclusterouterregions.
Keywords. X-rays:galaxies:clusters–radiationmechanisms:thermal–galaxies:clusters:intraclustermedium–
cosmology:observations–submillimeter:general
1. Introduction theformofturbulence,bulkmotions,cosmicrays,andmagnetic
fieldsisexpectedtobesignificant,evenifstillpoorlyconstrained
bytheoryandsimulations.
Galaxy clusters are the largest gravitationally bound systems
in the Universe. According to the concordance cosmological Spectroscopic X-ray measurements of cluster outskirts be-
model, they are the latest structures to be formed. For this came possible recently with the Suzaku experiment thanks to
reason, they are expected to continue growing at the present its low particle background (Mitsudaetal. 2007). With the
epoch through the accretion of matter in their outskirts. Thus, help of Suzaku, many bright galaxy clusters have been ob-
informationontheprocessesgoverningstructureformationcan served out to the viral radius (∼R ; e.g., Reiprichetal. 2009;
200
be obtained through the study of galaxy cluster outskirts (see Hoshinoetal. 2010; Akamatsuetal. 2011; Simionescuetal.
Reiprichetal. 2013, for a review). The distribution of matter 2011; Walkeretal. 2012, 2013; Urbanetal. 2014; Okabeetal.
in the outer regions of galaxy clusters is expected to become 2014). These works studied the radial profiles of the density,
clumpy (Nagai&Lau 2011; Vazzaetal. 2013) and asymmet- temperature, and entropy out to R . In several cases, the au-
200
ric (Vazzaetal. 2011), and the impact of nonthermal energy in thors observed a flattening of the entropy profile beyond R
500
ArticlepublishedbyEDPSciences A42,page1of22
A&A595,A42(2016)
comparedtotheexpectationoftheself-similaraccretionmodel In this paper, we combine SZ and X-ray observations
(Voitetal.2005).Severalstudiesalsoobservedadecreaseinthe (X-SZ) from the Planck and XMM-Newton satellites to study
hydrostatic mass profile in the same radial range, which might the outskirts of Abell 2142. This cluster belongs to the sam-
suggestthatthemediumisoutofhydrostaticequilibrium.This ple selected in the framework of the XMM Cluster Outskirts
couldbecausedbyasignificantnonthermalpressureintheform Project(X-COP),averylargeprogramonXMM-Newtonwhich
of turbulence, bulk motions, or cosmic rays (e.g., Vazzaetal. aims at studying the outskirts of an SZ-selected sample of
2009; Lauetal. 2009; Battagliaetal. 2013), nonequilibration 13 massive, nearby clusters. Abell 2142 is a massive cluster
betweenelectronsandions(Hoshinoetal.2010;Avestruzetal. (M ∼ 1.3 × 1015 M ; Munarietal. 2014) at a redshift of
200 (cid:12)
2015), or weakening of the accretion shocks (Lapietal. 2010; 0.09(Owersetal.2011).Theclusterhostsamoderatecoolcore
Fusco-Femiano&Lapi2014). (K = 68 keVcm2; Cavagnoloetal. 2009) and exhibits multi-
0
pleconcentriccoldfrontsinitscentralregions(Markevitchetal.
Alternatively, Simionescuetal. (2011) proposed that the
2000; Rossettietal. 2013), which are indicative of ongoing
measured gas density is overestimated because of gas clump-
sloshing activity extending out to 1 Mpc from the cluster cen-
ing, which would lead to an underestimated entropy (see
ter (Rossettietal. 2013). The sloshing activity may have trig-
also Eckertetal. 2013b; Walkeretal. 2013; Urbanetal. 2014;
gered the formation of an unusual radio halo (Farnsworthetal.
Morandietal. 2013; Morandi&Cui 2014). Recently, several
2013). Owersetal. (2011) studied the three-dimensional (3D)
numericalstudieshavefocusedonquantifyingtheeffectofgas
galaxy distribution out to ∼2 Mpc from the cluster core and
inhomogeneities on X-ray observations (see, e.g., Nagai&Lau
identified several substructures associated with minor mergers.
2011; Zhuravlevaetal. 2013; Eckertetal. 2015; Vazzaetal.
Eckertetal.(2014)discoveredaninfallinggalaxygrouplocated
2013;Roncarellietal.2013).Forinstance,usinghydrodynami-
∼1.5Mpcnortheast(NE)ofthemaincluster.Thissubclusteris
calsimulationsZhuravlevaetal.(2013)showedthatthedensity
intheprocessofbeingstrippedfromitshotgasbytherampres-
distribution inside a shell at a given distance from the cluster
sure applied by the main cluster, forming a spectacular X-ray
centercanbedescribedbyalognormaldistributionplusahigh-
tail.Onlargerscales,A2142islocatedinthecoreofacollaps-
density tail (see also Rasiaetal. 2014; Khedekaretal. 2013).
ing supercluster (Einastoetal. 2015; Gramannetal. 2015). To-
Whilethelognormaldistributioncontainsinformationaboutthe
gether, these studies reveal that A2142 is a dynamically active
bulk of the intracluster medium (ICM), the high-density tail is
clusterlocatedatanodeofthecosmicweb.
duetothepresenceofinfallinggasclumps.Theauthorsshowed
Thepaperisorganizedasfollows.InSect.2wedescribethe
that the median of the distribution coincides with the mode of
analysisoftheX-raydatatoobtainradialprofilesofthesurface-
the lognormal distribution, whereas the mean is biased high by
brightness, temperature, and metal abundance of A2142. In
the presence of clumps. This result has been confirmed obser-
Sect.3,weperformadeprojectionoftheprofilesofX-raysur-
vationallybyEckertetal.(2015),wheretheauthorsreproduced
facebrightnessandSZyparameterfromPlanckassumingspher-
thisresultusingROSATandXMM-Newtondata.Theseauthors
ical symmetry to recover the 3D gas density and pressure pro-
computed the surface-brightness distribution in an annulus at
files. In Sect. 4, we combine the resulting SZ pressure profile
∼1.2×R fromtheclustercenterandshowedthatthemedian
500 with the X-ray density profile to obtain radial profiles of en-
of the distribution corresponds to the mode of the lognormal
tropy, temperature, hydrostatic mass, and gas fraction. We also
distribution, while the mean is shifted toward higher surface- estimatetheeffectsofgasclumpingbycomparingtheresultsob-
brightness values. They concluded that the azimuthal median
tainedwiththeazimuthalmedianmethodwiththoseobtainedus-
method allows us to recover the true gas density profile even
ingthetraditionalapproach.OurresultsarediscussedinSect.5.
inthepresenceofinhomogeneities. Throughoutthepaper,weassumeaΛCDMcosmologywith
Inaddition,therecentyearshaveseengreatprogressinthe ΩΛ = 0.7, Ωm = 0.3 and H0 = 70 kms−1Mpc−1. At the red-
study of the ICM through the Sunyaev-Zel’dovich (SZ) effect shiftofA2142,1arcmincorrespondsto102kpc.Uncertainties
(Sunyaev&Zeldovich 1972). The SZ effect arises when pho- throughoutthepaperareprovidedatthe1σconfidencelevel.We
tons of the cosmic microwave background photons (CMB) in- useasreferencevaluesforR200 andR500,R200 = 2160kpc,and
teract with the electrons of the ICM through inverse Compton R500 = 1408 kpc, which are the results of a joint analysis per-
scattering.TheobserveddistortionoftheCMBspectrumispro- formedinMunarietal.(2014)basedonkinematics,X-ray,and
portional to the thermal electron pressure integrated along the gravitationallensingobservationsofA2142.
lineofsight(theComptonyparameter).Therefore,theSZsig-
naldecreaseslesssharplywithradiusthantheX-rayemissivity.
Furthermore, it is less sensitive to density inhomogeneities. In- 2. X-rayspectralanalysis
deed,ithasbeenshownthatatR ,variationsintheX-raysignal
200 2.1. DescriptionoftheXMMdata
are∼3timeslargerthanintheSZflux(seeforinstanceFig.6of
Roncarellietal.2013)sincethefluctuationsarenearlyisobaric Abell 2142 was mapped by XMM-Newton through five point-
(Khedekaretal. 2013). This makes the SZ signal highly com- ings: a central one (50 ks) and four 25 ks offset pointings ob-
plementarytoX-rayobservations.RecentSZexperiments(e.g., tained in extended full frame mode for pn and full frame for
Planck,Bolocam,SPT)enabledustoextendthemeasurements MOS.ThedatawereprocessedwiththeXMM-NewtonScientific
of the SZ signal well beyond R (PlanckCollaborationInt.V AnalysisSystem(XMMSAS)v13.0.usingtheExtendedSource
500
2013;Sayersetal.2013).Thesebreakthroughsopenedthepos- AnalysisSoftwarepackage(ESASSnowdenetal.2008).Wefil-
sibility of combining the SZ signal with X-ray observations to teredoutthetimeperiodsaffectedbysoftprotonflaresusingthe
studythethermodynamicalpropertiesofthegas,therebybypass- tasks MOS-filter and pn-filter to obtain clean event files.
ing the use of X-ray spectroscopic data (Ameglioetal. 2007; In Table 1 we provide the OBSID and the clean exposure time
Nordetal.2009;Basuetal.2010;Eckertetal.2013a).JointX- ofthepointings.Pointsourcesweredetectedandmaskeddown
rayandSZimagingstudiescanalsoleadtoareconstructionof toafixedfluxthreshold(10−14 erg/cm−2s−1)viatheESAStask
the cluster mass profile through the hydrostatic equilibrium as- cheese.ThepresenceofanomalousMOSCCDswasalsotaken
sumption(Ameglioetal.2009;Eckertetal.2013b). intoaccount.
A42,page2of22
C.Tcherninetal.:JointX-rayandSZanalysisofAbell2142
1.51e-04 – The sky background can be modeled with three compo-
27.7 NE NW 7.58e-05 nents: the cosmic X-ray background (CXB), the Galactic
halo, and the local hot bubble. The emission of the CXB
27.6
can be described by a power law with a photon index fixed
3.80e-05
27.5 to 1.46 (DeLuca&Molendi 2004). This component is ab-
sorbedbytheGalacticcolumndensityalongthelineofsight.
27.4 1.89e-05
We used a hydrogen column density of 3.8×1020 cm−2 in
on 27.3 9.49e-06 thisanalysisasmeasuredfromtheLABHIGalacticsurvey
eclinati 27.2 4.74e-06 (bKearlebperrelsaeentteadl.b2y00a5)th.eTrhmeaelmciosmsipoonnoefntthaetGaatleamctpicerhaatulorecaonf
D
27.1 0.22 keV (McCammonetal. 2002). We modeled this ther-
27.0 2.34e-06 malemissionwiththethinplasmamodelAPEC(Smithetal.
2001), with solar abundance. This emission is also affected
26.9 1.15e-06
byabsorptionalongthelineofsight.Thelocalhotbubbleis
SE
26.8 SW 5.48e-07 modeledwithanunabsorbedthermalcomponentat0.11keV.
WeusedtheAPECmodeltorepresentthisthermalcompo-
26.7
240.2 240.0 239.9 239.7 239.6 239.4 239.3 239.1 2.50e-07 nent,againwithsolarabundance.Thenormalizationofthese
Right ascension componentswasfittoeachbackgroundregionindependently
100e07 andthenrescaledtotheareaoftheregionusedforthespec-
Fig. 1. Combined XMM-Newton mosaic in the energy band tral extraction. For these three background components, we
[0.7−1.2] keV corrected for the different exposure times and for the onlyallowedthenormalizationtovary.
NXB. The units in the color bar are MOS count/s. The concentric – The second source of background, the NXB, is induced by
white circles show the regions chosen for the source spectral extrac- charged particles interacting within the detector. It is domi-
tion.Theoutermostcirclehasaradiusof15arcmin(correspondingto nated by cosmic rays, i.e., relativistic charged particles that
∼1530kpc).Thefourregionsdelimitedbytheredcurveswereusedto
hit and excite the detector. Fluorescence emission lines are
estimatethelocalskybackgroundcomponents.Thelabelsrepresentthe
then emitted once the atoms of the detector de-excite. The
fourregionsusedintheanalysis:thenortheast(NE),northwest(NW),
spectrum of this background contribution can be estimated
southeast(SE),andsouthwest(SW)observations.Thewhitearrowin-
fromthespectrumobtainedduringclosed-filterobservations
dicatesthelocationoftheoutermostcoldfront(Rossettietal.2013,see
Sect.5.1.3).Thetipoftheaccretingsubstructureobservedintheregion usingthemethodoutlinedinSnowdenetal.(2008).Amodel
NE, as reported in Eckertetal. (2014), is located at approximatively of the NXB for all three EPIC detectors (pn, MOS1, and
(RA=239.72◦,Dec=27.40◦). MOS2) was extracted from filter-wheel-closed data using
the ESAS procedures MOS-spectra and pn-spectra. For
each observation, we rescaled these spectra by comparing
In Fig. 1 we show the combined EPIC mosaic of the clus- thecountratesmeasuredintheunexposedcornersofthede-
terintheenergyband[0.7−1.2]keVcorrectedfortheexposure tectorswiththemeancountratesoftheclosed-filterobserva-
timeforthethreeinstruments(Eckertetal.2014).Circularblack tions.Theresultingclosed-filterspectracanbecharacterized
areasinthisimagerepresentmaskedpointsources. byaflatcontinuumwithseveralfluorescenceemissionlines.
For each considered region, we modeled these spectra with
aphenomenologicalmodelconsistinginabrokenpowerlaw
2.2. Spectralanalysis
andseveralGaussiansandusedtheresultingfitasanappro-
We performed a spectral analysis in the [0.5−12] keV energy priatemodeloftheNXB.
band of the cluster in the concentric regions shown in Fig. 1 A priori, soft protons could also affect the data. In Table 1,
and estimated the spectra of the local sky background compo- we show the IN/OUT ratio (DeLuca&Molendi 2004;
nentsfromtheregionsinthefourredsectorsinthesameenergy Leccardi&Molendi 2008), which is the ratio between the
band.Theseregionsarelocatedatadistanceof28arcminfrom surface brightness in the FOV and the surface brightness
the cluster center, where we see no evidence for cluster emis- in the unexposed corners (out the FOV) in the hard energy
sion.SpectraandresponsefileswereextractedusingtheESAS band. Since soft protons are focused by the telescope mir-
tasksMOS-spectraandpn-spectra.Foreachoftheannulifor rors,whilecosmicrayscaninduceX-rayemissionoverthe
which it was possible, we combined the different observations entire detector, this ratio is used as an indicator of the con-
(center,NE,SE,SW,NW,seeFig.1)inthespectralanalysis. tamination of the soft protons to the NXB background. We
The modeling of the background and of the source is de- find that the contamination by soft protons is very low, ex-
scribedinSects.2.2.1and2.2.2,respectively.Thefittingproce- ceptfortheNWobservation,whereitreachesalevelof25%.
durewasperformedusingXSPECv12.7.1. Leccardi&Molendi(2008)estimatedtheeffectofsoftpro-
tonsonthespectralfittinganalysisandfoundthatforregions
that are bright enough (R < R ) this contribution is sub-
2.2.1. Backgroundmodeling 500
dominant.GiventhatwestopthespectralextractionatR ,
500
As shown in a number of recent studies (e.g., Leccardi & wedecidedtoneglectthecontributionofthesoftprotonsin
Molendi 2008; Ettori&Molendi 2011), the modeling of the thespectralfittingprocedure.
background is critical to obtain reliable measurements of the The Solar Wind Charge Exchange (SWCX; Carter &
propertiesoftheICMinclusteroutskirts.Thetotalbackground Sembay 2008; Carter et al. 2011) is also a potential source
is made of two main components: the sky background and the of background in X-ray observations of cluster outskirts.
non-X-ray background (NXB). The procedure adopted here to GiventhatSWCXemissionistimevariable,theconsistency
modelthesecomponentsfollowsEckertetal.(2014)andisde- of the spectral fits of the sky components at different times
scribedinthefollowing. in the four regions considered in our analysis (see Table 2)
A42,page3of22
A&A595,A42(2016)
Table1.OBSID,cleanexposuretimeandIN/OUTratioforthefiveobservationsusedinthispaper.
Observation OBSID Total[ks] pn[ks] MOS1[ks] MOS2[ks] IN/OUTratio
Center 0674560201 59.1 48.8 52.3 53.8 1.074
NW 0694440101 24.5 12.5 19.6 18.2 1.260
SE 0694440501 34.6 29.8 33.1 32.5 1.139
SW 0694440601 38.6 24.1 30.0 31.7 1.154
NE 0694440201 34.6 29.7 32.9 33.2 1.060
Table2.Fitofthelocalskybackgroundcomponents(localhotbubble,LHB;Galactichalo,GH;andcosmicX-raybackground,CXB)usingthe
modelconstant(apec+wabs(apec+powerlaw),onthefourregionsdelimitedbytheredsectorsinFig.1.
LHBnorm LHB∆norm GHnorm GH∆norm CXBnorm CXB∆norm
NE 1.69 [1.29;2.04] 1.20 [1.07;1.30] 0.938 [0.878;0.988]
NW 3.39 [2.71;3.90] 1.11 [0.978;1.30] 0.949 [0.832;1.00]
SE 0.430 [0.181;0.921] 1.36 [1.20;1.42] 0.844 [0.770;0.912]
SW 1.64 [1.13;1.93] 1.34 [1.25;1.48] 0.925 [0.832;0.971]
ALL 1.53 [1.35;1.81] 1.25 [1.21;1.32] 0.896 [0.866;0.931]
Notes.Thenameoftheobservationrepresentstheconsideredregion.ALLmeansthatthefourregionshavebeenfittedsimultaneously.Onlythe
normalizationparameterswereallowedtovaryinthismodel.Unitsare[10−6/cm−5]forthenormalizationofthelocalbubbleandoftheGalactic
haloand[10−6photons/(keVcm2s)]forthenormalizationoftheCXB.
argues against an significant contamination by this compo- thetemperatureprofileareshowninFigs.2and3,respectively.
nent.Furthermore,thelevelofthesolarprotonfluxdetected The excellent data quality allowed us to extract the abundance
with the Alpha Monitor (SWEPAM) instrument on board profileupto15arcmin(∼R ).Theresultingabundanceprofile
500
the Advanced Composition Explorer (ACE) satellite is be- is shown in Fig. 4 and exhibits a slightly decreasing behavior
low4×108protons/(scm2),whichistypicalofthequiescent fromZ =0.35Z inthecoredownto∼0.15Z atR ,whereZ
(cid:12) (cid:12) 500 (cid:12)
Sun, and is not sufficient to trigger SWCX. Therefore, we represents the solar abundance (Anders&Grevesse 1989). The
neglectthisbackgroundcomponentinourspectralanalysis. best-fit temperature and normalization are relatively unaffected
bythemetalabundanceevenintheoutermostbins.Indeed,fix-
We estimated the normalizations of the various components of ing the metal abundance to 0.25 Z instead of leaving it free
(cid:12)
thelocalskybackground(CXB;Galactichaloandlocalbubble) to vary does not change the output parameters. For complete-
andoftheNXBfromthecombinedanalysisofthefourregions ness,wealsoshowthetwo-dimensionalspectroscopictempera-
delimitedinredinFig.1.Theresultsofthefitsoftheskyback- tureprofileobtainedbySuzaku(Akamatsuetal.2011)inFig.3.
groundcomponentsforeachofthefourobservationsseparately ThetemperaturesmeasuredbySuzakusignificantlyexceedthose
andforthecombinedfitareprovidedinTable2.Tofitthespec- obtainedinouranalysisinthecentralregions,however,thetem-
trumoftheseregions,theintensityoftheNXBfluorescencelines peratureprofilederivedbyAkamatsuetal.(2011)wasextracted
intheenergyrange1.2−1.9keV(andalsointhe7−9keVenergy only along the NW, while that obtained in our analysis is az-
range for the pn instrument), as well as that of the continuum, imuthally averaged. The spectroscopic temperature profile ex-
wereleftfreetovary.ThenormalizationoftheCXBwasfitted tractedwithXMM-NewtonintheNWdirectionagreeswiththe
locallytotakecosmicvarianceintoaccount,whichisexpected profileofAkamatsuetal.(2011,seeFig.D.2),whichshowsthat
tobeofthelevelof15%(Morettietal.2003). thedifferenceiscausedbygenuinelyhighertemperaturesinthe
By the comparison of the result of the fit in the four re- NWdirectionratherthanbysystematicdifferencesbetweenthe
gions, we note that the normalization of the local hot bubble two instruments. This conclusion is reinforced by independent
is not well constrained by these measurements. This is easily observationsperformedwithChandra(seethetemperaturemap
explainedbythelowtemperatureofthiscomponent(0.11keV), intheworkofOwersetal.2009),whichalsoindicateanincrease
whichisbelowtheenergyrangecoveredbyXMM-NewtonEPIC ofthetemperatureintheNWdirection.
(0.5−12keV).Thisrenderstheoverallmodellargelyinsensitive
The best-fit values for the parameters are listed in Table 3.
tothiscomponent,suchthatuncertaintiesinthelocalhotbubble
Fortheoutermostthreeannuli(7−9,9−12,and12−15arcmin),
normalizationarenotexpectedtoaffecttheresultofthepresent weperformedacombinedfitofthedifferentobservations(NE,
study.
NW, SW, SE, and center, as defined in Fig. 1). To do so, we
fixedtheskybackgroundcomponentsofeachobservationtothe
valuesobtainedintheprevioussection(seeTable2)andrescaled
2.2.2. Thesourceemission thembytheratioofthesourceareatothebackgroundarea.
We extracted spectra from concentric annuli centered on the TheparametervaluesshowninTable3aretheresultsofthe
cluster (RA = 239.58◦, Dec = 27.23◦) as depicted in Fig. 1 combinedfit.Theresultsofthefitperformedineachregionsep-
by the white circles. In each annulus, we fitted the resulting aratelyarelistedinTablesD.1−D.3.WedidnotincludetheNE
spectra with the thin plasma emission code APEC and we de- regioninthecombinedfitoftheannulus7−9arcminorthecen-
rived projected radial profiles of emission measure, tempera- tralregioninthecombinedfitoftheannulus12−15arcmin,be-
ture, and metal abundance. The surface-brightness profile ob- cause the areas of overlap were too small to be included in the
tained from the normalization of the APEC thermal model and analysis.
A42,page4of22
C.Tcherninetal.:JointX-rayandSZanalysisofAbell2142
Table3.FitoftheXMM-NewtonspectrawithanAPECmodelintheregionsdelimitedbytheconcentricwhitecirclesinFig.1.
R(arcmin) T ∆T Norm ∆norm Z ∆Z
0−0.3 6.26 [6.12,6.37] 7.67 [7.60,7.71] 0.321 [0.295,0.350]
0.3−0.6 6.19 [6.10,6.28] 6.38 [6.33,6.41] 0.319 [0.301,0.342]
0.6−1 6.68 [6.61,6.75] 3.92 [3.90,3.93] 0.293 [0.278,0.310]
1−2 7.34 [7.27,7.43] 1.82 [1.81,1.82] 0.252 [0.240,0.264]
2−3 7.93 [7.86,8.03] 7.38×10−1 [7.34×10−1,7.40×10−1] 0.277 [0.263,0.294]
3−4 8.15 [8.02,8.24] 3.77×10−1 [3.75×10−1,3.78×10−1] 0.221 [0.203,0.239]
4−5 8.15 [8.03,8.29] 2.34×10−1 [2.33×10−1,2.36×10−1] 0.244 [0.223,0.267]
5−6 7.89 [7.70,8.10] 1.53×10−1 [1.52×10−1,1.54×10−1] 0.248 [0.224,0.279]
6−7 7.86 [7.65,8.15] 9.98×10−2 [9.90×10−2,1.01×10−1] 0.266 [0.226,0.307]
7−9 7.30 [7.10,7.49] 5.77×10−2 [5.72×10−2,5.81×10−2] 0.320 [0.290,0.352]
9−12 7.09 [6.71,7.36] 2.23×10−2 [2.21×10−2,2.25×10−2] 0.182 [0.140,0.225]
12−15 4.75 [4.36,5.13] 8.34×10−3 [8.12×10−3,8.57×10−3] 0.174 [0.102,0.252]
Notes.Thefreeparametersofthemodelarethetemperature(inkeV),norm(in10−3cm−5),andabundance(insolarmetallicity).Fortheoutermost
threeradialbins,alltheavailableobservationswerecombined.Fordetails,seetextandTables D.1–D.3fortheresultsoftheindividualfits.
10
2)]
n
mi 9
c10-12
r
a
s 8
2
cm V]
x [erg/(10-13 T[kekB 7
flu 6
y
g
er10-14 5
n
E
10 102 103 40 200 400 600 800 1000 1200 1400 1600
R [kpc]
R [kpc]
Fig.2.Surface-brightnessprofileobtainedbyspectralfittingofthere-
Fig.3.Temperatureprofile.Red:XMM-Newtonmeasurementsforthe
gionsshowninFig.1.ThedashedlinerepresentsthelocationofR .
500 regions shown in Fig. 1. Blue: Suzaku results (from Akamatsuetal.
2011).ThedashedlinerepresentsthevalueofR .
500
3. X-rayandSZimaginganalysis
surface-brightness peak (RA = 239.58◦, Dec = 27.23◦), taking
3.1. X-raysurface-brightnessprofile
vignetting effects into account. We accumulated NXB profiles
Because of the faint cluster emission and the relatively inthesameregionsfromtheNXBmaps,takingboththecontri-
high background of XMM-Newton, spectroscopic measure- butionofthequiescentparticlebackgroundandthesoftprotons
ments beyond ∼R are affected by systematic uncertainties into account. To model the contamination from residual soft
500
(Leccardi&Molendi 2008; Ettori&Molendi 2011). For this protons,weextractedthespectraoftheentireobservationsand
reason, we adopted a different approach that allows us to ex- fitted the high-energy part of the spectra (7.5−12 keV) using a
tract surface-brightness profiles with much poorer signal-to- brokenpower-lawmodel(seeLeccardi&Molendi2008).A2D
noisethanspectroscopicprofilesand,therefore,outtoR and modelforthecontaminationofresidualsoftprotonswascreated
200
beyond (see Appendix B). We refer to this surface-brightness using the ESAS task proton following Kuntz&Snowden
profileasphotometricinthefollowing,tobedistinguishedfrom (2008). The details of the soft-proton modeling technique
thespatiallylimitedspectroscopicsurface-brightnessprofile. are provided in Appendix A, and a careful validation using
We extracted photon images in the energy band blank-sky pointings is presented in Appendix B together with
[0.7−1.2] keV and created exposure maps for each instru- anassessmentofsystematicuncertainties.
mentviatheSAStaskeexpmapandthePROFFITv1.2software In addition, we also derived the azimuthal median surface-
(Eckertetal.2011)toobtainthephotometricsurface-brightness brightnessprofilefollowingthemethoddescribedinEckertetal.
profile. The choice of the [0.7−1.2] keV band is motivated by (2015). Namely, Voronoi tessellation was applied on the count
the fact that this particular band maximizes the signal-to-noise image to create an adaptively binned surface-brightness map
ratio (Ettorietal. 2010; Ettori&Molendi 2011) and avoids withaminimumof20countsperbin.Themediansurfacebright-
the bright and variable Al Kα and Si Kα fluorescence lines ness was then estimated in each annulus by weighting the sur-
without affecting the statistics too much. Surface-brightness face brightness of each bin by its respective surface. To esti-
profileswereaccumulatedinconcentricannulistartingfromthe matetheuncertaintyinthemedian,weperformed104 bootstrap
A42,page5of22
A&A595,A42(2016)
0.4 10-12
2)]
n
0.35 mi10-13
c
r
a
0.3 s
e 2
c m10-14
n c
da0.25 g/(
n r
u e
Ab 0.2 x [10-15
u
fl
y
0.15 rg10-16
e
n
E
0.1
10-17
500 1000 1500 2000 2500 3000
200 400 600 800 1000 1200 1400 1600
R [kpc]
R [kpc]
Fig. 4. Metal abundance profile for the regions shown in Fig. 1. The Fig. 5. Surface-brightness profiles of A2142 obtained with different
dashedlineindicatesthelocationofR . methods.Thedatapointsshowthespectroscopicmeasurements(red),
500
the azimuthally averaged profile (blue), and the azimuthal median
(green).Thegreenandbluethindashedlinesshowthecorresponding
resampling of the surface-brightness distributions binned uni- best fits obtained with the multiscale deprojection method. The solid
formlyusingVoronoitessellation.Thestandarddeviationofthe and dashed horizontal lines correspond to the total background level
bootstrap realizations was then adopted as the error on the me- andtotheuncertaintyonthebackground,respectively.Thedashedand
dian. In the [0.7−1.2] keV energy band, the systematic uncer- dash-dottedverticallinesrepresentR500andR200,respectively.
taintyinthesubtractionofthebackgroundamountsto5%ofthe
skybackgroundcomponent,asshownbyananalysisofasetof
componentcanthenbeeasilydeprojectedtoreconstructthe3D
22blank-skypointings(seeAppendixB).Thisuncertaintywas
profile. Following Eckertetal. (2016), we decompose the pro-
addedinquadraturetothesurface-brightnessprofiles.Toconvert
jected profile into a sum of King profiles, with s the projected
the resulting surface-brightness profiles into emission measure,
radius,relatedtotheline-of-sightdistanceandthe3Dradiusr,
wefoldedtheAPECmodelthroughtheXMM-Newtonresponse byr2 = s2+(cid:96)2,
and computed the conversion between count rate and emission
mtteemmeappseeurrraaett.uuTrreehdienocethosennveoentresfraiogllnybbfeaalcontwdor[∼0i1.s7.5−ro1ku.e2gV]h.lkyeVin,dperpoevniddeedntthoafttthhee EM(s)=(cid:88)i=N1 Ni1+(cid:32)rcs,i(cid:33)2−3βi/2, (2)
InFig.5weshowthecomparisonbetweenthespectroscopic
andphotometricsurface-brightnessprofiles.Anexcellentagree- whereirepresentstheithbasisfunctionand stheprojectedra-
mentisfoundbetweentheprofilesobtainedwiththetwometh- dius. The parameters of this fit are the normalization (Ni), core
ods.WecanseethatXMM-Newtondetectsasignificantemission radii(rc,i),andslopes(βi).Thenumberofcomponentsandcore
outtoalmost3Mpcfromtheclustercore,whichcorrespondsto radiiusedforthefitoftheprojectedprofilearedeterminedadap-
thevirialradiusR ∼2×R . tively from the total number of data points with the condition
100 500
thatonebasisfunctionisusedforeachblockoffourdatapoints.
Therelationbetweentheprojectedand3Dprofilescanthenbe
3.2. XMM-Newtondeprojectedelectrondensityprofile computedanalytically(seeAppendixAofEckertetal.2016,for
The normalization of the APEC model, in units of cm−5, is re- details).Thismethodprovidesanadequaterepresentationofthe
observedprofileandunderlyingdensity3Dprofile,althoughthe
latedtotheelectrondensity(n )by
e
derivedparametershavenoactualphysicalmeaning.Theconfi-
10−14 (cid:90) denceintervalsarederivedusingtheMarkovchainMonteCarlo
Norm= ((1+z)·D )2 nenpd3r, (1) (MCMC)codeemcee(Foreman-Mackeyetal.2013).Inthefol-
a
lowing,allchainshaveaburn-inlengthof5000stepsandcontain
where D ∼ 349.8Mpcistheangulardistancetotheclusterin 10000steps.Chainsarestartedfromthebest-fitparameters.All
a
cm,z=0.09isitsredshift,andn istheprotondensity(incm−3), reported errors correspond to 68% confidence interval around
p
whichisrelatedtotheelectrondensitybyn =1.21n ,assuming themedianoftheMCMCdistribution.
e p
thattheplasmaisfullyionized. As an alternative, we used a direct nonparametric geomet-
After having converted the surface-brightness profile into rical deprojection method based on the method of Fabianetal.
emission measure, we deprojected the resulting profiles to es- (1981, see also Krissetal. 1983; McLaughlin 1999; Buote
timatethe3Delectrondensityprofile.Forthedeprojection,we 2000).Theobservedsurface-brightnessprofileisconsideredthe
compared the output of two different methods: the multiscale sum along the line of sight of the gas emissivity weighted by
method described in Eckertetal. (2016) and an onion-peeling the fraction of the shell volume sampled in the given annu-
method(Ettorietal.2010).Bothmethodsassumesphericalsym- lar ring. From the outermost radial bin, and moving inward
metry.Thedifferencesbetweentheoutputofthetwoprocedures with the onion-peeling method, the gas emissivity (and den-
thus gives us a handle on the uncertainties associated with the sity) is recovered in each shell. To avoid unphysical solutions
deprojection. induced by sharp fluctuations in the surface-brightness profile,
In the multiscale deprojection method, the projected profile the radial points that deviate more than 2σ from the median-
is decomposed into a sum of multiscale basis functions. Each smoothedprofilearereplacedbythecorrespondingvaluesofthe
A42,page6of22
C.Tcherninetal.:JointX-rayandSZanalysisofAbell2142
1.6
1.5
1.4
10-3
-3]m 1.3
C
c
[ne 1.2
10-4 1.1
photometric median
photometric mean
1
spectroscopic, multiscale
spectroscopic, onion-peeling
0.9
103 103
R [kpc] R [kpc]
Fig.6.Electrondensityprofile.Thedatapointsshowthedeprojected Fig.7.Clumpingfactorprofile.Solidline:medianoftheMCMCsim-
spectroscopic data (from Table 3) using the multiscale method (black ulation;shadedarea:68%confidenceintervalaroundthemedian.The
triangle; Eckertetal. 2016) and the onion peeling method (red dot; dashed and dash-dotted vertical lines represent R and R , respec-
500 200
Ettorietal. 2010). The green and blue data curves show the density tively.Thetripledot-dashedlineshowstheapproximativepositionof
profilesrecoveredusingtheazimuthalmedianandazimuthalmeanpho- maximalradiusofthesloshingregionreportedinRossettietal.(2013).
tometric surface-brightness profiles, respectively. Both profiles were
deprojectedusingthemultiscalemethod.Thedashedanddash-dotted
verticallinesrepresentR andR ,respectively. region(Zhuravlevaetal.2013;Eckertetal.2015).Thustheratio
500 200
between the azimuthal mean and the azimuthal median density
profiles (see Fig. 6) can be used as an estimator of the square
median-smoothedprofile.Inthepresentcase,only2(outof64) rootoftheclumpingfactorprofile.
datapointshavebeenreplaced.Theerrorbarsareestimatedfrom The resulting clumping factor is shown in Fig. 7. Beyond
thedistributionofthedeprojectedvaluesofthe100MonteCarlo R ,weobservethattheclumpingfactorincreaseswiththedis-
500
realizationsoftheX-raysurface-brightnessprofile. tance to the cluster center, while at smaller radii, the clumping
√
The density profiles obtained with these two methods for factorisroughlyconstantatthevalue C = 1.1,followedbya
the spectroscopic surface brightness are shown in Fig. 6. They
decreaseatabout1Mpcfromtheclustercore.Thisbehavioris
are in excellent agreement. In this figure, we also compared
discussedindetailinSect.5.1.
thesespectroscopicprofilestotheazimuthalmeanandazimuthal
mediandensity profilesobtainedfrom thephotometric analysis
(Sect. 3.1). We calculated both photometric profiles using the 3.4. Planckdeprojectedelectronpressureprofile
multiscale deprojection method. Hereafter, we adopt the multi-
Toderivetheelectronpressureprofile(P ),wefirstneedtoesti-
scaledeprojectionmethodtoprovidethegasdensityprofilesof e
matethethermalSZsignalfromA2142.TheSZeffectprovides
reference.Asexpected,thespectroscopicdatapointsarefollow-
ameasurementofthethermalpressureintegratedalongtheline
ingthetrendoftheazimuthalmeandensityprofile,andoveresti-
ofsight(throughthedimensionlessyparameter),
matethedensityineachshellcomparedtotheazimuthalmedian.
ThesystematicdifferenceisevenmorevisiblethanintheAPEC (cid:90)
σ
normprofiles(Fig.5).Thisillustratesthepotentialbiasinduced y(s)= m Tc2 Pe((cid:96))d(cid:96), (3)
bygasclumpingwhenusingthespectralfittingprocedure. e
where(cid:96) isthedistancealongthelineofsight,σ theThomson
T
cross section, m the mass of the electron, and c the speed of
3.3. Clumpingfactorprofile e
light.
InX-rays,themeasuredemissivityprovidesinformationon(cid:104)n2(cid:105), Wemakeuseoftheall-skysurveyfromthePlanck mission
e
where (cid:104)·(cid:105) represents the mean inside spherical shells. The level (Tauberetal. 2010; PlanckCollaborationI 2016), and more
ofinhomogeneitiesintheICMcanbeestimatedbytheclumping specifically from the full survey data from the six frequency
factorC,asC =(cid:104)n2(cid:105)/(cid:104)n (cid:105)2(Mathiesenetal.1999). bands of the high frequency instrument (Lamarreetal. 2010;
e e
This definition of the clumping factor reflects variations PlanckHFICoreTeam 2011). The SZ signal map was recon-
of the gas density in a given volume. Such variations are ex- structed over a patch map of 1024 × 1024 pixels2 centered
pectedtobeaccompaniedbyvariationsofothersthermodynamic at the location of A2142 and with a size of 20 × R (i.e.,
500
properties. In the following, we exploit the fact that the X-ray 4.6 degrees). We applied the Modified Internal Linear Com-
volume emissivity in the energy range addressed in this work bination Algorithm (MILCA; Hurieretal. 2013) to produce
([0.7−1.2] keV) is essentially independent of the gas temper- a map of the Comptonization parameter, y, in a tangential
ature, which allows us to use the analysis based on the X-ray Galactic coordinates referential. This algorithm was also used
photometryasadirectproxyoftheclumpingfactor. to produce the full sky ymap delivered by the Planck Col-
Given that the density distribution inside a shell can be laboration to the community (PlanckCollaborationXXI 2014;
described by a lognormal distribution skewed with denser PlanckCollaborationXXII 2016); MILCA offers the possi-
outliers, the median of the density distribution is robust bility to perform the SZ signal reconstruction in multiple
against the presence of outliers, whereas the mean of the bins of angular scales. As a consequence, we were able to
distribution overestimates the density inside the considered produce a SZ map of A2142 at 7 arcmin FWHM angular
A42,page7of22
A&A595,A42(2016)
6.61e-05 matrix of the y profile with a Monte Carlo procedure and
27.80 led to the estimation of the covariance matrix of the pressure
5.36e-05
profileP (r).
e
To compare the resulting SZ pressure profiles with that ob-
27.60 4.24e-05
tained from purely X-ray analysis, we estimated the 3D pres-
3.24e-05 sure profile from the spectroscopic X-ray measurements using
27.40 the method outlined in Vikhlininetal. (2006). In this method,
n
atio 2.38e-05 the 3D temperature profile is assumed to be represented by a
clin27.20 1.66e-05 parametricformwithalargenumberoffreeparameters,
e
D27.00 1.06e-05 T(r)=T0(r/r(cro/orl)caocoolo)la+cooTl +min1/T0(1+((rr//rrtt))−ba)c/b)· (4)
5.95e-06
This functional form was projected along the line of sight
26.80
2.63e-06 weighted by the 3D emissivity profile, and subsequently fit to
the observed temperature profile described in Sect. 2.2.2. We
26.60 240.20 240.00 239.80 239.60 239.40 239.20 239.00 6.57e-07 then ran an MCMC to sample the parameter space and draw
Right ascension the 3D temperature profile. The 3D X-ray pressure profile was
000e+00
computed by combining the deprojected temperature with the
Fig. 8. Planck map of the Comptonization parameter, y, for A2142. electrondensityprofileobtainedfromthespectralX-rayanaly-
The blackand white circles indicatethe approximate location ofR
500 sis(blackpointsinFig.6).
and R ∼ 2×R , respectively. The white circle in the bottom left
100 500 In Fig. 10 we show all three pressure profiles: the two
cornerindicatesthesizeofa7arcminbeamFWHM.
SZ pressure profiles obtained by the two different deprojec-
tion methods described above (method 1: multiscale method;
resolution.OurA2142SZ-maphasthereforeasignificantlybet- method 2: same methodology as PlanckCollaborationInt.V
ter resolution than the public full sky SZ-map at 10 arcmin 2013) and the spectroscopic X-ray pressure profile. All three
FWHM. Thus, our SZ map uses the information from the pressure profiles are consistent, although we note a slight ex-
100 GHz Planck channel (roughly 10 arcmin FWHM) only cess of the X-ray pressure profile compared to the SZ pressure
for large angular scales (see Hurieretal. 2013, for a more profile at a distance of 500 kpc from the cluster center. Given
detailed description of the procedure). The resulting y-map that the thermal SZ signal is less affected by clumping (e.g.,
for A2142 is shown in Fig. 8. A2142 was very well de- Roncarellietal.2013),thisobserveddifferencecanbeexplained
tected as an SZ source in the Planck survey, with an overall by fluctuat√ions in the X-ray signal (see the value of the clump-
signal-to-noiseratioof28.4(PlanckCollaborationXXXII2015; ingfactor C ∼1.1inthisradialrangeinFig.7).Also,around
PlanckCollaborationXXVII2016).Owingtoitsextensionover R200 the two pressure profiles recovered from SZ observations
the sky A2142 is among the clusters spatially resolved in the areslightlydifferent.Thismaybebecausethemultiscaledepro-
PlancksurveythroughitsSZsignal,whichclearlyextendswell jection method smoothes the fluctuations to fit the data with a
beyondR outtoR ∼2×R (asshowninFig.8). superpositionofKingprofiles.Inadditiontothat,thepointson
500 100 500
We further proceeded in extracting the y-parameter profile thedeconvolvedanddeprojectedprofileobtainedusingthesame
of A2142 from our MILCA y-map following the exact same methodasinPlanckCollaborationInt.V(2013)are correlated.
methoddevelopedbyPlanckCollaborationInt.V(2013).They However,theerrorsshownonthisfigureareonlythesquareroot
profileisextractedonaregulargridwithbinsofwidth∆θ/θ = ofthediagonalofthecovariancematrix.Thisfactlikelybiasesa
500
0.2.Thelocalbackgroundoffsetisestimatedfromtheareasur- directvisualcomparison.TheobserveddiscrepancyaroundR200
roundingtheclusterbeyond5×θ =69arcmin.Theresulting maythereforenotbeaphysicaleffect.Wecomebacktotheex-
500
profileisshowninFig.9togetherwithafittothedataobtained cessinthepurelyX-raypressureprofilecomparedtotheSZpro-
with the multiscale method. For the fitting procedure, we take fileinthediscussionsection.
intoaccountthecovariancebetweenthedatapoints,whichcon- Owing to the moderate resolution of the Planck satellite
veys the statistical properties of the noise of each Planck fre- (translating into 7 arcmin on our y-map), we can not recover
quency band used to compute the y-map and the oversampling constraintsontheSZpressureprofilefromtheyparametermea-
factor of our patch with respect to the 1.71 arcmin resolution surementsclosetotheclustercenter.Therefore,weconsiderin
elementinthePlanckHEALPIXmap(Górskietal.2005).Inad- thefollowingonlytheradialrangebeyond400kpc(∼4arcmin),
dition,themodelwasconvolvedwiththePSFoftheinstrument, whichistheradiusbeyondwhichtheconstraintsonthepressure
which we approximated as a Gaussian with a full width at half profile from the SZ data are less impacted by the PSF blurring
maximum(FWHM)of7arcmin.Theresidualbetweenthebest and,therefore,morereliable.
fitconvolvedwiththePSFandtheyparameterdataisshownin
thebottompanelofFig.9.
4. JointX-rayandSZanalysis
The best-fit y-parameter profile (shown in Fig. 9) was then
converted into a 3D electron pressure profile using the multi- ThecombinationoftheX-rayandSZsignalcanbeusedto re-
scale deprojection method. For completeness, we also depro- coverthethermodynamicalquantitiesthatcharacterizetheICM.
jected the y parameter data using the same methodology as the Inthissection,wecombinethe3DSZpressureprofilewiththe
PlanckCollaborationInt.V(2013).Inthelattercase,theunder- X-ray gas density profile to recover the radial distribution of
lying pressure profile was obtained from a real space decon- temperature,entropy,hydrostaticmass,andgasfraction.More-
volution and deprojection regularization method adapted from over,wecanrecoverthesequantities,whicharelargelycorrected
Crostonetal.(2006),assumingsphericalsymmetryfortheclus- for the effect of the clumped gas. This is obtained by compar-
ter. The correlated errors were propagated from the covariance ing the X-ray surface brightness measured using the mean of
A42,page8of22
C.Tcherninetal.:JointX-rayandSZanalysisofAbell2142
10−4
10-2
er 10−5 3]m
et c
m V/10-3
a e
r k
Y pa 10−6 ure [
s
s
re10-4 SZ, deprojection method 1
p
SZ, deprojection method 2
10−7
2.5 102 103 X-ray
2
χ 01..551 10-5 103
0 R [kpc]
−0.5
−1
−1.5 Fig. 10. Electron pressure profile. The gray solid line and shaded
−2 102 103 area show the best-fit pressure profile obtained by deprojecting the
R [kpc] SZ data using the multiscale method (deprojection method 1). The
Fig.9.Toppanel:compton-yparameterprofilefromPlanck data(red
red points show the spectroscopic X-ray data deprojected with the
points). The gray solid line and shaded area show the best-fit profile
method of Vikhlininetal. (2006) and the blue triangles show the re-
convolvedwiththeinstrumentPSF.Thedatapointsarecorrelatedand
sultofthedeprojectionoftheyparameterdatausingthesamemethod-
theassociatederrorscorrespondtothesquarerootofthediagonalele-
ology as PlanckCollaborationInt.V (2013) (deprojection method 2).
mentsofthecovariancematrix.Bottompanel:residualofthefittothe
The blue data points are correlated and the associated errors corre-
Planck data. The dashed and dash-dotted vertical lines represent R
500 spond to the square root of the diagonal elements of the covariance
andR ,respectively.
200 matrix. The dashed and dash-dotted vertical lines represent R and
500
R ,respectively.
200
theazimuthalphotoncountsdistributionwiththeX-raysurface
brightnessestimatedwiththemedianofthedistribution(asde-
tailedinEckertetal.2015). 10
9
4.1. Temperatureprofile
8
Assuming that ICM is an ideal gas, the joint X-ray and SZ 3D
7
temperature profile can be recovered by combining the X-ray V]
density profiles obtained in Sect. 3.2 (Fig. 6) with the SZ pres- e 6
k
sure profile derived in Sect. 3.4 (Fig. 10). Using the equation T [ 5
k T = P /n , we derived the 3D temperature profile for both k
B e e
the azimuthal mean and the azimuthal median density profiles. 4
Whilethedensityprofileobtainedusingtheazimuthalmedianis
3
correctedforthepresenceofclumps,thedensityprofileobtained X-ray/SZ, photometric median
usingtheazimuthalmeanisnot. 2 X-ray/SZ, photometric mean
X-ray spectroscopic data
TheresultingjointX-rayandSZ3Dtemperatureprofilesare
1
500 1000 1500 2000 2500 3000
shown in Fig. 11. The uncertainties in the temperature profile
R [kpc]
were estimated by combining the MCMC runs for the pressure
anddensity.Ateachradius,thetemperatureanditsuncertainty Fig.11.Deprojectedtemperatureprofile.Redpoints:spectroscopicdata
were drawn from the distribution of output temperature values. (fromFig.3)deprojectedusingthemethodofEttorietal.(2010);green
In this figure we also show the deprojected spectroscopic tem- andblue:combinedX-rayandSZprofileusingtheazimuthalmedian
andazimuthalmeandensityprofiles,respectively.Thedashedanddash-
peratureprofileobtainedwiththemethodofEttorietal.(2010).
As expected, we observe different behaviors of the temper- dottedverticallinesrepresentR500andR200,respectively.
ature profile depending on whether gas clumping is taken into
account or not. Indeed, the increase in the clumping factor to-
wardtheoutskirts(seeFig.7)causesthetemperatureprofileob- 4.2. Entropyprofile
tained from the azimuthal mean to steepen with cluster-centric
distance compared to the profile estimated with the azimuthal Assuming that entropy is only generated by spherical virializa-
mediantechnique.WealsonotethatthespectroscopicX-raypro- tion shocks driven by hierarchical structure formation, we ex-
filecloselyfollowstheX-rayandSZprofileobtainedusingthe pect an entropy profile that follows the gravitational collapse
azimuthalmedian(exceptfortheverylastdatapoint,butthisis model. In such a case, the gas with low entropy sinks into the
an artefact of the deprojection method). We come back to this cluster center, while the high-entropy gas expands to the clus-
pointinthediscussionsection. teroutskirts(Voitetal.2005;Prattetal.2010)andtheresulting
Theeffectoftheoverestimatethedensityhasaclearsigna- entropyprofilehasapower-lawshapegivenby
tureinthetemperatureprofile.Similareffectsarealsoexpected
in the other thermodynamic quantities derived from the X-ray (cid:32) R (cid:33)1.1
K(R)= K ·1.42 keVcm2. (5)
analysis. 500 R
500
A42,page9of22
A&A595,A42(2016)
X-ray/SZ, photometric median
X-ray/SZ, photometric mean
X-ray spectroscopic data
1015
Purely gravitational collapse model
0 1
0
5
K M
K/ /ot
Mt
X-ray/SZ, photometric median
X-ray/SZ, photometric mean
X-ray, spectra-photometric data
Weak Lensing, Umetsu et al. (2009)
1014 X-ray, Piffaretti et al. (2011)
X-ray, Akamatsu et al. (2011)
1.2 1 R/R500 Galaxy kinematics, Munari et al. (2014)
Kth 1 103
/Kobs 00..68 R [kpc]
0.4 Fig.13.MassprofileofA2142.Green:X-SZcombinedprofileusing
0.2
theazimuthalmediandensityprofile.Blue:X-SZcombinedprofileus-
1
R/R ing the azimuthal mean density profile. Red: NFW fit to the spectro-
500
scopic X-ray data using the method of Ettorietal. (2010). For com-
Fig.12.Deprojectedentropyprofile.Toppanel:thereddotsshowthe parison,wealsoplotthemassmeasurementsreportedintheliterature.
X-ray spectroscopic data, while the green and blue curves represent Browntriangle:M fromL −Mrelation(Piffarettietal.2011);pink
500 X
theX-rayandSZprofilesobtainedusingtheazimuthalmedianandaz- reversedtriangle:M fromSubaruweaklensing(Umetsuetal.2009);
200
imuthalmeandensityprofiles,respectively.Theblacklineshowstheex- dark green square: M from Suzaku X-ray (Akamatsuetal. 2011);
200
pectationfrompurelygravitationalcollapse(Eq.(5),Voitetal.2005). blackemptytriangle:M fromgalaxykinematics(Munarietal.2014).
200
Thedashedanddash-dottedverticallinesrepresentR andR ,re-
500 200
spectively. Bottom panel: ratio of the X-ray and SZ entropy profile
(K ) over the entropy profile expected from the purely gravitational
obs
collapsemodel(K ):fortheazimuthalmedian(inblue)andazimuthal completely disappears and at R the entropy falls within just
th 200
mean(ingreen)densityprofiles.Thehorizontaldashedlinerepresents 1σoftheself-similarexpectation.
theexpectationforKobs=Kth. We stress that the SZ effect is nearly insensitive to clump-
ing (e.g., Battagliaetal. 2015), the difference between the two
profiles is caused only by our treatment of gas clumping in the
ThequantityK isdefinedas(Prattetal.2010)
500 X-raydata.Thisshowstheimportanceoftakingtheeffectsdue
(cid:32) M (cid:33)2/3(cid:32)1(cid:33)2/3 tothepresenceofclumpsinthederivationofthethermodynam-
K500 =106· 101450M0 f h(z)−2/3keVcm2, (6) icsquantitiesintoaccount.
(cid:12) b
where M = 8.66 × 1014 M is the cluster mass at R =
500 (cid:12) 500 4.3. Hydrostaticmass
1408 kpc (values derived from Munarietal. 2014), f =
b
Ω /Ω = 0.15 is the cosmic baryon fraction, where Ω is AssumingthattheICMisinhydrostaticequilibriumwithinthe
b m b
the baryon density, Ω is the matter density, and h(z) = gravitational potential of the cluster, the total enclosed mass at
(cid:112) m
Ωm(1+z)3+ΩΛ theratiooftheHubbleconstantatredshiftz thedistancerfromtheclustercentercanbeestimatedas
toitspresentvalue.
dP (r) GM (<r)
We derived the combined SZ and X-ray 3D entropy profile g =−ρ (r) tot , (7)
using the equation K = P /n5/3 with the X-ray density profiles dr g r2
e e
obtainedinSect.3.2(Fig.6)andtheSZpressureprofilederived whereP = P +P isthegaspressureprofile,ρ =(n +n )·m µ
g e p g e p p
in Sect. 3.4 (Fig. 10). In Fig. 12 we show the entropy profiles isthegasmassdensity,wherem isthemassoftheproton,µ =
p
obtainedusingtheazimuthalmeanandmediandensityprofiles. 0.6themeanmolecularweight,andGtheuniversalgravitational
Forcomparison,wealsoshowtheentropyprofileobtainedwith constant.
the spectroscopic X-ray information (K = k T/n2/3) from our Following Ameglioetal. (2009), we combined the Planck
B e
deprojected temperature and gas density spectroscopic profiles. electronpressureprofile(Sect.3.4)withtheXMM-Newtonelec-
All profiles are rescaled by K and compared to the expecta- tron density profile (Sect. 3.2) to derive the hydrostatic mass
500
tionsoftheself-similarmodel(Voitetal.2005). profile.Asabove,weinvestigatedtheeffectofclumpingonthe
ExcellentagreementisfoundbetweentheX-SZandspectro- hydrostaticmassbycomparingtheresultsobtainedwiththeaz-
scopicX-rayprofilesouttoR . imuthalmeanandmediandensityprofiles.
500
Atlargerradii,theuseofamethodsensitivetooutliersleads InFig.13weshowthecombinedX-rayandSZhydrostatic
to an entropy profile that deviates from the self-similar predic- mass profiles obtained for the different input density profiles.
tion(∝R1.1)intheoutskirtsandproducesafeaturewhichresem- Themassprofileobtainedusingtheazimuthalmedianincreases
blesanentropyflattening. steadily, while the mass profile obtained with the azimuthal
Onthecontrary,wecanseethattheX-SZprofileobtainedus- mean density profile shows an unphysical turnover at R >
ingtheazimuthalmedianmethodrisessteadilywithradiusoutto R . Such turnovers have been reported in the literature and
200
themaximumradiusaccessibleinthisstudy(3000kpc ≈ R ). interpreted as evidence for a significant nonthermal pressure
100
Therefore,ifthepresenceofclumpsistakenintoaccountinthe contribution to sustain gravity (e.g., Kawaharadaetal. 2010;
X-ray data the deviation observed with the blue curve almost Bonamenteetal.2013;Fusco-Femiano&Lapi2014).
A42,page10of22