A&A597,A24(2017) Astronomy DOI:10.1051/0004-6361/201629043 & (cid:13)c ESO2016 Astrophysics Probing the dynamical and X-ray mass proxies of the cluster of galaxies Abell S1101(cid:63) AndreasRabitz1,Yu-YingZhang2,AxelSchwope1,MiguelVerdugo3,ThomasH.Reiprich2,andMatthiasKlein4 1 Leibniz-InstitutfürAstrophysikPotsdam(AIP),AnderSternwarte16,14482Potsdam,Germany e-mail:arabitz@aip.de 2 Argelander-InstitutfürAstronomie,AufdemHügel71,53121Bonn,Germany 3 DepartmentforAstrophysicsUniversityofVienna,Türkenschanzstr.17,1180Vienna,Austria 4 Max-Planck-InstitutfürextraterrestrischePhysik,Giessenbachstr.1,85748Garching,Germany Received2June2016/Accepted23August2016 ABSTRACT Context.ThegalaxyclusterAbellS1101(S1101hereafter)deviatessignificantlyfromtheX-rayluminosityversusvelocitydispersion relation(L−σ)ofgalaxyclustersinourpreviousstudy.GivenreliableX-rayluminositymeasurementcombiningXMM-Newtonand ROSAT, thiscould mostlikely be causedby the biasin thevelocity dispersion dueto interlopers andlow member statisticin the previoussampleofmembergalaxies,whichwassolelybasedon20galaxyredshiftsdrawnfromtheliterature. Aims.Weintendtoincreasethegalaxymemberstatisticstoperformprecisionmeasurementsofthevelocitydispersionanddynamical massofS1101.Weaimforadetailedsubstructureanddynamicalstatecharacterizationofthiscluster,andacomparisonofmass estimatesderivedfrom(i)thevelocitydispersion(M ),(ii)thecausticmasscomputation(M ),and(iii)massproxiesfromX-ray vir caustic observationsandtheSunyaev-Zel’dovich(SZ)effect. Methods.WecarriedoutnewopticalspectroscopicobservationsofthegalaxiesinthisclusterfieldwithVIMOS,obtainingasample of∼60membergalaxiesforS1101.Werevisedtheclusterredshiftandvelocitydispersionmeasurementsbasedonthissampleand alsoappliedtheDressler-Shectmansubstructuretest. Results.Thecompletenessofclustermemberswithinr wassignificantlyimprovedforthiscluster.Testsfordynamicalsubstructure 200 donotshowevidenceofmajordisturbancesormergingactivitiesinS1101.Wefindgoodagreementbetweenthedynamicalcluster massmeasurementsandX-raymassestimates,whichconfirmstherelaxedstateoftheclusterdisplayedinthe2Dsubstructuretest. TheSZmassproxyisslightlyhigherthantheotherestimates.TheupdatedmeasurementofσerasedthedeviationofS1101inthe L−σ relation. We also noticed a background structure in the cluster field of S1101. This structure is a galaxy group that is very closetotheclusterS1101inprojectionbutatalmosttwiceitsredshift.Howeverthemassofthisstructureistoolowtosignificantly biastheobservedbolometricX-rayluminosityofS1101.Hence,wecanconcludethatthedeviationofS1101intheL−σrelation inourpreviousstudycanbeexplainedbylowmemberstatisticsandgalaxyinterlopers,whichareknowntointroducebiasesinthe estimatedvelocitydispersion. Keywords. galaxies:clusters:individual:AbellS1101–cosmology:observations–X-rays:galaxies:clusters– galaxies:clusters:intraclustermedium–galaxies:kinematicsanddynamics–methods:dataanalysis 1. Introduction dispersion (L − σ) relation of 62 clusters in an X-ray flux- bol limitedsampleof64clusters(Zhangetal.2011).Theobserved Galaxy clusters memorize structure formation (for instance scatterintherelationinourobservationaldatawasthoughttobe Borgani&Guzzo 2001), and cluster surveys have thus been mainlyrelatedtothepresenceofcoolcoresbutwasevenpresent widely used to constrain the cosmological parameters such as after the cool-core correction in deriving the X-ray luminosity. the dark energy content (e.g. Mantzetal. 2014). Various meth- Tostudytheotherpossibleoriginofthisscatter,inZhangetal. odssuchasoptical(seealsoGladders&Yee2005),X-rays(for (2011)wealsocomparedtheL −σrelationsbetweenourob- example Böhringeretal. 2001), weak lensing (e.g. Schneider bol servationalsampleandasampleof21clustersandgroupsfrom 1996), and the Sunyaev-Zel’dovich (SZ; Sunyaev&Zeldovich veryhigh-resolutionsimulationswithandwithoutactivegalactic 1972) effect (compare for instance Vale&White 2006), could nuclei(AGN)feedbackprovidedbyPuchweinetal.(2008).The potentially lead to biases in determining the mass function simulatedsamplewithAGNfeedbackmatcheswellwiththeob- in the cluster cosmological experiments. X-ray selects sys- servationalsampleof56clusters,excludingsixclusterswithless tems containing hot gas, as a sign of virialization (for instance than45clustergalaxyredshifts(n <45),inwhichAGNfeed- Weinberg&Kamionkowski 2002), and are considered to pro- backindifferentphasesexplainsthgealincreasingscatterofourob- videacleanerandmorecompleteselectionregardingmass. servationalsampletowardsthelow-massend.Thevelocitydis- To improve our knowledge of the X-ray selection method, persionestimatesforthosen <45clustersareaboutafactorof weinvestigatedtheX-raybolometricluminosityversusvelocity gal twolowerthantheL −σpredictionssuchthattheycausemore bol (cid:63) We have made use of VLT/VIMOS observations taken with thantwotimeslargerscatterthanthatoftheremainingclusters. ThisindicatesthatAGNfeedbackcannotbethemainoriginof the ESO Telescope at the Paranal Observatory under programme 087.A-0096. the scatter of the Lbol −σ relation for those ngal < 45 systems. ArticlepublishedbyEDPSciences A24,page1of17 A&A597,A24(2017) We suspect that systematic uncertainties in the velocity disper- resultingimproperphotometriccalibration.Theexisting2MASS sion estimates (e.g. Biviano et al. 2006; Saro et al. 2013) may (Skrutskieetal.2006)dataalsofailedtoimprovethephotomet- playastrongerrolethantheclusterphysics,suchasAGNfeed- ric calibration. Most 2MASS sources are also saturated for the back, in causing the scatter. We confirmed our guess by care- galaxiesinourobservations.Thestandardfieldsarenotofsuffi- fullytestingsystematicuncertaintiesusingthesimulatedsample cientqualitytocalibratetheB-bandFORSdata. due to interlopers and the selection of cluster members regard- Still, from the reduced imaging data we are able to ex- ingtheapertureradiusandmasslimitinZhangetal.(2011).The tractcataloguesusingSExtractor(Bertin&Arnouts1996)in systematicuncertaintiesdueto thoseeffectsareupto 40%;the dual-image mode with the R /162 band as detection image. c low member statistics in recovering the caustic amplitude may WefilteredthecatalogueforobjectswheretheCLASS_STARof playanimportantroleincausingthebias(alsoseeClercetal., SExtractor indicates a likely galaxy and the fluxes in the re- inprep). spectivebandsarelessthanthoseoftheapparentbrightcentral As a second-order effect, we found in Zhangetal. (2011) galaxy(BCG). that interlopers always bias the velocity dispersion measure- OurVIMOSspectroscopicfollow-upactuallycoversalarger mentstowardslowervaluesforoursimulatedsampleexceptfor sky area than the WFI field. Therefore, we have to rely on the one cluster. There are significant numbers of galaxies within VIMOS pre-imaging, performed with the R filter, to select ob- 1.2 Abell radii that are not in the virialized regions for poor jectsthatappearasbrightellipticalsfortheincrementalregion. systems in our simulated sample. As also shown in Fig. 10 in Wealsoreducedthepre-imagingofourVIMOScampaignwith Bivianoetal. (2006), unrecognized interlopers that are outside theTHELIpipeline.ThephotometryiscalibratedagainsttheSu- the virial radius (r ) but dynamically linked to the host clus- perCOSMOScataloguesintheVegasystem.Theoffsetbetween vir ter, and that do not form major substructures, bias the σ es- SuperCOSMOSandthecalibratedVIMOSR-bandcatalogueis timate towards lower values than cluster galaxies. There are about0.3mag,whichisrathersignificant.Itmaybecausedby also similar studies based on other simulations (e.g. Saroetal. calibrationsineitheroftheobservationsand/orfilterdifferences. 2013).Particularly,theline-of-sightvelocityofthegalaxieswith Nevertheless,weareabletoprovideuniformphotometryforall available spectroscopic redshifts (deVaucouleursetal. 1991; VIMOS spectroscopic sources thanks to the calibrated VIMOS Shectmanetal. 1996; Zabludoff&Mulchaey 1998; Jonesetal. pre-imaging. 2009) as a function of the projected radius shows a box-shape Follow-up priorities were assigned according to their lu- insteadofacausticshapeforoneofthengal <45clusters,thatis minosities to maximize the signal-to-noise ratio (S/N herafter) AbellS1101(S1101hereafter).Thisindicatesthatthechanceof and the effective survey area within the given observation time having a high percentage of unrecognized interlopers at large andpositionalconstraintssetbymulti-objectspectrographs.We radii is likely high for this cluster. To disentangle the scatter presenttheskypositionsoftheobjectsinoursurveyfieldinthe drivenbyinterlopersandbyotherphysicsintheLbol−σrelation leftpanelofFig.1.Furthermore,therightpanelofFig.1shows andtoconstrainpossiblebiasintheX-rayselectionmethod,we acolour–colourdiagramofthegalaxiesintheWFIfield,which carried out a detailed study on S1101 based on newly awarded weusedtoselectedthecandidatesfortheVIMOSspectroscopic VLT/VIMOS(VeryLargeTelescope/VIsibleMulti-ObjectSpec- follow-up.Ouraimtocoverallavailablespaceontheslitmasks trograph; LeFèvreetal. 2003) spectroscopic observations to- ledtotheselectionofadditionalsourcesthatappearedasbright getherwithXMM-NewtonandROSATX-raydata.Wenotethat ellipticals in cases where colour-selected sources could not be S1101 was detected as RXC J2313.9-4243 in Böhringeretal. targeted as a result of typical technical restrictions of multi- (2004) in the ROSAT All-Sky Survey (RASS; Trümper 1992). object spectrographs. Qwing to bad weather, the spectroscopic ItisalsolistedasSPT-CLJ2313-4243detectedthroughtheSZ follow-up shows an artificial elongation along the southeast- effectinBleemetal.(2015). northwestdirectionasnotallscheduledVIMOSpointingsinthe Throughoutthepaperweassumeastandardcosmologywith clusterfieldwereperformed. ΩM = 0.3, ΩΛ = 0.7 and H0 = 70 kms−1 Mpc−1. Thus, with an angular diameter distance of D = 224 Mpc, a scale of 1(cid:48) A correspondstoanextentof∼65kpcattheclusterredshiftz = 3. Opticalspectroscopicdataanalysisandresults cl 0.05601±0.00027.Errorsaregivenas95%confidenceintervals, 3.1. Spectroscopicdataanddatareduction unlessstatedotherwise. The spectroscopic follow-up of potential member galaxies of S1101 was conducted under ESO proposal ID 087.A-0096 (PI: 2. Opticalimagingandtargetselection Zhang). We applied for the wide-field and survey-probed capa- The cluster S1101 was observed at the ESO/MPG 2.2m tele- bilities of VIMOS at the UT3 (Melipal) of the ESO VLT, and scope with the wide-field imager (WFI; Baadeetal. 1999) in weregranted22.5hintotalforS1101andA2597,inwhichonly the V/89-, R /162, and I bands under non-photometric con- the observations of S1101 were almost completed for ∼11.5 h. c c ditions (PI: Reiprich) as a bad weather backup target. We re- The field of view of VIMOS is split into quadrants of one sin- duced the data using the THELI pipeline (Erbenetal. 2005; gle CCD each, 4× 7(cid:48) ×8(cid:48) with small gaps between the quad- Schirmer2013).Theco-addedimageshave1(cid:48).(cid:48)5seeinginV/89 rants. Using spectroscopic mode, multi-object slit masks were andR /162,and3(cid:48).(cid:48)1seeingin I .Therelativelypoorqualityof manufactured for seven pointings that cover the cluster field of c c theimagingcombinedwithsub-optimalweathermakesthede- S1101 out to the virial radius. All spectroscopic data for this terminationofthezeropointnotbetterthan0.15mag. programmeweretakenbetweenJuneandSeptember2011.Typ- Thecombinationofthosefiltersisnotthebesttobracketthe icalscienceexposuretimeswere1150sandbetweenthreeand 4000Åbreaktoisolatefullytheredsequenceforthecolourse- nineindividualexposuresperpointingweretaken.Weusedthe lectionofthecandidateclustergalaxiesattheredshiftofS1101, HR-Blue grism of VIMOS in order to achieve a redshift accu- but this combination was also chosen to select active galaxies. racy high enough to identify cluster substructures and obtain a Furthermore, a precise preselection of cluster member galaxies reliableσestimateanditsdeviationfromtheGaussiandistribu- according to their colours was hindered by the bad seeing and tion(e.g.Maurogordatoetal.2008).Wemeasuredthefullwidth A24,page2of17 A.Rabitzetal.:ProbingthedynamicalandX-raymassproxiesofAbellS1101 1:6 ¡42:2 1:4 ¡42:4 1:2 g] [deg] ¡42:6 R[ma 1:0 c e ¡ d ¡42:8 V 0:8 0:6 ¡43:0 0:4 ¡43:2 348:0 348:5 349:0 0:2 0:4 0:6 0:8 1:0 1:2 1:4 ra[deg] R¡I[mag] Fig.1.Skypositions(leftpanel)andWFIcolour–colourdiagram(rightpanel)oftheobjectsintheclusterfieldofS1101.Smallgreydotsshow allsourcesdetectedfromtheVIMOSpre-imagingandtheWFIimagingfortheleftandtherightpanel,respectively.GreencirclesindicateWFI colour–colourselectedcandidatesforthespectroscopicfollow-up.Theimagingcandidatesthatwerespectroscopicallyobservedbutclassifiedas non-membersareindicatedwithmagentaandcyandotsforgalaxieswithpassiveandactivespectraltypesandyellowdotsforstars.Largedots inred,blue,andgreycorrespondtospectroscopicallyverifiedclustermemberswithpassive,active,andunknownspectraltypes.Theblackcross denotestheclusterX-raycentre.Thebigblackcircleshowstheareawithinaprojecteddistanceofr .Becauseofbadweather,thespectroscopic 500 follow-upshowsanartificialelongationalongthesoutheast-northwestdirectionasnotallscheduledVIMOSpointingsintheclusterfieldwere performed. at half maximum (FWHM) of unblended emission lines in arc- We chose to correct our individual redshifts with respect to lampexposures,takenwiththesamemaskandhenceslitwidth thebarycentreofthesolarsystemtoreducethesystematicswhen as the science frames. This information allowed inferences on averagingmultipleobservedsourcesandcombiningwithgalaxy the spectral resolution, R ≡ λ · ∆λ−1. Our chosen set-up falls samplesfromtheliterature,asdescribedinthenextsubsection. within 1400 (cid:46) R (cid:46) 2070, considering the instrumental wave- By comparing acquisition images of slit masks with VIMOS length range of 4200–6200 Å and central 1(cid:48)(cid:48) slits. The quality pre-imagingdata,wewereabletoallocateindividualredshifted of the reduced spectra allows us to not only detect emission spectra to object coordinates from the Guide Star Catalogue-II. lines, but because of their high S/N we can also detect promi- We take the unweighted average of the measured redshifts for nentabsoptionfeaturesofearly-typegalaxies,forexample,CaII objectsobservedmultipletimes. H&K(3934Å&3969Å),Hβ(4861Å),Hδ(4103Å),and[OIII] The accuracy of our redshift determination is affected by (4959Åand5007Å). the accuracy of the wavelength calibration, the precision with which emission and absorption lines can be determined and by The data were reduced within ESO-Midas (Banseetal. thescatterofrepeatedredshiftmeasurementforagivengalaxy. 1983)withasuitablytailoredsetofscriptsbundledtogetherfor These were added quadratically and result in a typical redshift alargelyautomaticpipelinereduction.Thereductionworkflow error of ∆z ∼ 0.00007 (∼20 km s−1), a value also found by includes the following tasks: de-biasing of raw input frames, Maurogordatoetal.(2008)usingthesamespectroscopicset-up. flat-fielding and cosmic filtering of scientific frames, wave- lengthcalibration,weightedextractionofone-dimensional(1D) TheVIMOSspectroscopicsamplecomprises392individual spectra (following Horne 1986) including the generation of re- objects.Accordingtothespectralclassification,thereare220ac- spective error spectra, the creation of two-dimensional (2D) tivegalaxies(withaclearindicationofemissionlines),129pas- sky-subtractedframesand,finally,theco-additionofsingleflux- sive galaxies, 42 most likely late-type stars, and one Lyman-α calibratedspectra. emitter at redshift ∼3.4. A redshift histogram of their redshift Wewereabletoextractatotalof492spectra,ofwhich457 distribution,omittingtheLyman-αemitter,isgiveninFig.2. were of sufficient quality forour scientific use. We initially ex- aminedallspectrausingEZ(Garillietal.2010)togettheinitial 3.2. Incorporatingpublicredshiftstoourdata measure of the quality and redshift of each reduced spectrum. For spectra within a generous range around the cluster redshift We queried the NASA/IPAC Extragalactic Database (0.04 ≤ z ≤ 0.08) the final redshift was computed as the av- (NED) and merged the 20 redshifts in the literature erageofindependentGaussianfitstoavailablespectralfeatures (i.e. deVaucouleursetal. 1991; Shectmanetal. 1996; in the individual spectra to sustain high accuracy for tentative Zabludoff&Mulchaey 1998; Jonesetal. 2009) from ob- cluster members. The CaII H&K (3934 Å & 3969 Å) absorp- jects at the tentative cluster redshift with our sample. We tion lines for passive galaxies were fitted primarily. In addition observed a scatter in redshift between galaxies from the litera- we used the G band (4304 Å), Hδ (4103 Å), Hγ(4340 Å), Hβ ture and re-observations from this study but no systematics for (4861 Å), and MgII (5175 Å) absorption features, as well as the individual publications were found. Since not all sources [OII](3726Å/3729Å)and[OIII](4959Åand5007Å)emission in the literature have published quality assessments of their lines,whenpermittedbythespectralrangeandfeaturequality. spectra,weuseourredshiftsinsteadoftheirNEDcounterparts, A24,page3of17 A&A597,A24(2017) 12 20 80 10 10 60 frequency 40 0 0:04 0:06 0:08 0:10 0:12 0:14 frequency 68 4 20 2 0 0 0 0:1 0:2 0:3 0:4 0:5 0:6 0:7 0:045 0:050 0:055 0:060 0:065 redshift redshift Fig.2.RedshifthistogramoftheVIMOSspectroscopicsampleexclud- Fig.3.Redshiftdistributionofinitiallyselectedmembergalaxiesinthe ingtheLyman-αemitteratz∼3.4.Theinsetintheupperrightallows galaxyclusterS1101.Allvisiblegalaxieswereinitiallyselectedby|cz− a closer inspection of a redshift window around S1101 at z ∼ 0.056. cz|≤4000kms−1asdescribedinSect.3.3.Estimatorsoflocationanid Here,alargenumberoffieldgalaxiesaswellasapossiblebackground scale(z andσ,respectively;seeBeersetal.1990)wereusedtoclip structureatz∼0.1inoursamplebecomerecognizable. cl interlopers.Theresultingclustergalaxycandidatesareindicatedbythe shadedhistogram,whiletheblueverticallinesrefertothe±3σinterval ofσ aroundz usedfortheclipping. andliteratureredshiftscomplementarytoourwork(e.g.outside cl cl thefieldcoveredbytheVIMOSspectroscopy)wereincluded. Within the range of 0.05 ≤ z ≤ 0.065 our redshift cata- considerations. The equatorial coordinates and redshifts for all loguecomprises61distinctgalaxies(including11sourcesfrom spectroscopicmembergalaxiesidentifiedinthisworkaregiven theNED).Wedescribetheclustermemberselectioninthefol- inTableB.1. lowingsubsection.Additionally,aratherlargenumberofback- Figure1showstheskypositionsofallspectroscopicmember groundgalaxiesinthepoolofourspectraatredshiftsofaround galaxiesidentified,togetherwiththeirtypesbeingeitherpassive twice the cluster redshift (see Fig. 2) were detected. This ap- orstar-formingaccordingtotheircharacteristicspectralfeatures parentoverdensityofgalaxiesatz ∼ 0.1isdiscussedfurtherin (absorption- or emission-line dominated spectrum) once avail- Sect.6. able.Wenotethatsomeliteraturesourceshavenopubliclyavail- able spectra for the classification. The restriction to this simple 3.3. Memberselectionfromspectroscopicdata classification was chosen to gather information on the distribu- tionofstar-formingandpassivelyevolvinggalaxieswithrespect In order to investigate the dynamics of the cluster S1101, we to the cluster centric radii and a possible resulting bias for the need to assign cluster membership to the galaxies in our red- σ measurement. There is an obvious overdensity of passively shift catalogue. This is not trivial considering the fact that in- evolvinggalaxiesinoursamplebecausewetargetedthegalaxy falling or merging structures exist even in relaxed systems (see candidatesselectedbythephotometriccolouraroundtheredse- e.g.Zhangetal.2012).Weinitiallyselectedthosegalaxiesful- quenceinourobservations. filling |cz −cz| ≤ 4000 kms−1 as cluster member candidates. i The final values of the cluster redshift and its velocity dis- Here,cz istherecessionalvelocityoftheindividualgalaxy,and i persion following the procedure of Beersetal. (1990) are z = czthemeanvelocityofthegalaxyclusterS1101basedonitsred- (cid:16) (cid:17) cl 0.05601±0.00027andσ = 574+38 kms−1,respectively,are shiftintheREFLEXClusterSurveycatalogue(Böhringeretal. cl −36 2004),z=0.0564. summarized in Table 2 with additional characteristic values of A revised cluster redshift (z ) and velocity dispersion (σ ) the cluster. Unfortunately the fraction of active galaxies is too cl cl was computed using the biweight estimates of location and lowtocomputeanaccurateσtodirectlycompareσpas andσact. scalefollowingBeersetal.(1990).FollowingBiviano&Girardi The value measured for the passive fraction, however, agrees (2003),weappliedthe|z −z|·c≤3σ clippingtofinalizethe wellwithintheerrorswiththetotalsampleofclustermembers cl i cl selectionofmembergalaxiesandrepeatedthecomputation.The (seeTable2). resulting sample consists of 58 member galaxies, as visualized The cluster radius r∆ (e.g. r500) was defined as the radius inFig.3. within which the mass density is ∆ (e.g. 500) times of the crit- A different approach of assigning cluster membership to ical density at the cluster redshift, ρc(z) = 3H02(8πG)−1E2(z), galaxiesisthemethodof“fixedgaps“.Followingtheprocedure in which E2(z) = ΩM(1+z)3 +ΩΛ +(1−ΩM −ΩΛ)(1+z)2. byKatgertetal.(1996),weusedagapsizeof1000kms−1 and Theclustermasscanbeestimatedbythescalingrelationscali- identified 59 galaxies as likely cluster members: the same 58 brated by simulations from the velocity dispersion. An isother- fromaboveplusoneadditionalatz∼0.0635(seeFig.3).Since malsphericalmassmodelgenerallydoesnotfitwelltothemass the differences in velocity dispersion (+5%) and mean cluster distribution of clusters. The scaling relation based on such a redshift (+0.02%) are negligible, we stick to the previous pro- model (e.g. Carlbergetal. 1997) thus provides a biased esti- cedurewithiterativeclippingbasedontheσ forthefollowing mate. Instead, a NFW model (Navarroetal. 1997) is a better cl A24,page4of17 A.Rabitzetal.:ProbingthedynamicalandX-raymassproxiesofAbellS1101 description of the halo mass profile of clusters. Based on the Table 1. Results of the Dressler-Shectman test applied to the galaxy lattermodel,Munarietal.(2013)analyseddifferentsimulations clusterS1101. of group- and cluster-sized structures involving various physical models. Therein they estimated the velocity dispersion ver- Nloc ∆DS P sus cluster mass relation of the following tracers of the cluster 5 30.781 0.882 massdistribution:(i)darkmatterparticles,(ii)subhalosand(iii) 6 32.986 0.857 galaxies, 7 40.360 0.768 8 41.710 0.739 σ (cid:34)h(z)M (cid:35)α 9 42.239 0.720 1D = A 200 (1) kms−1 1D 1015 M(cid:12) 10 42.999 0.700 wthheereHuσb1bDleispathraemleinteer-ofa-tsigthhteverelodcsihtyiftdizspenrosiromnalaizneddh(bzy) Nanodte∆sD.STwheassucbaslctruulcattuedreatcecsotrwdainsgpteorfEoqrms.e(d3)foarndva(r4i)oufrsogmroSuepcts.iz3e.4s.NTlhoce, 100kms−1 Mpc−1.Munarietal.(2013)concludethatthebest- listedprobability PwascalculatedfromMonteCarlosimulationsand rejectssubstructureinclusterS1101withprobilities≥70%,depending fitvaluesof A and α usingdarkmatter particlesasthetracer 1D onthelocalgroupsize. are in general agreement with the NFW mass profile and pro- vide consistent results as that from Evrardetal. (2008). The Following Dressler&Shectman (1988), the value of Eq. (3) fits for subhalos and galaxies as tracers, on the other hand, would exceed the number of all member galaxies (N ) for show a steeper σ – M relation. Since we aim to determine the mem systemswithsubstructure.Wecalculated∆ foroursampleof cluster mass of S1101 from the velocity dispersion of member DS 58clustermembergalaxiesbyvaryinggroupsizes,5 ≤ N ≤ galaxies, we used the full range of parameters found by trac- loc ing galaxies for the various physical models (ceased star for- 10.TheresultsarelistedinTable1.D√espitethefactthataccord- ing to Pinkneyetal. (1996) N ∼ N , for all considered mation and AGN feedback; compare Table 1 in Munarietal. loc mem 2013), A = 1169.75 ± 11.45, and α = 0.3593 ± 0.0068. valuesofNloc,theresulting∆DS/Nmem turnedouttobewellbe- 1D lowunity.Thetestthereforeyieldednoevidenceforthepresence The corresponding mass and radius for the cluster S1101 are M = 1.92+0.52×1014 M andr = 1.169+0.097 Mpc,given ofsubstructureintheclusterS1101. 200 −0.42 (cid:12) 200 −0.093 However, a method more robust that using the “crit- theuncertainiesinA ,αandtheerrorofourvelocitydispersion 1D ical value” of unity persists in analysing the probability σ (seealsoTable2).Thebiasinusingthegalaxiesasthetracer cl of ∆ exceeding the observed ∆ . According to is low for low-z and low-mass clusters (Fig. 7 in Munarietal. DS,sim DS,obs Dressler&Shectman (1988) ∆ is calculated from an ar- 2013),whichisthecaseofS1101. DS,sim tificial sample of randomly reassigned redshifts to the galaxy positions in the sample, the so-called “Monte Carlo shuffling”. 3.4. Two-dimensionalkinematicstructure The randomization process of the galaxy systems destroys any truecorrelationbetweenpositionandvelocitywithinthosesim- The velocities of member galaxies scatter around the Hubble ulated clusters. Accordingly, the probabilities can be computed flow velocity of the underlying dark matter halo. According to using thehierarchicalclusteringmodel,clustersgrowthroughtheac- cretion of galaxies and groups of galaxies falling into the clus- f (cid:0)∆ >∆ (cid:1) ter potential well. Knowledge of the substructures of a galaxy P= DS,sim DS,obs , (4) n sim cluster is however crucial for the measurement of the line-of- sight velocity dispersion as well as its resulting mass proxy as where∆ isderivedfromEqs.(2)and(3)fortheobserved DS,obs substructuresintroducebiasesinitsvelocitydispersionestimate sample,while∆ iscomputedforthesampleofthereshuf- DS,sim (e.g. Bivianoetal. 2006). The spatial and line-of-sight velocity fledmembers.Onlysystemswith∆ largerthanthecorre- DS,sim distributionsofgalaxiesallowustodistinguishmembergalaxies spondingobservedvaluecontributetothefunction f intheprob- takingpartinanidealizedGaussianvelocitydistributionaround ability PgivenbyEq.(4).Forsystemswithclearsubstructures the cluster mean velocity from the infalling galaxies, groups of ∆ > ∆ isunlikelyperformedbyrandomizationsand DS,sim DS,obs galaxiesorevenlargermergingevents. theprobabilitytakeslowvalues.Henceweconsideraprobabil- Pinkneyetal.(1996)extensivelyprobedvariousapproaches ityofP<0.01(correspondingto<1%rejectionofsubstructure) of substructure tests based solely on velocities, positions, or a asaclearindicationofsubstructure. combination of both. Accordingly, an advanced and robust test WecalculatedPusingn =100000realizationstorandomly s forsubstructurewasdescribedbyDressler&Shectman(1988). shuffle our data for different local group sizes (5 to 10); the re- They provided a statistical approach to test the 2D kinematic sultsaregiveninTable1.Wefindnoevidenceofsubstructures structureofaclusterusingitsgalaxypositionsandvelocitiesas in S1101 using either the method based on ∆ or the method DS follows: based on P. S1101 is rather relaxed compared to, for example, the cluster RXC J1504.1-0248 (R1504), for which Zhangetal. δ2 = Nloc+1(cid:104)(cid:0)v −v(cid:1)2+(cid:0)σ −σ(cid:1)2(cid:105). (2) (2012) found P = 0.06 and with evidence of an infall group at i σ2 i,loc i,loc aboutr . 500 Equation (2) makes use of v , σ , and N being the mean i,loc i,loc loc velocity,meanvelocitydispersion,andgalaxynumberofthelo- 3.5. Dynamicalanalysisusingthecausticmethod calgroup.Herevandσaretheglobalmeanvelocityandtheve- locitydispersionofthecluster.Theindexirunsoverallgalaxies As mentioned in Kaiser (1987), cluster member galaxies tend toforma“trumpetshape”intheprojectclustercentricdistance inthesample.Thereducedstatisticsforthistestisgivenby versus velocity diagram owing the proportionality between the (cid:88) ∆ = δ. (3) maximum allowed velocity, the escape velocity relative to the DS i cluster, and the enclosed cluster mass. Galaxies with velocities i A24,page5of17 A&A597,A24(2017) Table2.PropertiesofthegalaxyclusterS1101. The mathematical basics of this method can be found in Silverman (1986) and the 1D approach is outlined in Pisani Spectroscopicproperties(58galaxies) (1993), whereas the multi-dimensional extension is developed zcl(58) 0.0(cid:16)5601±(cid:17)0.00027 inPisani(1996). σ (58) 574+38 kms−1 The input sample for the caustic analysis is based on all σcl (40) (cid:16)593+−7306(cid:17)kms−1 galaxiesthatfulfil|czi−czcl|≤4000kms−1,wherezclistheclus- pas (cid:16) −63 (cid:17) ter redshift calculated from the biweight estimator of location r 1.169+0.097 Mpc 200 (cid:16) (cid:17)−0.093 (Beersetal. 1990, compare Table 2). In the following, we use M 1.92+0.52 ×1014 M our own implementation of the caustic code. Nevertheless, we 200 −0.42 (cid:12) rcaustic (0.715±0.005) Mpc were fortunate to validate our results against available routines M50c0austic (1.10±0.72)×1014 M (The Caustic App – Ana Laura Serra & Antonaldo Diaferio, rca5u0s0tic (1.033±0.005) Mp(cid:12)c privatecommunication)andpointoutmajordifferencesbelow. 200 We first computed the projected radial distance of each Mcaustic (1.32±0.93)×1014 M 200 (cid:12) galaxy and its line-of-sight velocity in the cluster rest frame. X-rayproperties Contrary to the procedures described in Serraetal. (2011) and L (1.17±0.10)×1044ergs−1 Diaferio (1999), we did not weight or average the galaxy po- bol,500 r (0.84±0.02) Mpc sitions to derive the cluster centre but for simplicity used the 500 M (1.87±0.10) ×1014 M BCGposition(23:13:58.60,–42:43:39.0)asthereferenceclus- 500 (cid:12) M (1.9±0.13) ×1013 M tercentre.SincetheBCGoftheclusterS1101isalargeandlu- r(cid:5)gas,500 (cid:16)1.37+0.26(cid:17) Mp(cid:12)c minouscentraldominantgalaxyandS1101isratherrelaxed,we 200 (cid:16) (cid:17) −0.18 arguethatitspositionisagoodproxyfortheglobalcentreofthe M2(cid:5)00 2.91+−10..9999 ×1014 M(cid:12) darkmatterhalo,whichisafactalsodiscussedinBeers&Geller SZproperties (1983). MSZ (4.06±0.92)×1014 M WeusedthefollowingformulasfromZhangetal.(2012)to 500 (cid:12) computeprojecteddistanceandvelocityintheclusterrestframe: r = D sinθ and v = (cz−cz cosθ)/(1+z ), respectively, for Notes.Thenumberinparenthesisforspectroscopicalmeasuresrelates a cl cl allgalaxies.Here,z ,D ,θ,andzaretheclusterredshift,angular tothenumberofinputspectra.Wecalculatedtheclusterredshift(z ) cl a cl and velocity dispersion from all cluster members (σ ) and from the diameterdistanceattheclusterredshift,angularseparationfrom cl fractionofpassivegalaxiesalone(σ ),followingBeersetal.(1990) the cluster centre and galaxy redshift. Observables and uncer- pas asdescribedinSect.3.3,andusedthevaluestocomputer andM taintieswererescaledtomatchthesameunits(Mpc)throughout 200 200 followingtheNFW-fitbasedscalinginMunarietal.(2013).Theden- thecomputation. sity normalized to the critical density, ρc(zcl), was estimated for all Nowthe2Ddensitydistributionwascalculatedaccordingto radii of Eq. (10), and used to derive the radii and masses from the causticmassprofilefor∆ = 500and200,respectively.Inthemiddle partX-raypropertiesarelisted.L isthecool-corecorrectedX-ray 1 (cid:88)N 1 (cid:32)x−x (cid:33) luminosity. Mgas,500 is the gas mabosls,5.00M500 and r500 are the total mass fq(x)= N h2K h i , (5) andclusterradiusderivedfromthegasmassdistributionusingthegas i=1 i i mass vs. mass scaling relation. Those X-ray measurements are based where x = (r,v) is the vector of our input data, whose compo- on the combined XMM-Newton and ROSAT data from Zhangetal. nentsareweightedbythelocalsmoothinglengthh,togetrea- (2011).ValueswithdiamondsuperscriptionaretheX-rayresultsfrom i sonablerelativescalesbetweenradiusandvelocity.ThevalueN Reiprich&Böhringer(2002)usingonlyROSATpointedobservations. denotes the number of data points taken into account. The in- dex q is defined as q = σ /σ , indicates the relation between beyond the “trumpet shape” are not considered to be bound to v r the measurement uncertainties in velocity and radius, and will theclusterpotentialwellandare,therefore,notconsideredclus- beusedlaterasinputforEq.(7).Theinputcoordinateshaveto termembers.Theborderofthe“trumpetshape”definesroughly berescaledinamannerthatqisintheacceptablerangeof10to the maximum velocity scatter within the cluster, and is known 50(e.g.Diaferio1999).ThekernelK,isdefinedas: astheso-called“caustic”,anestimatoroftheescapevelocityfor tmheemhbaelor mstaattitsetricdsisatrlliobwutiofonrwaitmhoarespchoemripclaeltesysmammpeltirny.gHoifghtheer K(t)= 4π−1(cid:16)1−t2(cid:17)3 , t<1 (6)  0, otherwise caustic,whichyieldsmorerobustmeasurementsoftheunderly- ingdarkmatterdistributionofthecluster(e.g.Diaferio&Geller witht= x−xi.Toderiveabsolutevaluesforthesmoothinglength, 1997). The method to measure the caustic is described in de- hi (cid:113) tail, for example in Diaferio (1999) and Gelleretal. (1999). A westartwithh =h h λ.Hereλ = γ f (x)−1,withlogγ= i c opt i i 1 i good summary and detailed application can also be found in (cid:80) N−1log f (x),where f canbederivedfromEq.(5)byfixing Serraetal.(2011). i 1 i 1 h forallitotheoptimalsmoothinglength Thealgorithmofthecausticmethodusesa2Dadaptiveker- i (cid:114) nel to calculate a smoothed density distribution from the phase 6.24 σ2+σ2 space coordinates of the input galaxies. In this context, the hopt = N1/6 r 2 v· (7) phase-space spanned along the projected distance and line-of- sight velocity of the galaxies with respect to the cluster centre ThefactorinEq.(7)isdifferentintheliterature,hereweadopted and its mean velocity, respectively. By definition, the method thevaluefromSerraetal.(2011). can be used to identify the membership of galaxies based on Aminimizationof ttchiuoernv,deeacnsastnihtyebedcuiusrstvreiedbuitsotioadnne,reiwvstehimitchahetomfroaromsfsstphareocfiersliectiacopafilnthcgeuvrcveleluo.sctIeintrya,hdathdloiis-. M0(hc)= N12 (cid:88)N (cid:88)N h12K2 − N(N2−1)(cid:88)N (cid:88)h12K (8) i=1 j=1 j i=1 j(cid:44)i j A24,page6of17 A.Rabitzetal.:ProbingthedynamicalandX-raymassproxiesofAbellS1101 returns the smoothing parameter h . The returned value works the caustic mass may be underestimated because statistical un- c fine, in general, with well-sampled cluster populations. Sub- dersamplingofclustergalaxiesespeciallyatlargeclustercentric optimized scaling can, however, result in global under- or radiicouldcauseunderestimationofthecausticamplitude. overestimationofthecontributionfromtheconsideredgalaxies, We tested a possible bias in the mass estimate introduced leadingtoadensitydistribution fq thatiseithertoofineorover- from the fact that our input data consist of only preselected smoothed,whichbiasestheestimationoftheescapevelocityand cluster members (see Sect. 3.3), while established implemen- thusmass.Theminimizationgiveshc =0.5682accordingtoour tations of the caustic code do not make assumptions on mem- data. bership beforehand. In the following, we increased the sample Following the procedure of Diaferio (1999), the position of by including additional galaxies from our spectroscopic galaxy the caustic in the (r,v)-diagram is constrained by fq(r,v) = κ. sample at 0 < z ≤ 1.0. All steps computing the caustic were Wethenfindtheproperκbysolving repeated. The resulting density distribution is slightly different from the previous one due to the presence of fore- and back- S(κ,R)≡(cid:104)v2 (cid:105) −4(cid:104)v2(cid:105) =0. (9) esc κ,R R ground galaxies. Nevertheless, the caustic method still robustly identifies as the members the same galaxies as those in Fig. 4. Equation(9)expressesthebalancingoftheescapevelocityand This confirms that the caustic method, in which the member thevelocity dispersionfrom galaxieswithinthe radius R,justi- statisticsonlyimpacttheprecisionofthecausticmassdistribu- fiedbytheassumptionofvirialequilibriumandquasi-isotropic tion,candistinguishclustermembersfrominterloperswell(see velocity field in the inner part of the cluster. We encompass R = 0.8958Mpcand(cid:104)v2(cid:105) = 476.23(kms−1)2 frombinarytree alsoSerra&Diaferio2013).Wecalculatedthecontrastdensity (∆) distribution and found that the cluster radii and masses at calculations of our input data as measures for the mean radius ∆ = [500,200]varylessthan20%betweenthetwosamplesof and squared velocity dispersion of the galaxies associated with theinputcatalogues.Thisisreasonablycausedbythedifference theclusterbranchofthebinarytree.Descriptionsofthebinary in the optimal smoothing and the critical value of the density treeareprovidedinSerraetal.(2011).Themeanescapeveloc- distribution. ityinEq.(9)remainstheonlyκ-dependentquantityandcanbe derived from (cid:104)v2 (cid:105) = (cid:82)RA2(r)ϕ(r)dr /(cid:82)Rϕ(r)dr. We use R esc κ,R 0 (cid:82)κ 0 from the binary tree, ϕ(r) = f (r,v)dv and the caustic ampli- q 4. X-raydataanalysisandresults tudeA (r) = min{|v |,|v|}.Theparametersv andv aretheup- κ u l u l perandlowervelocityboundarysolutionsof f (r,v)=κ(which The XMM-Newton and ROSAT X-ray data analysis was de- q could be determined to κ = 0.0016461) for r running from 0 tailed in Zhangetal. (2011). In the surface brightness analysis, toR.Theclustermasswithinanenclosedradiuscanbederived we directly converted the ROSAT surface brightness profile to fromthecausticamplitudeas the XMM-Newton count rate using the best-fit spectral model (cid:90) r obtained from the XMM-Newton data. We then combined the GM(≤r)=F A2(x)dx, (10) XMM-Newtonsurfacebrightnessprofilewithinthetruncationra- β 0 dius,wheretheXMM-NewtonhasaS/Nof∼3,withtheROSAT convertedsurfacebrightnessprofilebeyondthetruncationradius with G denoting the gravitational constant and F the veloc- β forfurtheranalysis. ityanisotropy.FollowingSerraetal.(2011),weassumetheve- The X-ray luminosity is estimated by integrating the X-ray locity anisotropy to be independent on the radius, as a first- orderapproximation,andhencechoseF = 0.7.Anexpression surface brightness. At 3σ significance, the surface brightness for the error of the mass estimate was cβomputed using δM = profile was detected beyond r500 combining XMM-Newton and (cid:80)i |2m δA(r )/A(r )|,whereδA(r)/A(r) = κ/max{f(r,v)i}is ROSATdata.Inpractice,weestimatedthetotalcountratefrom j=1 j j j thebackground-subtracted,flat-fielded,pointsource-subtracted, therelativeerrorandm themassofashellatfixedradius. j and point spread function-corrected surface brightness profile The caustic mass estimates of the cluster S1101 for rcaustic 500 in the 0.7–2 keV band. We converted this to X-ray luminosity andrcaustic are Mcaustic = (1.10±0.72)×1014 M and Mcaustic = 200 500 (cid:12) 200 using the best-fit “mekal” model in XSPEC of the spectra ex- (1.32±0.93) × 1014 M(cid:12), respectively, and are also listed in tracted in the aperture within the XMM-Newton field of view Table 2. The lower part of Fig. 4 presents the computed mass defined in Sect. 3.2 in Zhangetal. (2009). Combined observa- distributionouttoacluster-centricradiusof∼1.6Mpc.Inthetop tionsofROSATandXMM-NewtoninZhangetal.(2011)yield panelofFig.4weshowthedensitydistribution fq asgreyscale consistent total X-ray luminosity measurements as those based and the critical curve (fq = κ), as thick grey contour. The on ROSAT observations alone in Reiprich&Böhringer (2002) critical curve shows the caustic (blue dashed curve) that de- withinthe15%levelasshowninFig.A.1inZhangetal.(2011). fines member galaxies as those in it. Galaxies with their pro- This15%differenceisaresultofintroducingthecorrectionsfor jected distances below or above R = 0.8958 Mpc are shown as pointsourcesandsubstructuresinZhangetal.(2011). red dots or black diamonds, respectively. The literature values Thevalueinthisworkisacool-corecorrectedmeasurement included in the study (highlighted as green diamonds) appear (L =(1.17±0.10)×1044ergs−1),asdefinedinSect.2.2.2 bol,500 as a box shape (a constant velocity dispersion approximately in Zhangetal. (2011), which is thus much lower than the total along the radial distance) in the diagram, explaining the under- X-ray luminosity. With the cool-core corrected measurements estimation of the velocity dispersion in Zhangetal. (2011) for we can suppress the scatter from the cool core, which allows the cluster S1101. The increased sample of cluster members us to focus on the scatter due to other facts in studying the in this work facilitates the discovery of the “trumpet shaped” L −σscalingrelation. bol caustic expected for a relaxed galaxy cluster. The mean val- As detailed in Sect. 2.2.1 in Zhangetal. (2011), the clus- ues of the caustic mass, Mcaustic = (1.32±0.93) × 1014 M , 200 (cid:12) ter radius r500 was determined from the X-ray gas mass profile andthemassfromthevelocitydispersionbasedonthescaling, (cid:16) (cid:17) throughthegasmassversustotalmassscalingrelationunderthe M200 = 1.92+−00..5422 × 1014 M(cid:12),(seealsoTable2orlowerpanel assumption of spherical symmetry. Prattetal. (2009) showed a ofFig.4)agreewellwithinthecalculatederrors.Nevertheless, tight scaling between gas mass and total mass for a sample of A24,page7of17 A&A597,A24(2017) 2 1 ] 1 ¡ s m k 0 £ 3 0 1 [ v ¡1 ¡2 4 0:5 1:0 1:5 2:0 2:5 ] ¯ M 3 £ 4 1 0 1 2 [ ) r < 1 ( M 0 0 0:5 1:0 1:5 2:0 2:5 r [Mpc] Fig.4.Upperpanel:diagramofrelativeline-of-sightvelocityvs.projectedclustercentricdistanceofthecandidatemembergalaxiesinS1101. Greyshadowshowsthe f (r,v)contours.Thethickgreycurvehighlightstheequal-densitycurveof f (r,v)=κ.Redcirclesandblackdiamonds q q indicategalaxieswithinandbeyondr=0.896Mpc(usedforconstrainingκ),respectively.Thebluedashedcurvereferstotheestimatedcausticof thecluster,henceallgalaxieswiththeirvelocitiesbeyondareexcludedfromthemembersampleinthismethod.Greenopendiamondshighlight clustermemberspreviouslyknownintheliterature.Lowerpanel:massprofileofS1101.Themassprofilefromthecausticmethod(seeSect.3.5) isshownasabluethickcurve,wherethebluedashedcurvesshowthecorresponding1σerrorestimate.Thegreydashedanddottedlinestracethe measuredpositionsofrcausticandMcausticfor∆={500,200},respectively,accordingtothecausticmassdistribution.Forcomparison,weoverplot ∆ ∆ thedynamicalmassM derivedfromthevelocitydispersionaccordingtoMunarietal.(2013)aslargeblackdot,theX-raymassestimatesM 200 500 (Zhangetal.2011)and M(cid:5) (Reiprich&Böhringer2002)asblackXandopendiamond,respectively,andtheSZmassproxyasadashedline 200 withitslowererrorintervalasdottedlinesinmagenta.ValuesofallmassproxiesarealsogiveninTable2. 41groupsandclustersasfollows: For comparison in Fig. 4, we also include M(cid:5) (see also 200 Table 2) with an open diamond symbol, as X-ray mass es- (cid:32) (cid:33) (cid:32) (cid:33) E(z)23ln Mgas,500 =−2.37+0.21ln M500 · (11) timate under the assumptions of spherical symmetry and hy- M 2×1014 M drostatic equilibrium, derived by Reiprich&Böhringer (2002) 500 (cid:12) from ROSAT pointed observations. It is not clear that the WeinferthetotalmassprofileofS1101, M(2r ),butreliesonhighmem- 200 the v − r plot (Fig. 4) indicates an improved completeness of ber statistics in order to reach high precision (200 or more; see theconfirmedclusterpopulationandhenceareducedbiasinσ Serraetal.2011).ThememberstatisticsofS1101inthisstudyis A24,page10of17

Probing the dynamical and X-ray mass proxies of the cluster of galaxies Abell S1101

Similar Probing the dynamical and X-ray mass proxies of the cluster of galaxies Abell S1101