Simulations of the merging galaxy cluster Abell 3376

2.4 MB·English

by  Rubens E. G. Machado

Mon.Not.R.Astron.Soc.000,1–12(2012) Printed21January2013 (MNLATEXstylefilev2.2)
Simulations of the merging galaxy cluster Abell 3376
1⋆ 1
Rubens E. G. Machado and Gasta˜o B. Lima Neto
3 1InstitutodeAstronomia,Geof´ısicaeCieˆnciasAtmosfe´ricas,UniversidadedeSa˜oPaulo,R.doMata˜o1226,05508-090Sa˜oPaulo,Brazil
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0
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Accepted2013January18.Received2013January10;inoriginalform2012October25

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ABSTRACT

8 Observed galaxy clusters often exhibit X-ray morphologies suggestive of recent interaction
1 withaninfallingsubcluster.Abell3376isanearby(z =0.046)massivegalaxyclusterwhose
bullet-shapedX-rayemissionindicatesthatitmayhaveundergonearecentcollision.Itdis-
] playsa pairof Mpc-scale radiorelics andits brightestclustergalaxyis located 970h−1kpc
O 70
away from the peak of X-ray emission, where the second brightest galaxy lies. We attempt
C to recoverthe dynamicalhistory of Abell 3376.We performa set of N-bodyadiabatic hy-
. drodynamicalsimulationsusingtheSPHcodeGadget-2.Thesesimulationsofbinarycluster
h
p collisions are aimed at exploring the parameter space of possible initial configurations. By
- attempting to match X-ray morphology,temperature, virial mass and X-ray luminosity, we
o
setapproximateconstraintsonsomemergerparameters.Our bestmodelssuggestacollision
r
t of clusters with mass ratio in the range 1/6–1/8, and having a subcluster with central gas
s densityfourtimeshigherthanthatofthemajorcluster.Modelswithsmallimpactparameter
a
[ (b < 150kpc),ifany,arepreferred.We estimatethatAbell3376isobservedapproximately
0.5Gyraftercorepassage,andthatthecollisionaxisisinclinedbyi ≈ 40◦ withrespectto

1 theplaneofthesky.Theinfallingsubclusterdrivesasupersonicshockwavethatpropagates
v atalmost2600km/s,implyingaMachnumberashighasM∼4;butweshowhowitwould
4 havebeenunderestimatedasM∼3duetoprojectioneffects.
3
4 Keywords: methods:numerical–galaxies:clusters:individual:A3376–galaxies:clusters:
4
intraclustermedium
.
1
0
3
1
1 INTRODUCTION have frequently focused on the Bullet Cluster (e.g. Takizawa
:
v 2005, 2006; Milosavljevic´etal. 2007; Springel&Farrar 2007;
Mergersaretheprocessesthroughwhichgalaxyclustersassemble
i Mastropietro&Burkert 2008).Recently, vanWeerenetal.(2011)
X inthehierarchicalscenarioofstructureformation.Observedgalaxy
carriedouthydrodynamical simulationstomodelthegalaxy clus-
r clustersoftendisplayperturbedmorphologiessuggesting theyun-
ter CIZAJ2242.8+5301 and used its double radio relics to set
a derwentrecentinteractionswithlessmassivesubclusters.
constraints on the merger geometry, mass ratio and time-scale.
Anumberofgalaxyclustersexhibitdiffuseradioemissionin
Bru¨ggenetal. (2012) modelled 1RXSJ0603.3+4214, another ra-
theirperiphery,whichisnotassociatedwithgalacticsources(e.g.
dioreliccluster,asatriplemerger.
Feretti&Giovannini1996;vanWeerenetal.2009;Bonafedeetal.
In fully cosmological hydrodynamical simulations, clusters
2012).TheseMpc-scalestructuresareknowasradiorelicsandthey
mergers are studied in a more realistic but less well-controlled
are useful as probes of merger shocks. They are generally inter-
environment, and sometimes at the cost of lower spatial or mass
pretedasbeingdrivenbyshockwavesthatpropagateoutwardsat
resolution. They provide useful analyses of the statistical proper-
supersonicspeeds,re-acceleratingrelativisticelectronsthroughthe
ties of merger shocks, such as cold fronts (Hallmanetal. 2010)
Fermi mechanism in the very low-density outskirts of the cluster
and the distributions of Mach numbers (e.g. Vazzaetal. 2011;
(e.g.Fujitaetal.2003;Gabici&Blasi2003).
Araya-Meloetal. 2012; Planelles&Quilis 2012). Typical Mach
From the theoretical standpoint, idealised numerical sim-
numbersinshocksdrivenbyclustercollisionstendtobe . 3,
ulations of binary cluster mergers supply a wealth of insight M
butstrongshocksmayariseundersomecircumstances.Forexam-
into the outcomes of these events (e.g. Roettigeretal. 1993;
ple, Finoguenovetal. (2010) obtained 2 from the density
Schindler&Mueller 1993; Pearceetal. 1994; Roettigeretal. M ∼
andtemperaturedropsinAbell3667andMarkevitchetal.(2005)
1997; Ricker 1998; Roettiger&Flores 2000; Ricker&Sarazin
had found a similar value for Abell 520. A shock as strong as
2001; Ritchie&Thomas 2002; Pooleetal. 2006; ZuHoneetal.
4wasestimatedbyvanWeerenetal.(2010)fromtheradio
2009, 2010; ZuHone 2011). Hydrodynamical simulations of M ∼
relicsofCIZAJ2242.8+5301.
merging cluster designed to model specific observed objects
Using Suzaku X-ray observations, Akamatsuetal. (2012)
measured the temperature jump in the western radio relic of
⋆ E-mail:[email protected] Abell 3376, obtaining = 2.91 0.91. From polarisation
M ±
2 R. E. G.Machado&G. B. Lima Neto
and spectral indices studies of the radio relics of Abell 3376, mi=1 108M⊙ forbothspecies.Theminorcluster’smassand
×
Kaleetal.(2011,2012) estimated 2.2 3.3. From a cos- particle number are scaled down such that all particles have the
M ∼ −
mological simulation, Pauletal.(2011)wereabletoidentifyone samemass.
mergingclusterwhoseshockstructureresemblestheradiorelicsof Simulations were performed using the public version of the
Abell3376. parallelSPHcodeGadget-2(Springel2005)withasofteninglength
Abell3376(hereafterA3376)isanearby(z=0.046)massive ofǫ = 5kpcand amaximum timestepof0.001 Gyr.Theintra-
galaxyclusterwithadistinctivebullet-likemorphology,suggesting clustermediumisrepresentedbyanidealgaswithadiabaticindex
anongoingcollisiontakingplace.Itispossiblytheclosestcluster γ =5/3.Asafirstapproximation,coolingisnottakenintoaccount
exhibitingsuchamorphology.Initsoutskirts,apairofprominent in the simulations, since the cooling time-scale is larger than the
Mpc-scale radio relics are present (Bagchietal. 2006). Its virial merger time-scale. Galaxies themselves account for a small frac-
massisestimatedas5.0 1014M⊙(Girardietal.1998,basedon tionofthetotalclustermass( 3%,e.g.Lagana´etal.2008)and
× ∼
galaxyvelocitydispersion)andits0.1–2.4keVluminosityisL theirgravitationalinfluencemaybedisregarded. Sincewedonot
X
2.5 1044 erg/s (Ebelingetal. 1996, based on Rosat data). Th≃e includestarsinthesesimulations,feedbackandstarformationare
×
firstandsecondbrightestclustergalaxies(BCG)areseparatedby notpresent.Eventhoughmagneticfieldsarebelievedtogiveriseto
970h−1 kpc, but it isthesecond BCGthat coincides withthe theradiorelicsobservedinA3376,theyarenotexpectedtoplayan
70
∼
peakofX-rayemission. important roleindetermining theglobal cluster morphology, and
Bagchietal.(2006)haveanalysedearlyXMM-NewtonX-ray areignoredinoursimulations.Theevolutionofthesystemisfol-
andVLAradiodata,proposingthattheradiorelicsobserved may lowedfor5Gyr,buttherelevantphasestakeplaceinatime-scale
alsobethesiteofaccelerationofveryenergeticcosmicrays,upto of not more than about 1 Gyr. Because of that, and of the small
1018eV.Thiswouldbepossiblewithfirst-orderFermimechanism spatialextentofthesystem,cosmologicalexpansionisneglected.
attheshockwavefront.Theysetforthtwopossiblescenariosthat Simulationswerecarriedoutona2304-coreSGIAltixcluster.
couldberesponsibleforproducing theshock: (i)theaccretionof
intergalacticmediumflowingdowntowardsthecluster;or(ii)the
collisionoftwoclusters,buttheissueremainedunresolved. 2.2 Initialconditionsandmodels
Our goal in this work is to run N-body+SPH simulations For the dark matter halo, a Hernquist (1990) density profile is
tailored forthe specificcase of A3376 using more recent XMM-
adopted:
Newtondatainordertoconstraintheactual dynamical historyof
M r
thissystem. ρ (r)= h h (1)
Thispaperisorganizedasfollows.Simulationtechniquesand h 2π r(r+rh)3
initialconditionsaredescribedinSection2.X-rayobservationsare whereM isthedarkmatterhalomass,and r isascalelength.
h h
describedinSection3.InSection4wepresenttheglobalmerger ThisissimilartotheNFWprofile(Navarro,Frenk&White1997)
evolution, explore the parameter space of different possible col- except intheoutermost partsbeyond the r200 radius(alsounder-
lisions,andcomparethesimulationresultstoobservations; Mach stood as the virial radius), with the advantage of having a finite
numberanddarkmatterdistributionarediscussed.Finally,wesum- totalmass.Conveniently,manyofitsproperties(suchaspotential,
mariseandconcludeinSection5.Throughoutthisworkweassume cumulativemassanddistributionfunction) canbeexpressed ana-
a standard ΛCDM cosmology with ΩΛ = 0.7, ΩM = 0.3 and lytically.
H0=70kms−1Mpc−1. Forthegasdistribution,weemployaDehnen(1993)density
profile:
(3 γ)M r
2 SIMULATIONS ρg(r)= −4π g rγ(r+gr )4−γ (2)
g
We set up an idealised numerical model to represent the merg-
whereM isthegasmassandr isascalelength.Thishastheben-
g g
ingof twoinitiallyisolatedgalaxy clusters. Themainpurpose of
efitofpreserving theanalyticalsimplicityofseveral usefulquan-
these simulations is to reproduce certain features of the galaxy
tities(chieflythederivativesofthepotential),whilealsoallowing
clusterA3376,especiallytheglobalmorphologyoftheintracluster
thepossibilityofaflatcore,whichisachievedbysettingitsγ pa-
medium.Eventhoughthismodelreliesonseveralsimplifications,
rametertozero.Theresultingprofileresemblesthatofa β-model
itallowsustoreconstructapossiblescenarioforthedynamicalhis-
(Cavaliere&Fusco-Femiano1976)andisthussuitabletorepresent
toryofA3376.Bycomparingtheresultsofalargesetofsimula-
the intracluster medium of an undisturbed cluster without a pro-
tions,itispossibletosetapproximateconstraintsonsomecollision
nouncedcool-core,i.e.withoutasteepdensityprofileinthecentre.
parameters.
Tocreateanumericalrealisationofthisdarkmatter+gassys-
tem,wesetuptheinitialpositionsandvelocitiesfollowingthepro-
cedure outlined by Kazantzidisetal. (2006). First, the dark mat-
2.1 Techniques
tercumulativemassfunctionisuniformlysampledintheinterval
Weconsiderthecollisionoftwosphericallysymmetricgalaxyclus- [0,M ] and the inverse function r(M) is used to provide r, the
h
ters:amoremassiveclusterA(themajorcluster)andalessmas- distancefromthecentre,foreachdarkmatterparticle.Thesameis
siveclusterB(alsoreferredtoastheminorclusterorthesubclus- doneforthegasparticles.Fromtheseradii,cartesiancoordinates
ter).Arangeofmassratios M /M isexplored. Eachclusteris areobtainedbyassigningrandomdirectionstothepositionvectors.
B A
composedofdarkmatterparticlesandgasparticles,andabaryon One possible method to obtain the velocities of the colli-
fractionof0.18isadoptedthroughout. sionless particles is the so called ‘local Maxwellian approxima-
In all simulations, the major cluster has a total of tion’. It consists in drawing velocities from Maxwellian distribu-
N =6 106 particles proportionally divided between dark tions with dispersions obtained from solving the Jeans equation
A
×
matter and gas, such that the mass resolution is the same at each radius (Binney&Tremaine 1987). However, due to the
Simulationsofthemerginggalaxycluster Abell3376 3
inadequacies of this approach which have been pointed out by
Table1.Initalconditionparameters.Model233isthefiducialmodel.
Kazantzidisetal.(2004),onemustresorttothedistributionfunc-
tlioocnalitsshealfp.eInotfhtihsewvaey,loncoityassduismtrpibtiuotniosnne(eadpatrot bfreommatdheeaabsosuutmthpe- model label MMBA nn00,,BA v0 b0 Ntotal
(km/s) (kpc)
tionsofisotropyandsphericalsymmetry)andtheexactdistribution
function f( )isgiven byEddington’s formula(Eddington 1916; 231 mr2 1/2 4 1500 0 9×106
Binney&TEremaine1987): 232 mr4 1/4 4 1500 0 7.5×106
233 mr6 1/6 4 1500 0 7×106
1 E d2ρ dΨ 1 dρ 234 mr8 1/8 4 1500 0 6.75×106
f( )= h + h (3)
E √8π2 (cid:20)Z0 dΨ2 √E−Ψ √E (cid:18)dΨ(cid:19)Ψ=0(cid:21) 241 b150 1/6 4 1500 150 7×106
242 b350 1/6 4 1500 350 7×106
where Ψ = Φ = (Φh +Φg) is the relative total potential, 243 b500 1/6 4 1500 500 7×106
and = Ψ −v2/2 i−s the relative energy. For physically mean-
ingfuElρh(r)a−ndΨ(r),thelastterminequation(3)vanishes.This 238 v500 1/6 4 500 0 7×106
leavesanintegrandthatdependson(thesecondderivativeof)the 239 v1000 1/6 4 1000 0 7×106
dark matterdensity expressed asafunction of the totalpotential, 240 v2000 1/6 4 2000 0 7×106
ρ = ρ (Ψ). The integration is evaluated numerically and the
h h 235 n1 1/6 1 1500 0 7×106
function f( ) istabulated in a finegrid over a range of energies
E 236 n2 1/6 2 1500 0 7×106
andtheninterpolatedwherevernecessary.Randompairs( ,f)are
drawnandvaluesofv2areacceptedaccordingtothevonNEeumann 237 n6 1/6 6 1500 0 7×106
(1951)rejectiontechnique.Thisassignsaspeedtoeachcollision-
lessparticleandcartesianvelocitycomponentsareobtainedassum-
ingrandomdirectionsforthevelocityvectors. 3 X-RAYDATA
Sincethegasisassumedtobeinhydrostaticequilibrium,each
3.1 Observations
volumeelement of thefluidisinitiallyat rest.TheSPHparticles
requireanadditionalquantitytobesetup:theirinternalenergy(i.e. The numerical simulations presented here will be compared to
temperature). From the assumption of hydrostatic equilibrium, it archival X-ray observations. A3376 was observed twice by the
followsthatforachosengasdensityρ (r),thetemperatureprofile XMM-Newtonsatellite,in2003 (revolution 0606, P.I.M. Marke-
g
isuniquelyspecifiedas: vitch) and in 2007 (revolution 1411, P.I. M. Johnston-Hollitt).
Whilethe2003observationwaspartiallyanalysedbyBagchietal.
µm 1 ∞ GM(r′) (2006)(theydidnotusethepndetector),the2007observationis,
T(r)= p ρ (r′) dr′ (4)
k ρg(r)Zr g r′2 asfarasweknow,unpublished.
Both observations were done in Prime Full Window with
where µisthemeanmolecularweight, m istheprotonmass, k “medium”filter.WehaveruntheScienceAnalysisSystem(SAS1
p
istheBoltzmannconstantandM(r′) = M (r′)+M (r′)isthe 11.0)pipeline,removingbadpixels,electronicnoise,andcorrect-
g h
totalmassinsidetheradiusr′. ingforchargetransferlosses.FortheEPICMOS1andMOS2cam-
Eachclustermodelisallowedtorelaxinisolationforaperiod eraswehavekeptonlyeventswithPATTERN612andFLAG=
of5Gyr,typicallyafewdynamicaltime-scales,priortothebegin- 0(eventsonthefieldofview).Forthepncamera,havekeptevents
ning of the actual collision. Thisensures that transient numerical with PATTERN6 4 and FLAG = 0, following the standard pro-
effects,howeverminor,willhavehadtimetosubside.Theclusters cedure recommended by the SAS team. Both observations were
arethenplacedatasufficientlylargeinitialseparation d0,having screenedforhighparticlebackgroundperiods.Wehaveconstructed
aninitialrelativevelocityv0inthedirectionofthex-axis.Toavoid light-curvesinthe[1-12keV]bandandfilteredouttimeintervals
spurioustidaleffectsintheinitialconditions,weemployaninitial ofanomalouslyhighflux.Thefinalexposuretimesforthe2003ob-
separationofd0 = 4Mpc,whichisapproximatelytwiceaslarge servationwere23.0,22.9,and16.0ksfortheMOS1,MOS2,and
asthesumoftheclusters’virialradii. pn,respectively.Forthe2007observationtheywere36.8,39.8,and
Numerouscombinationsofplausibleinitialconditionparam- 25.6ksfortheMOS1,MOS2,andpn,respectively.
etersarepossibleand,inthesearchfora‘best-fitting’model,hun- When necessary, the background was taken into account by
dreds of simulations were run. Table 1 lists the initial condition usingthepubliclyavailableEPICblankskytemplatesdescribedby
parametersofthesampleofmodelsthatarereportedinthispaper. Read&Ponman(2003),takingintoaccounttheobservationmode
Thissamplefocusesonthevariationsoffourparameters,namely: andfilter.Eachblankskybackgroundwasfurthernormalisedusing
thetotalmassratioM /M ,rangingfrom1/2to1/8;theratioof theobservedspectrumobtainedinanannulus(between12.5–14.0
B A
thecentralgasdensitiesn0,B/n0,Arangingfrom1to6;theinitial arcmin),takingcaretoavoidtheclusteremission.
relativevelocityv0,rangingfrom500to2000km/s;andtheimpact
parameterb0,rangingfrom0to500kpc.
Themajorcluster’stotalmassisalwaysMA =6 1014M⊙ 3.2 Analysis
anditscentralgasdensityisn0,A =1.2 10−2cm−3×inallcases. Withthecleanedeventfiles,wehaveproducedtheexposure-map
×
Thesevalueswerechosentoensurethatboththetotalmassandthe corrected images in the [0.5–8.0 keV] band combining all XMM
totalX-rayluminosityoftheresultingobject arewithinthesame dataavailable.Thisimagewillbecomparedbelowtoasimulated
orderofmagnitudeastheobservedcluster.Theinitialrelativeve- imagefromtheN-bodysimulation.
locityisalwaysparalleltothex-axis,evenwhenanon-zeroimpact
parameter(ashiftintheinitialpositionofthesubclusteralongthe
y-axisdirection)ispresent. 1 Seehttp://xmm.esac.esa.int/
4 R. E. G.Machado&G. B. Lima Neto
Wehavealsoproduceda2Dtemperaturemap,usinganadap-
tive kernel technique (Durret&LimaNeto 2008). A cell of vari-
able size must have a minimum count number (of the order of
103 afterbackgroundsubtraction).Acellthatmeetsthiscriterium
hasitsspectrumfittedbyanabsorbed,singletemperatureMEKAL
model(bremsstrahlungandemissionlines,Kaastra&Mewe1993;
Liedahletal. 1995) using the XSPEC 12.5 package2 (Arnaud
1996). The free parameters are the intra-cluster plasma tempera-
tureandmetallicity(metalabundance,mainlyiron).
Thespectralfitsaredoneinthe[0.7–8.0keV]band.Wefixed
theabsorptionusingtheGalacticvalueoftheneutralhydrogencol-
umndensity(4.6 1020cm−2;Leiden/Argentine/Bonn(LAB)Sur-
vey),estimatedw×iththenhtaskfromFTOOLS3.Theeffectivearea
files(ARFs)andtheresponsematrices(RMFs)werecomputedfor
eachcellintheimagegrid.Weproducedatemperaturemapcom-
bining both observations, which will be compared toour simula-
tionsbelow.
4 RESULTS
4.1 Globalevolution
Toillustratethetemporalevolutionofaclustermergersimulation,
Fig.1displaysasequenceofsnapshots(ofmodel233)spacedby
0.2 Gyr, in frames of 1.6 1.6 Mpc. This is a head-on collision
×
alongthex-axis,whichappearsarbitrarilyrotatedontheplaneof
the sky merely to match the position angle of the observation, a
rotationhavingofcoursenofurtherrelevance.Themeaningfulori-
entationistheinclinationanglei,betweenthecollisionaxisandthe
planeofthesky.AllframesinFig.1areprojectedatainclination
i=40◦,discussedindetailinSection4.2.5.Toallowforasome-
whatfaircomparisonwithobservations,wecomputetheprojected
X-raysurfacebrightness(leftcolumnofFig.1)andtheprojected
emission-weightedtemperature(rightcolumnofFig.1).
Even though the simulationsthemselves areadiabatic, when
generating these simulated images we assume the X-ray radia-
tivelossescanbedescribedbyacoolingfunctionthattakesmore
thanjustbremsstrahlungintoaccount.Fromthesimulationoutput,
weestimatetheemissionusingacoolingfunctionΛ(T)thatwas
computed using the MEKAL emission spectrum model with the
XSPEC12.5package,appropriateforaplasmaofmetallicityequal
to0.3Z⊙.At highenergiesthefree-freeemission (∝ n2e√T) is
predominant(andthatisthequantityusuallyemployedasaproxy
foremissioningalaxyclustersimulations),butatlowenergiescol-
lisionalexcitationdominates.Theemissionisthenprojectedalong
theline of sight togive theX-ray surface brightness maps. Tem-
peraturemapsaregeneratedbyweightingparticletemperaturesby
theiremission,andprojectingthemalongthelineofsight.
InFig.1thesubclustercomesfromthelowerrightcornerof
theframetowardsthemajorcluster.Mostoftherelevantdynamical
evolutionofthemergertakesplacewithinanintervalof1Gyr.The
simulationstartsatt = 0whentheclustersare4Mpcapart,and
central passage occurs at t 2.15 Gyr. Approximately 0.5 Gyr
≃
aftercentralpassageaconfigurationisreachedinwhichtheoverall
gasmorphologyapproximatesfairlywelltheshapeoftheobserved
cluster.Atthismoment,thesubclusterhaspassedbeyondthemajor
cluster centre while remaining significantly denser, which makes Figure1. Temporal evolution ofmodel 233: (a) projected X-ray surface
theemissionslightlymoreintenseintheregionofthenoseofthe brightness, intheleft column; and(b)projected emission-weighted tem-
perature,intherightcolumn.Thesixrowsdisplaysinstants0.2Gyrapart.
Eachframeis1.6×1.6Mpc,thespatialscaleisthesameforallframes,and
2 Seehttp://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/ thesurfacebrightnessandtemperaturerangesarebothconstant.
3 Seehttp://heasarc.gsfc.nasa.gov/ftools/
Simulationsofthemerginggalaxycluster Abell3376 5
shockthaninthegasbehindit.Atearliertimesnosuchdistinction sensitivetothesamenumberofvisualcuesandatthesamelevel
isnoticeable,whereasatlatertimestheglobalshapeisexcessively offlexibilitythatevaluationbyeyecanafford.
elongatedandadetachmentdevelopsbetweenthesubclustercore Herewepresentasystematiccomparison ofasampleofthe
andthegasleftbehind. modelsweexplored.ThisismeanttoallowacomparisonoftheX-
In this particular model, the subcluster has 1/6 of the main raymorphologyofthemodelslistedinTable1.Takingmodel233
cluster’stotalmass,butthegasinitscoreismorecentrallyconcen- tobethestandard,Fig.2displaysvariationsaroundthatmodel.The
trated,beingdenserbyafactorof4.Thesubclusterisalsocolder, surfacebrightnessscaleandspatialscalearethesameasinFig.1.
havinganinitialcentraltemperatureof 1keV,whilethemajor EachrowinFig.2displaysvariationsofonegivenparameter:(a)
∼
clusterhas4 5keV.Theheatedgasaheadofthecoldsubclusteris mass ratio; (b) impact parameter; (c) initial relative velocity; (d)
−
visibleasabowshockintherightcolumnofFig.1anditisfurther relativecentralgasdensities;and(e)inclination.Foreachofthese
discussedinSection4.4. properties,fourvariantsaregiven, oneof thembeing thefiducial
Attheinstantofbestmatch(t = 2.625Gyrformodel 233) model itself.Thishighlightstheindividual effect of varyingeach
the system evidently lacks spherical symmetry. Nevertheless we parameterseparately.Withtheexceptionofrow(e),everymodelis
measure the spherically averaged density profile, centred on the shownwiththesameinclinationi=40◦toallowforafaircompar-
point of highest total density. This is located at the major clus- ison.Allsnapshotsareshownatthesameinstantt = 2.625Gyr,
ter’s dark matter peak, around which the bulk of the total mass withtheexceptionofrow(c),becausemodelswithdifferentinitial
stilllies(seeSection4.5).Weobtaintheradiusr200 1.5Mpc, velocitieshavesubstantiallydifferenttime-scales.
≃
at which the mean density has dropped to 200 times the critical
densityρ .Thisradiusalsoencompassestheminorcluster’sdark
c
matter peak, as well as all the gaseous structures discussed here.
The mass enclosed within r200 is M200 ≃ 4.0×1014M⊙. The 4.2.1 Massratio
integrated X-ray luminosity (within r200 and inthe energy range
0.1–2.4 keV) is LX 4.3 1044 erg/s if the emission comes Row (a) of Fig. 2 shows the outcome of cluster mergers having
solelyfrombremsstrah≃lung, o×r LX 6.8 1044 erg/sifmetals mass ratios of 1/2, 1/4, 1/6 and 1/8. It is clear that major merg-
≃ ×
andlineemissionarealsotakenintoaccount. ersresultinaquitedistinctmorphology.ModelshavingM /M
B A
in the range of 1/6 – 1/8 are to be preferred. Neistein&Dekel
(2008),basedontheextendedPress-Schechterformalism,provide
estimatesoftherateofmergershavingmassratioaboveacertain
4.2 Explorationofparameterspace
valueatagivenredshift.Aclusterofmodel233’sM200atA3376’s
In order to attempt to constrain some of the merger parameters, redshift will have undergone one merger per 4.8 Gyr having
∼
weexplorednumerousdifferentinitialconditionconfigurations,in MB/MA>1/6.
searchofa‘best-fitting’model.Suchamodelwouldhavetosimul-
taneouslysatisfy,toanapproximatedegree,thefollowingcriteria:
theoverallgasmorphologyshouldbereminiscentoftheX-rayob-
servation of A3376; thetemperature should bein theappropriate
4.2.2 Impactparameter
observed range; thetotalmassand totalluminosity should fallin
thesameorderofmagnitudeasthoseinferredfromobservations.A Typicalimpactparametersingalaxyclustermergersareoftheor-
possiblyimportantadditional criteriumregardingthedistancebe- derofafew100kpc(Sarazin2002;Ricker1998;Ricker&Sarazin
tweenthetwobrightestclustergalaxiesisdiscussedinSection4.5. 2001).Thefourmodelsshowninrow(b)ofFig.2haveinitialim-
WetaketheBCGsseparationtobeaproxyfortheseparationbe- pactparameters b0 = 0,150,350and500kpc.Themostevident
tweenthetwodarkmatterpeaks. Whilemodel233 maynot nec- effectofoff-centremergersisthelossofsymmetryaroundthecol-
essarilybetheonethatstrictlyoptimiseseachsinglecriterium,it lisionaxis.Thecurvedtrajectoryofthesubclusterispartlyrespon-
is the one that provided the most acceptable compromise among sibleforthedistinctiveshapeoftheresultingobjects.Inahead-on
them. It is of course not possible to rule out the existence of al- collision,themajorcluster’scentralgasisspreadoutasthedenser
ternativecombinationsofparametersthatmightresultinsimilarly subclusterpassesthroughit,decreasingitsdensity.Ifhoweverthe
acceptablemodels.Weexploredphysicallymotivatedrangesofpa- twoclustersdon’tpassthrougheachother’scentre,themajorclus-
rameters (albeit in a limited number of combinations due to the ter’scoreremainsrelativelyundisturbed, andasaresulttwosep-
computationalcost)and,atleastfortheseranges,certainconfigu- arateclumpsofdensegasarestillvisible.Theasymmetrydueto
rationsmaymereliablyexcluded. acurvedtrajectorycouldbehiddenfromviewiftheorbitalplane
Asfarasmorphologicalcomparisonisconcerned,werefrain wereseenexactlyedge-on.Butevenunderthatparticularconfigu-
from attempts to implement quantitative algorithms. Instead we ration,bothcoreswouldstillbediscernible.SinceA3376displays
relyonvisualinspection,whichmaynotbethemostobjectiveap- neithernoticeableasymmetrynortwocores,thereisnoreasonto
proach and conclusions drawn fromitought toberegarded care- gobeyondthescenarioofahead-oncollision.
fully. Nevertheless, thisisanapproach not without itsmerits.As Itshouldbenotedthatb0referstoashiftinthedirectionofy-
exemplifiedbytheage-testedpracticeofmorphologicalclassifica- axisintheinitialconditions,i.e.whentheclustersare4Mpcapart
tionof galaxies,visual inspection tendstoyieldsurprisinglyreli- in the x-axis direction. The minimum separation b , which is
min
ableresults,whichareoftendifficulttoreproducealgorithmically. thedistancebetweentheclustercentresattheinstantofclosestap-
The type of comparisons we carry out here fall within thiseffort proach,isconsiderablysmaller.Forthethreeoff-axismodelspre-
of making approximate judgements of morphology by eye, tak- sentedinFig.2b,theapproximatedistancesatpericentricpassage
ingintoaccount boththeoverallappearance andvarious detailed are respectively b = 100,200 and 250 kpc. Thissets a tight
min
aspects.Whilepixel-by-pixel subtraction(orsomevariationofit) constraint,sinceab assmallas100kpcwouldbesufficientto
min
couldprovidequantitativefigures,itcouldhardlybeexpectedtobe producenoticeableasymmetry.
6 R. E. G.Machado&G. B. Lima Neto
Figure 2. Projected X-ray surface brightness for different models. Each row displays four variations ofone given parameter: (a) mass ratio; (b)impact
parameter;(c)initialrelativevelocity;(d)relativegasconcentrations;(e)inclination.
Simulationsofthemerginggalaxycluster Abell3376 7
Figure3.ComparisonbetweenobservationsofA3376(left)andmodel233
(right).TheupperrowdisplaystheXMM-NewtonX-raysurfacebrightness Figure4.Theupperpaneldisplaystheshockvelocityvs(dot-dashedline)
inthe [0.5-8.0keV]band compared toasimulated image whose resolu- andthevelocityoftheupstreamgasu(dashedline),bothmeasuredinthe
tionhasbeendeliberatelydegraded.Inthelowerrow,theleftpanelshows centre-of-mass restframe;alsoshownisthesoundspeed cs (solidline).
theobservedtemperaturemaps.Inthesimulatedtemperaturemap,asemi ThelowerpanelshowstheresultingMachnumberasafunctionoftimefor
transparentmaskhighlightstheregioninwhichthereisdata. thismodel(233).Theshadedregionsrepresentupperandlowerboundaries
foreachquantity,computedfrommodelsv1000andv2000(andshiftedto
matchthesametimeinterval).
4.2.3 Initialrelativevelocity
GiventhemajorclustermassM ,thesubcluster’sfreefallvelocity
A
atd0 =4Mpcwouldbeapproximatelyv0 =1250km/s,ifitwere inclinations, the shape is excessively elongated at this time. For
apointmasshavingbeenreleasedfrominfinityatrest. very high inclinations it is excessively round. Unfortunately the
The models displayed in row (c) of Fig. 2 have initial rela- observations provide no information on the spatial orientation of
tivevelocitiesv0 = 500,1000,1500and2000km/s.Becausethe thecluster.Hereagain,thebestconfigurationischosennot solely
time-scales are not the same, they are compared at different in- from the X-ray morphology, although it is a good indicator. For
stants,eachchosentobethatwhichbestresemblesA3376.Asfar example, at latertimean inclination of i = 60◦ provides amor-
asthegasmorphologyisconcerned,thedifferentvelocitiesaffect phologythatisalsoacceptable.Howevertheprojectedseparation
thesharpnessof thenoseof theshock. Modelsv1000 and v2000 ofthedarkmatterpeaksisverytimedependentandalsoverysen-
weredismissednotonaccountoftheirX-raymorphologies,which sitivetoinclination(seeSection4.5).Bythetimethedarkmatter
arenotinadequate.However,modelv2000givesrisetoexcessively peaksaresufficientlyseparated with i = 60◦,themorphology is
hightemperaturesintheshockregion.Inmodelv1000,ontheother nolongeradequate.Thereforethei=40◦ projectionprovidesthe
hand,ittakesalongtimeforthedarkmatterpeakstobesufficiently bestcompromise.
separated(seeSection4.5)andbythattimethemorphologyhasde-
teriorated.The1500km/smodelprovidesatolerablecompromise
between morphology, temperature and dark matter peaks separa-
4.3 Comparisontoobservations
tion.TheMachnumberscorrespondingtothesevelocitiesaredis-
cussedinSection4.4. A comparison between observations of A3376 and model 233 is
giveninFig.3.Despitethehigh-resolutionofthenumericalmodel
itself,thesimulatedimagesaredeliberatelydegradedbyundersam-
4.2.4 Centralgasdensity pling the particles, by applying a gaussian smoothing and by the
additionofnoise.
Row(d)ofFig.2highlightstheeffectsofrelativecentralgasdensi-
In the observed temperature map (see Section 3.2, there is
ties,i.e.theeffectsoftheconcentrationofthesubcluster.Itshows
data only within a relatively small region approximately 20 ar-
models with n0,B/n0,A = 1,2,4 and 6. There isa cleardepen- cmin wide. To make the comparison more straightforward, a re-
dence on the concentration of the subcluster. When the clusters
gion of the same shape is overlaid on the simulated temperature
havecomparableconcentrations,thesubclustergasishardlydistin-
map,whilethesurroundingareaismadesemiopaque.Thisempha-
guishablefromthemajorclustergas.Theoutcomeisasomewhat
sisestheregioninwhichdataexists,andunderscoresthesimulated
uniformemissionwithnoX-raypeak.Ifthesubclusterisconsider-
temperaturefeatureswhicharenotobservationallyavailable.Apart
ablydenser,itisabletocrossthemajorclustercoreandtoremain
fromtherangeofvalues, theobserved temperaturemapdoesnot
relativelycohesive asit emerges. Because inmodel n6 theX-ray
exhibit remarkable features that could impose particularly strong
peakisexcessivelyprominent,thepreferredmodelisthatinwhich
constraints on the simulations parameters. We were able to rule
thesubclustercentralgasis4timesdenserthemajorcluster’s.
out collisions that heated the gas to above 10 keV, for example,
andthiswasusedtoconstrainvelocitiesandconcentrations.Nev-
ertheless,thesmallscaledetailsoftheobservedtemperaturemap
4.2.5 Inclination
are not reproduced, probably due to the simplifying assumptions
Row(e)ofFig.2showsmodel 233inthesameinstantprojected ofouradiabaticnumericalmodels,whichtakeintoaccountneither
underfourdifferentinclinationsi=0◦,30◦,40◦and60◦.Forlow substructuresnorthevariousgalaxy-relatedphysicalprocessesthat
8 R. E. G.Machado&G. B. Lima Neto
mightaffecttheintraclustergas,suchasfeedbackfromsupernovae
andAGN.
4.4 Machnumber
In a cluster merger simulation, the Mach number can be directly
measured,asallvelocityinformationisavailable.Oneofthemost
pronounced featuresisthetemperature dropafterthebow shock.
Thesuccessive positionsof thisdiscontinuity areused todirectly
computetheshock velocityv (inthecentre-of-massrestframe).
s
AsshownbySpringel&Farrar(2007)insimulationsof1E0657-
56,thegasaheadoftheshockisnotatrest.Insuchmergers,the
upstreamgasisinfactfallingtowardstheincomingsubclusterwith
aconsiderablevelocityu(inthecentre-of-massrestframe).There-
fore,theeffectiverelativevelocitywithwhichtheshockfronten-
countersthepre-shockgasisv u.Consequently,theMachnum-
s
−
beroughttobecomputedas
v u
= s− (5)
M cs
wherec2 = γkT isthesoundspeedofthepre-shockgas.Boththe
s µmp
upstreamvelocityandthesoundspeedaremeasuredintheregion
immediatelyaheadoftheshock.
Formodel 233at t = 2.625Gyrtheshockfrontmovesfor-
ward with v = 2114 km/s while the upstream gas falls back
s
at u = 468 km/s. The sound speed c = 666 km/s implies
s
−
= 3.9 at this instant. Figure 4 shows how these quantities
M
evolveoveranintervalof0.4Gyr.Toprovideanindicationofthe
typical ranges of these velocities, the shaded areas represent the
boundaries given by models v1000 and v2000 (shifted to match
their respective time-scales to that of model 233). The resulting
Machnumbers, bounded bytheseextremecases,wouldbeinthe
rangeofroughly =3 4.
M −
Once has been computed directly from the velocities, it
M
may be used to obtain the expected shock discontinuities from
theRankine-Hugoniotconditions.Figure5displaysfivequantities
measured along the collision axis: temperature; electron number
density; pressure; entropy; and gas streaming velocity in the x-
axisdirection.Asaproxyforentropy,theconventional definition
S = k T n−2/3 isadopted. Alloftheseprofileshavebeenmea-
e
suredusingnottheprojectedimages,butusingtheparticleswithin
acylinderofradius150kpcpassingthroughthenoseoftheshock.
Theupperpanelsof Fig.5displaythesurfacebrightness and the
temperaturebothprojectedunder i = 0◦ inclination.Thevertical
dashedlinesatx=1148kpcmarkthepositionoftheshockfront,
whichhasbeendeterminedasthepointwherethetemperaturedrop
ismostintense.Theverticalsolidlinesatx=980kpcmarkthepo-
sitionofthecontactdiscontinuity(thecoldfront),thepointwhere
thedensitydropsthemost.Atthecontactdiscontinuityvelocityand
thermalpressurearecontinuous. Thehorizontal linesindicatethe
expecteddropsineachofthefivequantitiesattheshockposition,
Figure5.Propertiesoftheshockformodel233att = 3.3Gyr.Thefirst
ascomputedfromtheRankine-Hugoniotconditionsusingthemea-
andsecondpanelsshowrespectivelytheX-raysurfacebrightnessmapand
sured .Assumingγ =5/3throughout,therelationsbetweenthe
M theemission-weightedtemperaturemap.Thethirdtoseventhpanelsdisplay
pre-shock(subscript1)andpost-shock(subscript2)quantitiesare thefollowingquantities measuredalongthex-axis:temperature, electron
(e.g.Landau&Lifshitz1959;Shu1992): numberdensity,pressure,entropy,andgasstreamingvelocity.Thelocation
ofthecontactdiscontinuity ismarkedbysolidverticallines;thelocation
T2 = 5M4+14M2−3 (6) olifnethsegbivoewtshheocvkaliusemsaorfkeedacbhyqduaasnhteidtyvebretfiocarellainneds.aTftheerdthaeshsehdohcko,rizwohnetrael
T1 16 2 theexpecteddropswerecomputedfromtheRankine-Hugoniotconditions
M
n2 4 2 usingthemeasuredMachnumber.
= M (7)
n1 2+3
M
Simulationsofthemerginggalaxycluster Abell3376 9
Figure6.Temperature anddensity measuredalong the x-axisformodel
233seeninprojection withinclination i = 40◦.Ifthetemperature drop
ismeasuredfromtheinclinedmodel,theinferredMachnumberissmaller
thantheactualvalue.
P2 5 2 1
= M − (8)
P1 4
S2 5 2 1 4 2 −5/3
= M − M (9)
S1 (cid:18) 4 (cid:19)(cid:18) 2+3(cid:19)
M
3 2 3
(vx,2−vx,1) = (vs−u) (cid:18) M4 −2 (cid:19) (10)
M
Thegoodmatchbetweentheexpecteddropsandthemeasured
profilesindicatesthattheMachnumbercould,inprinciple,bein-
ferredfromthesequantities.Foranobservedshock,thereishow-
everthedifficultyintroducedbytheunknowninclination.Toillus-
tratethisproblem,wetakethesamemodel233atthesameinstant
in time and now project it under the inclination i = 40◦. If we
nowtrytomeasurethetemperatureanddensityalongtheprojected
collisionaxis,weobtaintheprofilesshowninFig.6.Theresultis
thattheheightofthetemperaturepeakisloweredbecause, under
projection, the thin region of very hot gas is seen as spread over Figure7.TheupperpanelshowstheDSSopticalimageinwhichthecircles
a largerarea. Furthermore, thesharpness of the discontinuities is markpositionsofthegalaxiesattheclusterredshift.ThefirstBCG(right)
attenuated.Now,insteadofusingtheknownMachnumbertocom- andthesecondBCG(left)arehighlighted.Inthelowerpanel,whitecoun-
putethedrops,weconverselymeasurethetemperatureanddensity tourlines showthetotalprojected mass,overlaid ontheprojected X-ray
surfacebrightness,formodel233att=2.625Gyrwithi=40◦.
drops(horizontallinesinFig.6)attheshockposition.Theseratios
wouldleadto = 2.9forthisshock. AMachnumberinferred
M
inthismannerforaclusterofunknowninclinationshouldthusbe
ThelowerpanelofFig.7showswhitecontourlinesthatrep-
regardedasalowerlimit.
resentthetotalprojectedmassformodel233,overlaidontheX-ray
surfacebrightness. Theseparationbetweenthedarkmatter peaks
isapproximately800–850kpcatthebest-fittinginstant.Theupper
4.5 Darkmatterdistribution
panelofFig.7showsanoptical‘true-colour’(IR-Red-Blue)DSS
In A3376 the brightest cluster galaxy (first BCG) is located not image of A3376 in which the galaxies at the cluster redshift (se-
atthepeak ofX-rayemission, butatadistanceof approximately lectedusingNED4) aremarked bycirclesand thetwoBCGsare
970h−1 kpc from it. The X-ray peak coincides with the second highlighted.Thedarkmatterseparationofmodel233matchesthe
70
BCG.Apossibleinterpretationofthispeculiarityisascenarioin observed BCG distance to within 12%. Again, an even better
∼
whichalessmassiveclustercomesfromthesouthwesthostingthe matchwouldbeachievedataslightlylatertime,butatthepriceof
secondBCGandovertakesthemajorcluster’score,wherethefirst adeterioratinggasmorphology.
BCGlies.Ourbestmodelaccountsforthisfeature,inthefollowing Ofcourse,apossiblemassmapofA3376exhibitingtwoma-
sense.Astherearenogalaxiesinoursimulations,weassume the jor mass concentrations around the locations of the BCGswould
BCGseparationmaybeidentifiedwiththedarkmatterpeakssepa- lendmorecredencetothisscenario.Mappingthedarkmatterdistri-
ration.Intheabsenceofadditionalclues,itisreasonabletoassume butionbymeansofgravitationalweaklensingisparticularlychal-
thatthemostmassivegalaxiesshouldinprinciplebelocatedatthe
bottomsofthepotentialwell,i.e.atornearthecentroidsofthetwo
darkmatterpeaks. 4 NASA/IPACExtragalacticDatabase,http://ned.ipac.caltech.edu/
10 R. E.G. Machado&G. B. LimaNeto
lenginginthecaseofA3376duetoitsproximity.Onceorifsuch multaneously met, namely: overall gas morphology, temperature,
mapisavailable,itmighteithercorroboratethisscenario orover- virialmass, totalX-rayluminosity, and distancebetween thetwo
throwit.Ifthedarkmatterseparationturnsouttobesimilartothe dark matter peaks. While the best model presented here may not
BCGseparation,themassmapmightsetmorestringentconstraints necessarilyoptimiseeachofthesecriteriaindividually,itprovided
onthesimulationparameters.If,ontheotherhand,amorecompli- themostadequatecompromise.Itisofcourseimpossibletoargue
cateddarkmatterstructureisrevealed,thenalternativemodelswill fortheuniquenessofasolution,asalternativecombinationsofpa-
havetobesoughtout. rameterscouldconceivablyprovidesimilaroutcomes.Thisimpos-
An additional degree of freedom that has not been explored sibilitynotwithstanding,thephysicallymotivatedrangesofvalues
indepthinthispaperistherelativeconcentrationofthedarkmat- exploredhereatleastallowustoreliablyruleoutcertaincombina-
terhaloes.Forexample,ifthedarkmatteristoocentrallyconcen- tionsofparameters.
trated,gastemperaturesneedtobeinexcessof10keVeveninthe Herewesummarisethefivemainparametersthat havebeen
initialconditionstosatisfyhydrostaticequilibrium.Toobtainphys- constrainedandgiveapproximateestimatesofthebestranges:(a)
icallyplausibletemperaturesof5keVinthemajorcluster,weem- Wefind that the best matches are obtained for mass ratios in the
ployhaloscalelengthsr 500kpccomparabletothegasdensity interval1/6–1/8.Majormergersareexcludedduetotheirglobal
h
∼
scalelengthsrg.Ifthedarkmatterconcentrationsaretoolow,the morphology,whileinminormergersofverysmallmassratio, the
subcluster’sdarkmatterisabletoadvancefurtherthanitsgasand X-raypeakisnotsufficientlyintense.(b)Largeimpactparameters
adissociationdevelops.Asofyet,thereisnoreasontobelievethat are straightforwardly ruled out as they lead to obvious asymme-
thisisthecaseforA3376. Ifadarkmatter/gasoffsetisshownto triesthatarenotobserved inA3376. Anapproximate upperlimit
exist,thenitwouldhavetobeaccommodatedbyexploringdiffer- tob0issetat150kpc,whichimpliesaseparationof<100kpcat
entdarkmatterconcentrations.Amoresystematicanalysis ofthe pericentricpassage.(c)Thecollisionvelocityisconstrainednotby
darkmatterdistributionanditsdependenceonmergerparameters themorphologyalone,butalsobythetemperaturesanddarkmat-
isbeyondthescopeofthispaper. terpeakseparation.Forinitialvelocitiesof2000km/stheresulting
temperaturesareexcessivelyhighintheshockregion,whereasfor
1000km/sthedesireddarkmatterpeakseparationtakestoolong
tobereached.(d)Animportantparameteristherelativecentralgas
5 SUMMARYANDCONCLUSIONS
concentration.Wefindthemostadequatemorphologyisobtained
The peculiar cometary shape of A3376 is suggestive that it has whenthesubclusterisdenserthanthemajorclusterbyafactorof
undergone a recent merging event. This is, to best of our knowl- about4inthecentre.Thisdeterminesessentiallytheprominenceof
edge,theclosestgalaxyclusterdisplayingsuchmorphology. Fur- theX-raypeak,whichisexcessivelyoutstandingifthesubcluster
thermore, the diffuse radio emission in the form of double Mpc- centraldensityistoohigh,ornearlyunnoticeableotherwise.(e)Fi-
scale arcs in its periphery is understood to be caused by shock- nally,theinclination(theanglebetweenthecollisionaxisandthe
acceleratedrelativisticelectrons(Bagchietal.2006). plane of the sky) plays an important role in the morphology and
Using cosmological simulations, Pauletal. (2011) obtains a it is strongly time-dependent. Both the temperature and the total
cluster whose shock wave structure resembles the radio relics of X-ray luminosity are greatly increased at central passage. By the
A3376.Dedicatedhydrodynamicalsimulationsmeanttomodelone timethey reach adequate levels, the shape of the gas distribution
specific merging cluster have been mostly focused on the Bul- is excessively elongated when viewed on the collision plane. We
letClusteritself(e.g.Milosavljevic´etal.2007;Springel&Farrar findthat,projectedunderaninclinationangleofi=40◦,themor-
2007; Mastropietro&Burkert 2008). Recently vanWeerenetal. phologyisconsiderablylesselongatedandtheseparationbetween
(2011) and Bru¨ggenetal. (2012) carried out simulations of the thetwodarkmatterpeaksiscomparabletotheBCGseparationto
galaxyclustersCIZAJ2242.8+5301and1RXSJ0603.3+4214,re- within 12%.
∼
spectively, both of which also exhibit radio relics. In the case of Merging clusters generally exhibit complicated temperature
A3376, the morphology is sufficiently uncomplicated that it may structures. The observed temperature map, in a region approxi-
besatisfactorilymodelledastheencounterofonlytwoobjects,thus mately20arcminwide,showsameantemperatureof 3.5keV,
∼
renderingthereconstructionofitsdynamicalhistoryrelativelysim- but no discernible features that could be used to set strong con-
pler. straintsonthesimulations.Weuseittoruleoutmodelsinwhich
Thesimplenumericalmodelwesetupinordertoinvestigate theshockheatsthegasconsiderablyabovetheobservedrange.The
the problem consists in the collision of two spherically symmet- outcomeofthesimulationssuggeststhattheregioninwhichthere
ric galaxy clusters. Equilibrium initial conditions are prepared in isdataencompassesthecontactdiscontinuityatmost,butexcludes
whichthegalaxyclustersarerepresentedbyagascomponent and the shock front itself, i.e. the shock-heated gas ahead of the sub-
adarkmattercomponent. Thehydrodynamical simulationsthem- cluster’s X-ray peak. Furthermore, the small scale details of the
selvesareadiabatic,andweassumethatradiativelossesareunim- observed temperaturemaparenot reproduced inoursimulations.
portantduringthetimespanofthesimulations.Yetweusetheout- Iftheyaretheresultofinteractionsbetweengalaxiesandtheintr-
putofthesimulationstogeneratemapsofprojectedX-raysurface aclustermedium,theycouldnothavebeenrecoveredbyoursim-
brightnessandmapsofemission-weightedtemperature,inorderto plifiedsimulationswhichincludenosuchphysicalprocesses.The
comparethemtoXMMdata. simplifyingassumptions ofthesesimulationsalsoexcludetheef-
Startingfromaseparationof4Mpcandarelativeinitialve- fectsofadditionalsubstructure.
locityof1500 km/s,theclustersmeetonahead-on collision and Clustermergersareexpectedtodrivesupersonicshockwaves
the best-matching moment is reached approximately 0.5 Gyr af- of typical Mach numbers . 3 (Sarazin 2002) but stronger
M
tercentralpassage.Inordertoconstrainsomeofthecollisionpa- shocks may arise under some circumstances (e.g. Vazzaetal.
rameters,wecoveredasmuchparameterspaceasallowedbythe 2011; Planelles&Quilis2012). FromSuzaku X-rayobservations
computationally intensive nature of such effort. Ideally, in order ofA3376,Akamatsuetal.(2012)wereabletomeasureatempera-
toreacha‘best model’ anumberof criteriawould havetobesi- turejumpinthewesternradiorelicleadingto = 2.91 0.91.
M ±