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

17 Pages·2016·1.57 MB·English

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:[email protected]
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
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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 physi-
cal 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(<r),fromthemea- Reiprich&Böhringer (2002) mass overestimates the true mass
suredgasmassprofile, Mgas(<r),tofindtheradius,r500,which since only a single beta model was fitted to the surface bright-
fulfils ness profile. If the profile actually steepens at large radii then
this effect may roughly compensate the isothermal assump-
4π
M500 = 3 500ρc(z)r5300. (12) tion. The X-ray measurements discussed above are also listed
in Table 2. Additionally we plot these radii and masses in the
The resulting cluster radius is r = (0.84±0.02)Mpc, within lowerpanelofFig.4forcomparison.Whenconsideringatleast
500
whichthegasmassisM =(1.90±0.13)×1013 M andthe 10% scatter in the gas mass versus total mass relation (e.g.
gas,500 (cid:12)
totalclustermassisM500 =(1.87±0.10)×1014 M(cid:12).Theerrors Okabeetal. 2010), the mass, M500, from Zhangetal. (2011)
ofr andM areonlybasedontheerrorofM whichdo agrees rather well with the virial mass. The mass, M(cid:5) , from
500 500 gas,500 200
notincludetheintrinsicscatterofthescalingrelation. Reiprich&Böhringer(2002)basedonanisothermalgasmodel
A24,page8of17
A.Rabitzetal.:ProbingthedynamicalandX-raymassproxiesofAbellS1101
slightly overestimates the mass, but still agrees with the virial ¡42:2 0:20
estimateM withintheuncertainties(Table2).
200
0:18
5. SouthPoleTelescopedetectionofS1101 ¡42:4 0:16
Modernsurveyswithmillimeterorsubmillimetertelescopesare
0:14
able to measure tiny deviations in the cosmic microwave back-
g] t
gC(IrCoomuMnp)dtoo(nCfMsgcaaBlta)te.xrWyinhgceluwnshtpeihrleso,topanansssfiernffogmecbttyhketnhCoewMinnBtraauscnlduthesertegroSZminevedeffiruesmec-t dec[de ¡42:6 0:12 redshif
(Sunyaev&Zel’dovich1972),arelativetemperaturedifference 0:10
withrespecttothemeanCMBtemperatureisexpected.Thisef- ¡42:8
0:08
fecthasastrongcorrelationwiththemassoftheICMandputs
no redshift dependent luminosity constraints on the observabil-
0:06
ity,asforexampleinX-rays.Theoretically,SZeffectbasedob-
¡43:0
servations are able to detect a mass-limited sample of galaxy
0:04
clusters. 348:0 348:5 349:0
The South Pole Telescope (SPT; Carlstrometal. 2011) is ra[deg]
a 10 m telescope in Antarctica that observes the southern sky
Fig.5.Dressler-ShectmanplotofourspectroscopicsampleS0.Symbol
in three bands centred at 95, 150, and 220 GHz. We found sizescaleswithexp(δ2)aboveathresholdofδ = 3,belowthatvalue
S1101 in their public catalogue of the 2500 deg2 data (detailed galaxies are shown asisimple dots, and the sami ple S2 is emphasized
in Bleemetal.2015).ItislistedasSPT-CLJ2313-4243witha by larger green dots. Filled triangles and the filled star symbolize the
massderivedfromtheSZdetectionsignificanceusingthescal- central regions of galaxy groups and one galaxy cluster found in the
ing relation, MSZ = (4.06±0.92) × 1014 M , which is much vicinity of our survey field, as listed in the NED. The colour of each
500 (cid:12)
higherthanthecausticaswellasX-raymasses.Thescalingrela- symbolcorrespondstotheredshiftoftherespectivesource.
tionbetweentheSZdetectionsignificanceandtotalmassisnot
particularlytightforderivingarobustmassestimate.Indeed,the
provided MSZ forS1101ismuchlargerthanthecausticandthe These steps follow the same method we applied when se-
X-raymasse50s0,stillBleemetal.(2015)considerthatmassesde- lecting member galaxies for the cluster S1101 (compare
rived for low redshift clusters are possibly biased low. We list Sect.3.3).
themassmeasurementinTable2andplotteditasadashedma-
gentalineincomparisonwiththecausticmassprofileofS1101 Wenotethatbyusingthefixedgappermethodwiththetypical
inFig.4. gapof1000kms−1,thewholesampleS1isregardedasagroup
or cluster. Referring to Fig. 6, in addition to the objects within
thebluedottedlines(thefinalclippingforsampleS2)theover-
6. Discussiononbackgroundstructure densityof7galaxiescentredatz∼0.105wouldcontributetothe
memberpopulationaswell.Thefixedgapmay,however,maybe
As mentioned in Sect. 3.1, our spectroscopic dataset displays
toolargeforsuchlowmasssystems.Theadditionaloverdensity
an overdensity of background galaxies at approximately twice
mayindicatesomestructurethatmaybeconnectedwith,butnot
the cluster redshift (see Fig. 2). We thus examined the spectro-
directly belong, to S2. It is still possible that both systems are
scopicredshiftcataloguecomprising191galaxiesat0<z<0.2
interactinggravitationally,butthatisnotpartofthisdiscussion.
(from now on S0), which encloses cluster members and possi-
We derive z = 0.09974 ± 0.00017 and σ =
blebackgroundstructures.Inordertodetectsubstructureswithin (cid:16) (cid:17) S2 S2
195+49 kms−1 for the S2 sample. Following Munarietal.
thisbroadredshiftrange,weappliedtheDStest(asdescribedin −39 (cid:16) (cid:17)
Sect.3.4)withNloc =10,tothiscatalogue. (2013), we obtained a mass of M200 = 0.93+−10..0409 ×1013 M(cid:12),
InFig.5,weshowtheskypositionsofthesegalaxies,where whichindicatesthatS2isagalaxygroup,despiteitshighnum-
theirsymbolsizesscalewithexp(δ2i).Therearetwoclumpsthat berofmembergalaxies.
havehighprobabilitiesofbeingsubstructures.Ashighlightedby
A query in the NED for group or cluster counterparts re-
the colour-coded redshift information, the purple circles repre-
sulted in one cluster and several groups of galaxies near the
sentthedensecoreofgalaxyclusterS1101,whilegreencircles
cluster S1101. The cluster is visualized as a yellow star, while
indicate a potential background structure at 0.09 < z < 0.11.
the groups are shown as filled triangles in Fig. 5. The galaxy
Wemadeanattempttoassignmembershipofthegalaxiestothe
group that coincides best with our findings is LCLG −42230
tentativebackgroundstructureusingthefollowingprocedure:
fromthe“LasCampanasLooseGroup”catalogueandhasapub-
1) Weselectedthegalaxieswiththehighestδ atlargerredshift lished spectroscopic redshift of 0.0991 (Tuckeretal. 2000). In
i
thantheclusterS1101(comparecolour-codinginFig.5)and theLasCampanasRedshiftSurvey,theredshiftwasonlycalcu-
calculatedthemeanredshift,z,ofthose7galaxies. latedfrom6galaxies,comparedto27galaxiesforthiswork.We
2) Withagapclippingof|cz−cz | ≤ 4000kms−1 aroundz,a measuredaskydistanceof∼3.69(cid:48) betweentheS2meancoordi-
S0
firstoutlier-rejectedsamplecalledS1wasderived. natesandthepositionintheLCLGcatalogue,correspondingtoa
3) Application of the biweight estimators combined with the distanceof∼406kpcattheredshiftofthegroup.Thisdistanceis
|cz − cz | ≤ 3σ clipping in iterative manner resulted in comparabletothevirialradiusofS2.The27galaxiesserendipi-
S1 S1
thefinalsampleof27galaxiesforthisbackgroundstructure, touslyfoundinourdatamaywellbelongtoLCLG−42230.
calledtheS2sample. The scaling relation in Fig. 7 yields an X-ray luminosity of
4) FinalredshiftandvelocitydispersionoftheS2samplewere ∼4×1041 ergs−1 forthisgroupfromitsmeasuredσ.Thiscor-
computedusingthebiweightestimatorsoflocationandscale. respondstoafluxthatismorethanthreemagnitudeslowerthan
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10
8
y
c
n
e
u 6
q
e
r
f
4
2
0
0:095 0:100 0:105 0:110 0:115
redshift
Fig.6.RedshifthistogramofthesampleS1aroundz∼0.1.Thedotted
blue vertical lines refer to the borders of the final clipping, while the
actual members of the sample S2 are shown as a dark shaded region.
The redshift of galaxy group LCLG −42230 is indicated by a black Fig.7.Lbcooclc−σdiagramoftheHIFLUGCSclusters,inwhichthebest
fitisforthose56clusterswithmorethan45spectroscopicmembersper
and red vertical line, based on our sample S2 and previous work of
cluster. The orange circle and red box show the original (Zhangetal.
Tuckeretal.(2000),respectively.ThedefinitionofS1andS2aregiven
2011) and the revised values from this work, respectively, for S1101.
inSect.6;thecorrespondingdataarelistedinAppendixA.
Clusters with less than 45 spectroscopic members are shown as grey
circles.
that of S1101. It can therefore not cause any significant bias in
theX-raymeasurementofS1101.
with respect to the previous study of Zhangetal. (2011). Us-
ingtheclustervelocitydispersion,σ,weupdatedthepositionof
S1101intheL −σdiagram(Fig.7)withrespecttotheworkof
7. Conclusions bol
Zhangetal.(2011).WeconfirmedthehintinZhangetal.(2011)
We performed multi-object spectroscopic follow-up observa- based on the simulations sample that the severe deviation of
tions of the galaxies in the S1101 field in order to increase the S1101fromtheindicatedscalingrelationthereinismostlydueto
memberstatisticsforthedynamicalstudyofthisfield.Thecom- thevelocitydispersionmeasurementwithlowmemberstatistics.
bined sample of our survey and the redshifts from the NED Thisresultaddsconfidencefortheinterpretationasabiasdueto
yield58or42clustermembergalaxies,usingthememberiden- a small number of member galaxies. Given the ongoing efforts
tification method of Beersetal. (1990) or the caustic method, for large-scale cluster mass calibration with ∼20 members in a
respectively. cluster,forexample,SPIDERS(SPectroscopicIDentificationof
ERositaSources)and4MOST(4-mMulti-ObjectSpectroscopic
The number of 47 confirmed (from our VIMOS spectra
Telescope)fortheeROSITAclusters(e.g. Merlonietal.2012),
only) of 392 candidate cluster members, which corresponds to
(∼12%),mightappearrelativelylow.Consideringgalaxieswith itisusefultodetermineacorrectionfactorbasedonourwhole
magnitudes R < 18 mag the rate between confirmed and ob- sampleinZhangetal.(2011).Aspectroscopicfollow-upofthe
servedsourcesstillis24versus69,whichcorrespondsto∼35%. remainingoutlierclustersinoursampleinthenearfuturewould
helptorealizethisgoal.
Observational restrictions demanded to also include fainter tar-
gets but increased the influence of photometric uncertainties. (cid:16) The m(cid:17)ass estimate from the velocity dispersion, M200 =
Despite unfavourable conditions during pre-imaging a sound 1.92+−00..5422 × 1014 M(cid:12), agrees with the available X-ray mass
sample of member galaxies could be established by taking ad- proxies (Zhangetal. 2011; Reiprich&Böhringer 2002) within
vantage of the survey capabilities offered by VIMOS. Large the uncertainties. The SZ mass proxy (Bleemetal. 2015) is
MOS capabilities will however not necessarily be available for muchhigherthantheremainingmassestimates,namelythedy-
futurelarge-scaleautomizedsurveys,underlyingtheimportance namical,X-ray,andcaustic-basedmasses(compareTable2and
ofasuitablepreselection. Fig.4).Thismightbeduetothelargescatterinthescalingre-
The 2D dynamical substructure tests indicate no ongoing lationbetweentheSZdetectionsignificanceandtotalmassthey
mergingactivitiesinS1101;thisfindingisalsosupportedbythe used.Thecausticmethodmakesnoassumptiononthedynami-
largepercentageofpassivegalaxiesresidingintheclustercentre calstateofthecluster,andtracestheenclosedclustermassasa
andtheabsenceofsevereinhomogeneitiesintheavailableX-ray function of radius, solely by positions and redshifts of member
data. galaxies. The caustic mass profile might slightly underestimate
The increased number of member galaxies with spectro- theclustermassgivenarathersmallsampleofclustergalaxies
scopicredshiftsandtherelaxedclusterstructureindicatedinour distributeduptoalargeprojecteddistanceof2.5Mpc.Wethere-
2Dtestensurerobustconstraintsonthevelocitydispersionand forenotethatthecausticmethodisinprincipleabletotracethe
virial mass estimates. The recovery of the “trumpet shape” in clustermassouttolargeradii(>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
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