IV. Mass-temperature relation of the bright cluster sample

17 Pages·2016·0.73 MB·English

A&A592,A4(2016) Astronomy
DOI:10.1051/0004-6361/201526883 &
(cid:2)c ESO2016 Astrophysics
Special feature
TheXXLSurvey:Firstresults
The XXL Survey
(cid:2),(cid:2)(cid:2)
IV. Mass-temperature relation of the bright cluster sample
M.Lieu1,G.P.Smith1,P.A.Giles2,F.Ziparo1,B.J.Maughan2,J.Démoclès1,F.Pacaud3,M.Pierre4,C.Adami5,
Y.M.Bahé6,7,N.Clerc8,L.Chiappetti10,D.Eckert9,10,S.Ettori11,12,S.Lavoie13,J.P.LeFevre14,I.G.McCarthy15,
M.Kilbinger4,T.J.Ponman1,T.Sadibekova4,andJ.P.Willis7
1 SchoolofPhysicsandAstronomy,UniversityofBirmingham,Edgbaston,Birmingham,B152TT,UK
e-mail:[email protected]
2 H.H.WillsPhysicsLaboratory,UniversityofBristol,TyndallAvenue,Bristol,BS81TL,UK
3 ArgelanderInstitutfürAstronomie,UniversitätBonn,53121Bonn,Germany
4 Serviced’AstrophysiqueAIM,CEASaclay,91191Gif-sur-Yvette,France
5 UniversitéAixMarseille,CNRS,LAM(Laboratoired’AstrophysiquedeMarseille)UMR7326,13388Marseille,France
6 Max-Planck-InstitutfürAstrophysik,Karl-SchwarzschildStr.1,85748Garching,Germany
7 InstituteofAstronomy,UniversityofCambridge,MadingleyRoad,CambridgeCB30HA,UK
8 MaxPlanckInstitutfürExtraterrestrischePhysik,Postfach1312,85741GarchingbeiMünchen,Germany
9 DepartmentofAstronomy,UniversityofGeneva,ch.d’Ecogia16,1290Versoix,Switzerland
10 INAF–IASF-Milano,viaE.Bassini15,20133Milano,Italy
11 INAF–OsservatorioAstronomicodiBologna,viaRanzani1,40127Bologna,Italy
12 INFN,SezionediBologna,vialeBertiPichat6\2,40127Bologna,Italy
13 DepartmentofPhysicsandAstronomy,UniversityofVictoria,3800FinnertyRoad,Victoria,BC,V8P1A1,Canada
14 SEDICEASaclay,France
15 AstrophysicsResearchInstitute,LiverpoolJohnMooresUniversity,IC2,146BrownlowHill,LiverpoolL35RF,UK
Received3July2015/Accepted20October2015
ABSTRACT
Context. The XXL Survey is the largest survey carried out by XMM-Newton. Covering an area of 50 deg2, the survey con-
tains ∼450 galaxy clusters out to a redshift ∼2 and to an X-ray flux limit of ∼5×10−15 ergs−1cm−2. This paper is part of the
firstreleaseofXXLresultsfocussedonthebrightclustersample.
Aims.Weinvestigatethescalingrelationbetweenweak-lensingmassandX-raytemperatureforthebrightestclustersinXXL.The
scalingrelationdiscussedinthisarticleisusedtoestimatethemassofall100clustersinXXL-100-GC.
Methods.Basedonasubsampleof38objectsthatliewithintheintersectionofthenorthernXXLfieldandthepubliclyavailable
CFHTLenSshearcatalog,wederivetheweak-lensingmassofeachsystemwithcarefulconsiderationsofthesystematics.Theclusters
lieat0.1 < z< 0.6andspanatemperaturerangeofT (cid:4) 1−5keV.Wecombineoursamplewithanadditional58clustersfromthe
literature,increasingtherangetoT (cid:4)1−10keV.Todate,thisisthelargestsampleofclusterswithweak-lensingmassmeasurements
thathasbeenusedtostudythemass-temperaturerelation.
Results.The mass-temperature relation fit (M ∝ Tb) to the XXL clusters returns a slope b = 1.78+0.37 and intrinsic scatter
σlnM|T (cid:4)0.53;thescatterisdominatedbydisturbedclusters.Thefittothecombinedsampleof96cluste−r0s.3i2sintensionwithself-
similarity,b=1.67±0.12andσlnM|T (cid:4)0.41.
Conclusions. Overall our results demonstrate the feasibility of ground-based weak-lensing scaling relation studies down to cool
systemsof∼1keVtemperatureandhighlightthatthecurrentdataandsamplesarealimittoourstatisticalprecision.Assuchweare
unabletodeterminewhetherthevalidityofhydrostaticequilibriumisafunctionofhalomass.Anenlargedsampleofcoolsystems,
deeperweak-lensingdata,androbustmodellingoftheselectionfunctionwillhelptoexploretheseissuesfurther.
Keywords.gravitationallensing:weak–X-rays:galaxies:clusters–galaxies:groups:general–galaxies:clusters:general
1. Introduction
(cid:3) Based on observations obtained with XMM-Newton, an ESA sci-
Analyticalandnumericalcalculationsbothpredictthatthetem-
ence mission with instruments and contributions directly funded by
peratureoftheX-rayemittingatmospheresofgalaxygroupsand
ESA Member States and NASA. Based on observations made with
ofclustersscaleswiththe massoftheirhostdarkmatterhalos,
ESOTelescopesattheLaSillaParanalObservatoryunderprogramme
089.A-0666andLP191.A-0268. with M ∝ T3/2 (Kaiser1986;Evrardetal.2002;Borganietal.
(cid:3)(cid:3) TheMastercatalogueisavailableattheCDSviaanonymousftpto 2004).Testingthisso-calledself-similarpredictionisoffunda-
cdsarc.u-strasbg.fr(130.79.128.5)orvia mentalimportancetoabroadrangeofastrophysicalandcosmo-
http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/592/A2 logical problems, including constraining any non-gravitational
ArticlepublishedbyEDPSciences A4,page1of17
A&A592,A4(2016)
physics that affects the gas, and exploring galaxy clusters as statistical uncertainties, in Sect. 4. We also compare our re-
probesofcosmologicalparameters. sultswiththeliteratureinSect.4,andsummariseourresultsin
To date, any studies of the mass-temperature relation have Sect.5.WeassumeaWMAP9(Hinshawetal.2013)cosmology
employed X-ray observations to measure both the temperature of H0 = 70kms−1Mpc−1,ΩM = 0.28,andΩΛ = 0.72.Allsta-
and the mass of galaxy groups and clusters. Assuming hydro- tisticalerrorsarereportedto68%significanceandupperlimits
static equilibrium, the self-similar predicted slope value of 1.5 arestatedat3σconfidence.
can be derived from the virial theorem. Observational rela-
tions, however,generallysteepen from close to the self-similar
for hot systems to a slope of ∼1.6–1.7 when cooler systems 2. Sample,dataandanalysis
(T <∼ 3 keV) are included (see Böhringer et al. 2012; Giodini
2.1.Surveyandsampledefinition
etal.2013,forrecentreviews).Theseresultsaresubjecttosev-
eralproblems,mostprominentlythatthemassmeasurementsare The XXL Survey is described in detail by Pierre et al. (2016,
based on the assumption that the intracluster gas is in hydro- Paper I, hereafter). This ∼50 deg2 XMM-Newton survey has a
static equilibriumandalso thatthe samedata areusedforboth sensitivity of ∼5×10−15 ergs−1 cm−2 in the [0.5–2] keV band
temperatureandmassmeasurements,likelyintroducingasubtle thatprovidesawell-definedgalaxyclustersampleforprecision
covarianceintotheanalysis. cosmology. The survey is an extension of the 11 deg2 XMM-
Independentmeasurementsofmassandtemperature,andre- LSSsurvey(Pierreetal.2004)andconsistsoftwo 25deg2 ar-
liance on fewer assumptions, help to alleviate these questions. eas. The XXL-100-GC1 sample is a flux-limited sample based
Gravitational lensing mass measurements are useful in this re- on 100 clusters ranked brightest in flux. It is described in de-
gard, and have been shown to recover the ensemble mass of tail by Pacaud et al. (2016, Paper II, hereafter), some of
clusterstoreasonablygoodaccuracy(Becker&Kravtsov2011; theseclustershavepreviouslybeendescribedintheXMM-LSS
Bahéetal.2012),despiteconcernsthatindividualclustermass
and XMM-BCS studies (Clerc et al. 2014; Šuhada et al.
measurements may be affected by halo triaxiality and projec- 2012). We note that five systems (XLSSC113, 114, 115,
tioneffects(e.g.Corless&King2007;Meneghettietal.2010). 550, and 551) were observed in bad pointings that are con-
Lensingbasedstudiesofthemass-temperaturerelationhaveso
taminated by flaring. Subsequently, the sample was supple-
farobtainedslopesthatareconsistentwiththeself-similarpre- mented with five additional clusters: XLSSC091, 506, 516,
diction, albeit with large statistical uncertainties (Smith et al. 545 and 548. All systems within the XXL-100-GC sample
2005;Bardeauetal.2007;Hoekstra2007;Okabeetal.2010;Jee
are characterised as either C1 or C2 (Clerc et al. 2014). The
etal.2011;Mahdavietal.2013).Oneofthelimitationsofthese
C1 objects have a high likelihood of detection and exten-
studieshasbeenthattheyconcentrateonrelativelyhotclusters,
sion. The probability of contamination by spurious detection
T >∼4keV.
or point sources for these systems is low (<3%), whereas the
BuildingontheLeauthaudetal.(2010)weak-lensingstudy C2 objectshave∼50%contamination.TheXXL-100-GCsam-
ofthemass-luminosityrelationofgroupsintheCOSMOSsur- ple is estimated to be more than 99% complete down to ∼3×
vey, Kettula et al. (2013) recently pushed lensing-based stud- 10−14ergs−1cm−2andtohavespectroscopicredshiftsof0.05≤
ies of the mass-temperature relation into the group regime, z≤1.07(PaperII).
T (cid:4) 1−3 keV. Combining ten groups with complementary
The mass-temperature relation presented in this paper is
measurements of massive clusters from the literature, they ob-
based on weak-lensing mass measurements using the Canada-
tainedarelationspanningT (cid:4) 1−10keV,withaslopeingood
France-Hawaii Telescope Lensing Survey (CFHTLenS) shear
agreement with the self-similar prediction. This suggests that catalogue2(Heymansetal.2012;Erbenetal.2013).CFHTLenS
the assumption of hydrostatic equilibriummay be less valid in spans a total survey area of ∼154 deg2 that has considerable
coolersystemsthanhottersystemssincethediscrepancyisonly
overlap with the northern XXL field (Fig. 1). Their shear cat-
seen at the coolend of the M –T relation.However,Connor
HSE aloguecomprisesgalaxyshapemeasurementsforasourceden-
etal.(2014)obtainedaslopesteeperthanthehydrostaticresults sity of 17 galaxiesper arcmin2, as well as u∗g(cid:8)r(cid:8)i(cid:8)z(cid:8)-bandpho-
using a sample of 15 poor clusters. Their study was limited to
tometry and photometric redshifts for the same galaxies. The
clustercoreswithinr (i.e.theradiusatwhichthemeanden-
2500 median photometricredshift of the galaxies in the catalogue is
sity of the cluster is 2500 times the critical density of the uni- z =0.75(Hildebrandtetal.2012).
median
verseattheclusterredshift),incontrasttopreviousresults(e.g.
Fifty-twoofthe 100XXL-100-GCsourceslie inthenorth-
Kettulaetal.2013)thatwerederivedwithinr ,indicatingthat
500 ern XXL field, of which 45 lie within the CFHTLenS survey
themasstemperaturerelationmaydependontheclustercentric
area (Fig.1). A few ofthese 45 clusterslie at redshiftsbeyond
radiuswithinwhichthemassismeasured.
themedianredshiftoftheCFHTLenSshearcatalogue,thussig-
We present the mass calibration of the XXL bright cluster
nificantlyreducingthenumberdensityofgalaxiesbehindthese
sample (XXL-100-GC)based on a new mass-temperaturerela-
distant clusters. We therefore limit our analysis to clusters at
tion thatwe constrainusingthe largestsample used to datefor
z < 0.6, which corresponds to imposing a lower limit on the
such studies: 96 groups and clusters spanning X-ray tempera- sourcedensityof∼4arcmin−2(Fig.3).Thisgivesatotalsample
tures of T (cid:4) 1−10 keV and a redshift range of z (cid:4) 0.1−0.6.
of38galaxyclustersforwhichwehavearedshift,faintgalaxy
Thirty-eight of these systems come from XXL-100-GC itself.
shapemeasurements,andanX-raytemperature(Table1).All38
WecombinetheXMM-Newtonsurveydataandthehigh-fidelity
of these galaxyclusters are classified as C1 with the exception
weak-shearcatalogfromtheCFHTLenSsurveytoobtaininde-
ofXLSSC114,whichisaC2classsystem.
pendenttemperatureandhalomassmeasurements,respectively.
Wedescribethesample,data,andanalysis,includingdetailson 1 XXL-100-GCdataareavailableincomputer readableformviathe
the weak gravitational lensing analyses, in Sect. 2. In Sect. 3 XXL Master Catalogue browser http://cosmosdb.iasf-milano.
we present our main results, the mass-temperature relation of inaf.it/XXL and via the XMM XXL Database http://xmm-lss.
XXL-100-GC. We discuss a range of systematic uncertainties in2p3.fr
in our analysis, confirming that they are sub-dominant to the 2 www.cfhtlens.org
A4,page2of17
M.Lieuetal.:TheXXLSurvey.IV.
4
−
6
−
g)
e
d
δ( 8
−
0
1
−
2
1
−
40 38 36 34 32 30
α(deg)
Fig.1.OverlapofXXL-100-GCwiththeCFHTLenSW1field.TheboxesareindividualpointingsinCFTHTwithXXL-Northfieldclusters(filled
points).TheshadedboxesarepointingsthatfailtheCFHTLenSweak-lensingfieldselectioncriteria(seeSect.4.1).
2.2.X-raytemperatures
The temperature of the intracluster medium of each cluster is
measuredanddescribedindetailbyGilesetal. (2016,PaperIII,
hereafter).Herewe summarisethe keypointspertainingto our
analysis.
The spectra are extracted using a circular aperture of ra-
dius 0.3 Mpc centred on the X-ray positions, with a minimum
of5countsbin−1. Pointsourcesare identifiedusingSExtractor
and excluded from the analysis; the images are visually in-
spectedforanythatmighthavebeenmissed.Radialprofilesof
eachsourcewereextractedwithinthe0.5−2keVbandwiththe
backgroundsubtracted.Thedetectionradiuswasdefinedasthe
radius at which the source is detected to 0.5σ above the back-
ground. Background regions were taken as annuli centred on
theobservationcentrewithawidthequaltothespectralextrac-
Fig.2. Redshift versus X-ray temperature T for the 38 clusters
tionregionandtheregionwithinthedetectionradiusexcluded. 300kpc
from XXL-100-GC that are located within the CFHTLenS shear cat-
Wherethiswasnotpossible,thebackgroundwasmeasuredfrom
aloguefootprint.
anannuluscentredontheclusterwithinnerradiussettothede-
tectionradiusandouterradiusas400arcsec.
The X-ray temperaturesspan 1.1keV ≤ T < 5.5keV methodofSantosetal.(2008).Wesummariseafewkeypoints
300kpc
(Fig. 2) and are non-core excised owing to the limited angu- oftheanalysishere.TheX-raysurfacebrightnessprofileisex-
lar resolutionof XMM-Newton. The temperaturesare extracted tracted within concentric annuli centred on the X-ray peak, it
within a fixed physical radius of 0.3Mpc such that they are isbothbackground-subtractedandexposurecorrectedandthen
straightforward to calculate from shallow survey data without re-binnedto obtain a minimumsignal-to-noiseratio (S/N) of 3
needing to estimate the size of the cluster. This is the largest in each bin. The profiles are fit using three 3D density pro-
radiuswithin which it is possible to measure a temperaturefor file modelswhichare projectedon the skyand convolvedwith
thewholeXXL-100-GCsample.Tocheckthesensitivityofour the XMM-Newton point spread function (PSF). Depending on
main results to this choice of aperture, we also re-fit the mass- thenumberofbinsinthesurfacebrightnessprofile(n ),amore
bin
temperature relation discussed in the results section using the orlessflexibleβ-modelisfittothedata:β=2/3isassumedfor
temperaturesthatareavailableinlargeraperturesupto0.5Mpc, profiles with n < 3; β is a free parameter for 3 ≤ n ≤ 4;
bin bin
and find that the systematic differences between the respective a double β model is used for n > 4. The surface brightness
bin
fitparametersarenegligiblecomparedwiththestatisticalerrors concentrationparameter(CSB) isdefinedastheratioofthein-
onthefits. tegrated profile within 40 kpc to that within 400 kpc, CSB =
SB(<40kpc)/SB(<400kpc).Thecoolcorestatusisdefinedas
2.3.Coolcorestrength
– Non-coolcore:CSB<0.075.
The cool core strength of XXL-100-GC is estimated by – Weakcoolcore:0.075≤CSB≤0.155.
Démoclès et al. (in prep.) using the concentration parameter – Strongcoolcore:CSB>0.155.
A4,page3of17
A&A592,A4(2016)
Table1.Clusterpropertiesandmassestimates.
Name z T c M M r δr δr/r CSB S/N
300kpc 200 200,WL 500,WL 500,WL 500,WL
(keV) (1014h−701M(cid:9)) (1014h−701M(cid:9)) (Mpc) (10−2Mpc) (10−1) (10−2)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
XLSSC 006 0.429 4.8+0.5 2.7 5.3+6.0 3.4+3.7 0.9+0.3 10.1 1.1 8.0±1.0 3.4
−0.4 −2.3 −1.4 −0.2
XLSSC 011 0.054 2.5+0.5 3.4 1.6+2.0 1.1+1.3 0.7+0.2 0.4 0.1 12.7±0.9 3.6
−0.4 −1.1 −0.7 −0.2
XLSSC 022 0.293 2.1+0.1 3.4 0.5+0.9 0.4+0.5 0.5+0.2 4.5 1.0 34.6±2.6 1.5
−0.1 −0.4 −0.2 −0.1
XLSSC 025 0.265 2.5+0.2 3.1 1.7+1.6 1.1+1.0 0.7+0.2 0.0 0.0 27.9±2.7 2.3
−0.2 −1.3 −0.8 −0.2
XLSSC 027 0.295 2.7+0.4 2.9 3.3+3.9 2.1+2.4 0.8+0.2 8.1 1.0 4.7±2.5 3.5
−0.3 −2.1 −1.4 −0.2
XLSSC 041 0.142 1.9+0.1 3.4 1.0+0.9 0.7+0.6 0.6+0.1 1.3 0.2 29.9±2.5 3.1
−0.2 −0.7 −0.5 −0.2
XLSSC 054 0.054 2.0+0.2 3.5 1.1+1.6 0.7+1.1 0.6+0.2 0.5 0.1 11.1±1.3 2.7
−0.2 −0.7 −0.5 −0.2
XLSSC 055 0.232 3.0+0.3 2.8 8.1+7.6 5.2+4.7 1.1+0.3 4.2 0.4 11.3±1.9 3.7
−0.3 −3.1 −2.0 −0.2
XLSSC 056 0.348 3.2+0.5 2.8 4.5+2.7 2.8+1.7 0.9+0.2 6.4 0.7 5.6±1.7 3.4
−0.3 −2.4 −1.5 −0.2
XLSSC 057 0.153 2.2+0.3 3.7 ≤0.9 ≤0.6 ≤0.6 3.0 0.7 17.1±1.8 2.5
−0.1
XLSSC 060 0.139 4.8+0.2 3.2 2.1+1.4 1.4+0.9 0.8+0.1 13.5 1.8 2.3±0.1 4.4
−0.2 −1.5 −1.0 −0.3
XLSSC 061 0.259 2.1+0.5 2.9 3.8+0.9 2.4+0.5 0.9+0.1 2.9 0.3 9.9±3.3 3.8
−0.3 −2.1 −1.3 −0.2
XLSSC 083 0.430 4.5+1.1 2.7 4.0+3.6 2.5+2.2 0.8+0.2 4.1 0.5 7.0±2.4 3.2
−0.7 −2.8 −1.7 −0.3
XLSSC 084 0.430 4.5+1.6 2.7 4.3+3.2 2.7+1.9 0.9+0.2 10.9 1.3 3.0±0.7 2.8
−1.3 −3.2 −2.0 −0.3
XLSSC 085 0.428 4.8+2.0 3.2 ≤2.6 ≤1.21 ≤0.7 0.0 0.0 10.6±4.3 1.7
−1.0
XLSSC 087 0.141 1.6+0.1 3.6 0.5+0.4 0.3+0.3 0.5+0.1 0.9 0.2 41.5±2.9 3.5
−0.1 −0.4 −0.2 −0.2
XLSSC 088 0.295 2.5+0.6 3.1 1.8+1.3 1.2+0.9 0.7+0.1 28.2 4.2 2.7±0.4 2.4
−0.4 −1.5 −0.9 −0.3
XLSSC 090 0.141 1.1+0.1 4.1 ≤0.6 ≤1.2 ≤0.7 0.9 0.3 41.7±4.2 2.4
−0.1
XLSSC 091 0.186 5.1+0.2 2.8 9.7+3.3 6.2+2.1 1.2+0.1 5.0 0.4 2.5±0.1 6.2
−0.2 −2.9 −1.8 −0.1
XLSSC 092 0.432 3.1+0.8 3.2 ≤2.2 ≤1.4 ≤0.7 26.3 7.9 6.9±1.7 2.6
−0.6
XLSSC 093 0.429 3.4+0.6 2.7 5.9+3.5 3.7+2.1 0.9+0.2 2.9 0.3 5.4±1.6 3.8
−0.4 −3.0 −1.8 −0.2
XLSSC 095 0.138 0.9+0.1 3.6 ≤1.0 ≤0.6 ≤0.6 0.0 0.0 40.3±14.9 2.5
−0.1
XLSSC 096 0.520 5.5+2.0 3.5 ≤1.4 ≤0.9 ≤0.6 5.0 1.7 7.3±2.5 1.1
−1.1
XLSSC 098 0.297 2.9+1.0 3.0 2.8+3.6 1.8+2.3 0.8+0.2 2.3 0.3 17.1±6.7 3.1
−0.6 −2.3 −1.5 −0.3
XLSSC 099 0.391 5.1+3.1 3.5 ≤2.2 ≤1.4 ≤0.7 1.9 0.6 6.6±1.8 1.8
−1.5
XLSSC 103 0.233 3.5+1.2 2.8 8.5+4.2 5.4+2.6 1.1+0.2 4.2 0.4 6.9±2.6 5.3
−0.8 −3.0 −1.8 −0.2
XLSSC 104 0.294 4.7+1.5 3.0 2.6+4.1 1.7+2.6 0.8+0.3 14.9 2.0 9.9±3.7 3.7
−1.0 −1.3 −0.9 −0.2
XLSSC 105 0.429 5.2+1.1 2.4 19.8+6.5 12.1+3.9 1.4+0.1 14.3 1.0 3.5±0.7 5.0
−0.8 −7.7 −4.6 −0.2
XLSSC 106 0.300 3.3+0.4 2.8 6.8+3.0 4.3+1.8 1.0+0.1 27.2 2.6 7.0±1.3 4.5
−0.3 −3.3 −2.1 −0.2
XLSSC 107 0.436 2.7+0.4 2.8 2.8+4.8 1.8+3.0 0.7+0.3 0.0 0.0 13.0±2.6 2.4
−0.3 −2.2 −1.4 −0.3
XLSSC 108 0.254 2.2+0.3 3.9 ≤0.9 ≤0.6 ≤0.5 4.0 1.3 14.0±2.5 1.7
−0.2
XLSSC 109 0.491 3.5+1.3 2.6 7.6+6.6 4.7+4.0 1.0+0.2 3.1 0.3 60.5±19.7 3.9
−0.8 −4.5 −2.8 −0.3
XLSSC 110 0.445 1.6+0.1 2.7 4.6+5.3 2.9+3.2 0.9+0.2 17.7 2.0 2.6±0.4 4.0
−0.1 −1.6 −1.0 −0.1
XLSSC 111 0.299 4.5+0.6 2.7 10.1+3.0 6.3+1.8 1.2+0.1 1.6 0.1 13.8±4.5 6.1
−0.5 −2.9 −1.8 −0.1
XLSSC 112 0.139 1.8+0.2 3.4 1.2+0.9 0.8+0.6 0.6+0.1 6.9 1.1 9.3±1.5 2.5
−0.2 −0.8 −0.5 −0.2
XLSSC 113 0.050 1.2+0.0 3.9 0.4+0.6 0.3+0.4 0.5+0.2 0.4 0.1 19.4±2.9 3.5
−0.1 −0.2 −0.2 −0.1
XLSSC 114 0.234 4.7+4.2 3.1 2.1+1.9 1.4+1.2 0.7+0.2 5.5 0.8 5.0±1.9 4.0
−1.9 −1.0 −0.6 −0.1
XLSSC 115 0.043 2.1+0.6 4.3 ≤0.6 ≤0.4 ≤0.5 2.5 0.8 6.9±2.3 3.5
−0.2
Notes.Column1istheclustercatalogueidnumber;Col.2istheclusterredshift;Col.3X-raytemperaturemeasuredwithinanapertureof300kpc;
Col.4istheconcentrationparametermeasuredwithinr ;Cols.5and6arefittedestimatesofweak-lensingmasscentredontheX-raycentroid
200,WL
andmeasuredwithinfittedr andr respectively.Upperlimitsonmassaregivenat3sigmaconfidence.Columns7and8aretheweak-
200,WL 500,WL
lensingr andtheoffsetbetweentheX-raycentroidandtheBCG;Col.9istheBCGoffsetasafractionofr ;Col.10istheCSBparameter
500,WL 500,WL
andCol.11isthesignal-to-noiseratioontheweak-lensingshear.PositionsoftheclusterX-raycentroidsarelistedinPaperII,Table1.
2.4.Weakgravitationallensing wherez isthepeakoftherespectivegalaxy’sP(z),zistheclus-
s
terredshift,δz (3σ)isthe99.7%lowerconfidenceintervalonz ,
s s
We use the full photometric redshift probability distribution, and the last term representsa velocity offsetof 3000kms−1 as
P(z),ofeachgalaxyintheCFHTLenSshearcataloguetoiden- a conservative allowance for the velocity width of the cluster
tifygalaxiesbehindourclustersample.Galaxiesareselectedas galaxydistributions.
backgroundgalaxiesiftheysatisfy The method outlined in Velander et al. (2014) and Miller
etal.(2013)isusedtocalibratethegravitationalshearmeasure-
z −δz (3σ)>z+0.01, (1) ments.Therawellipticityvalues(e ,e )undergotwocalibration
s s 1 2
A4,page4of17
M.Lieuetal.:TheXXLSurvey.IV.
Fig.3.Left:numberdensityofbackgroundgalaxiesbehindeachgalaxyclusterversusclusterredshift.Right:weak-lensingshearsignal-to-noise
ratioasafunctionofclusterredshift.
corrections,amulitiplicativecomponent(m)derivedfromsimu- wherethetangentialshear,e+(r),isthesignalthatcanbemod-
lations(Milleretal.2013)andanadditivecomponent(c)derived elledintermsofthetotalmatterdensityprofileofthelens.The
fromthedata(Heymansetal.2012).Theobservedellipticitycan cross shear e×(r) is orientated 45◦ with respect to the tangen-
bewrittenas tialcomponentandshouldbeconsistentwithzeroasacheckon
systematicerrors.
eobs =(1+m)eint+c+Δe (2) We extract the shear profile of each cluster within
a 0.15−3 Mpc annulus. The inner radial cut helps to amelio-
where eint is the intrinsic ellipticity and Δe is the noise on the
ratecentringuncertainties,andtheouterradialcutismotivated
measurement.
bynumericalsimulations(Becker&Kravtsov2011).Thecluster
Themultiplicativecomponentmisdependentonbothgalaxy centreistakenastheX-raycentroid.Forreference,themeanoff-
sizeandS/Nandgives,onaverage,a6%correction.Theaddi-
set between the X-ray centroidand the brightestcluster galaxy
tivecomponentcissimilarlydependentonthegalaxysize,and (BCG)is(cid:10)δr(cid:11)=64.7kpc.Ourresultsareunchangedifwecentre
the S/N determinedby Lensfit. For the CFHTLenS data(cid:10)c (cid:11) is
1 theshearprofilesontherespectiveBCGs(seeSect.4.1formore
consistentwithzeroandc issubtractedfrome foreachgalaxy.
2 2 details).
Themultiplicativecorrectionisappliedasanaverageensemble
The shear is binned in eight radial bins equally spaced in
ofeachbin.
log and with a lower limit of 50 galaxiesper radial bin. If this
A weighting is also applied that corrects for the geometry threshold is not met, the bin is combined with the next radial
ofthe lens-sourcesystem in theformofthe lensingkernelξ =
bin. The errors on the shear in each radial bin are estimated
DLS/DS, where DLS and DS are the angulardiameterdistances from103bootstrapresampleswithreplacementandincludesthe
betweenthelensandthesource,andbetweenthe observerand
largescalestructurecovariance(Schneideretal.1998):
the source, respectively.This is applied as a ratio between that (cid:4)
ofthecluster-galaxysystemandthatofthereferenceη=ξ/ξ . ldl
ref CLSS = P (l)J (lθ)J (lθ ) , (7)
Thereferenceistakenasthemodesourceredshiftofthesumof ij k 2 i 2 j 2π
allbackgroundgalaxyweightedP(z ),i.e.themodeof
s
whereP (l)istheweak-lensingpowerspectrumasafunctionof
k
(cid:2)Ngal angular multipole l and J2(lθ) is the second-orderBessel func-
n(zs)= wiPi(zs) (3) tionofthefirsttypeatradialbinsθi andθj.
i=1 ShearS/NiscalculatedfollowingOkabeetal.(2010)as
w20h1e3re,Ewqi.is(8th))eaCpFpHlieTdLteoncSailnibvreartseefvoarrtihaencliekweleihigohotd(Mofilthleermeteaal-. (S/N)2 =(cid:2)Nbin (cid:10)e+(rn)(cid:11)2· (8)
σ2 (r )
sured ellipticity and intrinsic shape noise. The calibrated shear n=1 e+ n
atadistancerfromtheclustercentrethereforetakestheform Foroursampletheweak-lensingS/Nrangesfrom1≤S/N ≤7.
N(cid:3)gal N(cid:3)gal Howeverweincludeallobjectsinthemass-temperaturerelation
wiηiγiint wiηi regardlessoftheS/Nvaluetoavoidimposingalow-shearselec-
(cid:10)γ(r)cal(cid:11) = i=1 i=1 · (4) tionontopoftheoriginalX-rayselection.
N(cid:3)galwη(1+m)N(cid:3)galwη2 We model the shear profile as a (Navarro et al. 1997,
i i i i i NFW hereafter) profile following the formalism set out by
i=1 i=1
Wright & Brainerd (2000). A Markov chain Monte Carlo
Intheweak-lensinglimittheshearcanbeestimatedastheaver- (MCMC) sampler with a Gaussian likelihood is used to fit the
agecomplexellipticityγ ≈ (cid:10)e(cid:11),wheree ≡ e1+ie2.Intermsof NFW model to the shear profile. The algorithm returns 5 ×
tangentialandcross-componentellipticity, 104 samples of the target distribution using a jump proposal
based on a Metropolis-Hastings algorithm with a mean accep-
e+ = −(cid:14)e−2iφ =−(e2−c2)sin(2φ)−e1cos(2φ) (5) tance rate of 0.57. The autocorrelation length is computed to
e× = −(cid:15)e−2iφ =e1sin(2φ)−(e2−c2),cos(2φ) (6) thincorrelatedsampleswithinthechainandincorporatesburn-in
A4,page5of17
A&A592,A4(2016)
Fig.4.Mass-temperaturerelationfor38clustersdrawnfromXXL-100-GCforwhichweak-shearinformationisavailablefromCFHTLenS.The
lineisthehighestposteriordensityfitandtheshadedregionisthecredibleregion.Systemswithupperlimitsonmassareindicatedbyarrowsand
plottedat3σconfidence.
of150samples.TheGelman-Rubincriterion(Gelman&Rubin 3. Results
1992)iscomputedforthreechainsto ensureconvergence.The
Apositivecorrelationbetweenourweak-lensingmassandX-ray
massofeachclusteristakenasthemodeoftheposteriorandthe
temperature measurements is evident (Fig. 4). In this section,
errorsaregivenas68%credibleregionsofthehighestposterior
wedefinethescalingrelationmodelthatwewillfittothedata,
densityasthisisthebestrepresentationoftheskewedGaussian
describe the regression analysis, and present the main results.
posteriors.
Wedeferconsiderationofpossiblesystematicuncertaintiesand
Giventhewiderangeofpossibleclustermass,auniformin
log(Jeffreys)prioris used to ensurescale invarianceP(M|I) = comparisonwiththeliteraturetoSect.4.
Mln(10116/1013) (1013 ≤ M200 ≤1016 M(cid:9)).Giventhegenerallylow-
shear S/N, we fix cluster concentrationto values from a mass- 3.1.XXLmass-temperaturerelation
concentrationrelationbasedonN-bodysimulations(Duffyetal.
Wemodelthemass-temperaturerelationasapowerlaw:
2008):
⎛ ⎞ (cid:15) (cid:16)
c200 =5.71(1+z)−0.47(cid:5)2×1M01220h0−1M(cid:9)(cid:6)−0.084· (9) log10⎜⎜⎜⎜⎝MM50(cid:9)0hE−7(01z)⎟⎟⎟⎟⎠=a+blog10 kTeV (11)
(cid:17)
We test the sensitivity of our results to the choice of this rela- with intercept a and slope b, where E(z) = Ωm(1+z)3+ΩΛ
tionandfindthatitisnotadominantsourceofuncertainty(see describestheevolutionoftheHubbleparameter.Wenotethatby
Sect.4.1formoredetails). notallowinganyfreedomintheexponentofE(z),weareassum-
To estimate MΔ,WL for each cluster we integrate the NFW ingself-similarevolution.Thisismotivatedbythelargescatter
model out to the radius at which the mean density of the halo whichisapparentinourdata,thatprecludesusfromconstrain-
isΔρ (z),wherezistheclusterreshift(Table1)andΔ=500: ingevolutionatthistime.
crit
(cid:4) For the linear regression we use the Gibbs sampler im-
rΔ,WL plemented in the multivariate Gaussian mixture model routine
MΔ,WL = ρ(r)4πr2dr linmix_err(Kelly 2007)with the default of three Gaussians.
0 (cid:7) (cid:5) (cid:6) (cid:8) Weuse105randomdrawsofthesamplerandtakethefittedpa-
= 4πρr3 ln 1+ rΔ,WL − rΔ,WL · (10) rameters as the posterior mode and the error as the 68% high-
s s rs rs+rΔ,WL estposteriordensitycredibleinterval.Whenthenumberofdata
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M.Lieuetal.:TheXXLSurvey.IV.
Table2.Mass-temperaturerelationfitparametersforEq.(11).
Sample Intercept Slope Intrinsicscatter N
(a) (b) (σintlnM|T)
XXL 13.56+0.16 1.78+0.37 0.53+0.21 38
−0.17 −0.32 −0.17
XXL+COSMOS+CCCP 13.57+0.09 1.67+0.14 0.41+0.07 96
−0.09 −0.10 −0.06
XXLFS 13.67+0.07 1.50 0.48+0.19 38
−0.03 −0.08
XXLcoolcore 13.46+0.19 1.81+0.43 0.64+0.26 21
−0.24 −0.57 −0.23
XXLnon-coolcore 14.18+0.46 0.75+0.76 0.50+0.30 17
−0.39 −0.73 −0.22
XXLundisturbed 13.56+0.15 1.86+0.35 0.34+0.25 19
−0.19 −0.36 −0.20
XXLdisturbed 13.67+0.40 1.49+0.82 0.91+0.28 19
−0.49 −0.89 −0.32
XXLcoolcoreFS 13.59+0.04 1.50 0.72+0.03 21
−0.08 −0.16
XXLnon-coolcoreFS 13.83+0.04 1.50 0.50+0.15 17
−0.17 −0.14
XXLundisturbedFS 13.71+0.09 1.50 0.39+0.16 19
−0.08 −0.13
XXLdisturbedFS 13.62+0.05 1.50 0.75+0.31 19
−0.12 −0.16
Notes.FixedsloperelationsaredenotedbyFS.
pointsissmall,theGibbssamplerwillhavedifficultyinreach- scatter. The same is true if we repeat the fits to the two sub-
ing convergence. linmix_err also has the option of running samplesholdingtheslopeoftherespectiverelationsfixedatthe
asa Metropolis-Hastingsalgorithm,whichismoreefficientfor self-similarvalueofb=1.5(Table2).
smallsamplesize.TestsimplementingtheMetropolis-Hastings Second, we use the offset between the X-ray centroid and
algorithmgiveconsistentresults. the BCG (Lavoie et al., in prep.), expressed as a fraction
We fit the model to the measured values of M ofr ,toclassifyclustersasundisturbedδr/r < 0.05,
500,WL 500,WL 500,WL
and T . For some galaxy clusters, the weak-lensing S/N and disturbed δr/r > 0.05. The scatter in the mass-
300kpc 500,WL
is so low that the we are only able to obtain an upper limit on temperature relation for undisturbed clusters is less than that
M . The posteriors of these systems are truncated by the ofthedisturbedclusters,albeitwithlargeuncertainties.Wesee
500,WL
lower bound prior on mass. Despite this, it is important to in- similar results if we hold the slope ofthe relationfixedat self-
clude these systems in the fit because they are X-ray detected similar,asabove.Thissuggeststhatthedisturbedclustersdom-
at high significance, and to exclude them would add a further inatethescatterintheXXL-100mass-temperaturerelation.
selection in addition to the primary X-ray selection. The fit- It is tempting to attribute the large scatter in the mass-
tingmethodusedisabletoincorporateupperlimitsascensored temperaturerelationfordisturbedclustersto the physicsof the
data using a likelihood that integrates over the censored and cluster merger activity implied by a large value of δr/r .
500,WL
uncensored data separately (see Kelly 2007, for more details). Howeverwecautionthatdynamicallyactiveclusterslikelyhave
However their implementation is not suitable for our problem more complicated mass distributions than less active (“undis-
sincewehavepriorknowledgeoftheX-raydetectionweknow turbed”) clusters. Our ability to constrain reliable cluster mass
thatthesesystemsshouldhaveamassgreaterthan1013M(cid:9),flag- measurementsin the 1013 < M500 < 1014M(cid:9) regime with low
gingthemascensoreddatawouldcontradictthemasspriorused S/N survey data is likely a function of the complexity of the
in fitting the NFW profile. Tests to recoverscaling relation pa- massdistribution.Thismassrangehasnotyetbeenexploredto
rameters on simulated toy data show that censoring leads to a anygreatextentbysimulationstudies(e.g.Becker& Kravtsov
positivebiasintheslope.Forsystemswherethelowercredible 2011;Bahéetal.2012).We willreturntothisquestioninafu-
regionistruncatedbythemasspriorandhenceunderestimated turearticle.
wesetthelowermasserrorequaltotheuppermasserror.Inour
toymodelteststhisgavetheleastbiasinscalingrelationparam-
3.3.Combinationwithothersamples
eters,withbiases<10%.
Themass-temperaturerelationbasedonthe38clustersthat To improve the precision and to extend the dynamic range of
overlap between the XXL-100-GC and the CFHTLenS shear our mass-temperaturerelation we now include 10 groupsfrom
catalog has a slope of b = 1.78+−00..3372, with an intrinsic scatter COSMOS(Kettulaetal.2013)and48massiveclustersfromthe
in natural log of mass at fixed temperature of σintlnM|T (cid:4) 0.5 Canadian Cluster Comparison Project (CCCP; Mahdavi et al.
(Table2). 2013; Hoekstra et al. 2015) (Fig. 5). The COSMOS groups
are X-ray selected and their weak-lensingmasses are based on
deep Hubble Space Telescope observations, and follow a sim-
3.2.Coolcorestatusanddynamicaldisturbance
ilar analysis method to our own. Unlike our sample, the tem-
Weinvestigatewhetherthemass-temperaturerelationfitparam- peratures of the COSMOS systems are core excised. We have
etersdependonthestrengthofcoolingintheclusterscoresand therefore measured non-core excised temperatures for the ten
thedynamicalstateoftheclusters(Fig.6). COSMOS groupswithin the same 0.3 Mpcmeasurementaper-
First,wecollectivelyclassifyweakandstrongcoolcoresas ture using the same analysis process described in Sect. 2.2.
cool core systems and fit the mass-temperature relation to this Comparison between these non-core excised temperature and
coolcoresubsample,andthenon-coolcoresubsample.There- the core excised temperaturesused by Kettula et al. (2013)re-
sults of the fits have large statistical uncertainties and intrinsic vealsabiasof(cid:10)T300kpc/T0.1−0.5r500,WL(cid:11)=0.91±0.05(Fig.7),and
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A&A592,A4(2016)
Fig.5.Mass-temperaturerelationfortheextendedsample,including38systemsfromXXL(black),10fromCOSMOS(blue),and48fromCCCP
(red).Thesolidlineandlightgrayshadedregionarethebestfitscalingrelationand68%credibleintervalfortheXXL+COSMOS+CCCPsample.
ThedashedlineanddarkgreyshadedregionarethebestfitandcredibleregionfortheXXLonlysample.Systemswithupperlimitsonmassare
indicatedbyarrowsandplottedat3sigmaconfidence.
Fig.6. CSB parameter versus the offset between X-ray centroid and Fig.7. Comparison of core excised X-raytemperatures (Kettulaet al.
BCGasafractionofweak-lensingr .Thehorizontaldashedline 2013)andthere-derivedtemperaturesmeasuredwithina0.3Mpcaper-
500,WL
atCSB=0.075indicatestheseparationofcoolcoreandnon-coolcore ture.Thedashedlineisequality.
classedsystems.Theverticaldashedlineatδr/r =0.05separates
500,WL
undisturbed anddisturbedclusters.Thegreyshadedregionshowsthe
overlapbetweencoolcoreandundisturbedclusters. CCCPweb-site3,albeitwithina0.5Mpcaperture.Thisislarger
thantheaperturethatweuseforourowntemperaturemeasure-
ments.GiventhattheCCCPsystemsaremoremassivethanours,
wedonotexpectthisdifferenceinaperturetohaveasignificant
emphasisetheimportanceofensuringthatthetemperaturesare affectonourresults.Weconfirmthatthisisindeedthecase(see
measuredinaconsistentmannerwhencombiningsamples. Sect.4.1formoredetails).
We also obtained non-core excised temperatures for the
CCCP clusters analysed by Mahdavi et al. (2013) from the 3 http://sfstar.sfsu.edu/cccp/
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M.Lieuetal.:TheXXLSurvey.IV.
Wefitthemass-temperaturerelationtothejointdatasetfol- cuts (Sect. 2.4). Benjamin et al. (2013) use tests with spectro-
lowingthe same procedureasappliedto the XXL-onlysample scopic redshifts to find that within the CFHTLenS catalogue
in Sect. 3.1. The statistical precision of the fit is much higher the redshifts are most reliable between 0.1 < z < 1.3. This is
thanthatoftheXXL-onlyfit,andhasverysimilarcentralvalues duetoafundamentaldegeneracyintheangularcross-correlation
for all fit parameters between the two fits (Table 3). The slope method.Atz < 0.1, their contaminationmodeltendsto under-
parameterofthejointfitisb=1.67+0.14withanintrinsicscatter predictcontaminationbyhigherredshiftgalaxies.Atz>1.3the
−0.10
ofσint(lnM|T) =0.41−+00..0076. predicted contamination by lower redshift galaxies is also un-
derestimated.Wecomparedmassesderivedusingallgalaxiesto
massesrestrictedtothereliableredshiftrange0.1<z<1.3.The
3.4.MassestimatesforXXL-100-GC massesareimpervioustothetwosourceselectionswitharatio
of(cid:10)M0.1<z<1.3/M (cid:11) = 1.13±0.18.Inoursampleonly10%
The mass of each member of XXL-100-GC is computed from 500,WL 500,WL
the joint XXL+COSMOS+CCCP mass-temperature relation ofthesystemsincludethez<0.1contaminatedgalaxiesandthe
(see Table 2). The uncertainties on these masses are estimated low number of z > 1.3 galaxies should contribute little to the
bypropagatinguncertaintiesonindividualtemperaturemeasure- shear.Thisincombinationwiththelargestatisticaluncertainties
ments,andtheintrinsicscatteronthemass-temperaturerelation. onshearwouldexplaintheagreement.
The masses are presented in Paper II, and denoted as M
500,MT Outerfittingradius–Thesystemsconsideredinthisarticleare
toindicatethattheyarebasedonthemass–temperaturescaling
lowermassthanmostofthoseconsideredbyBecker&Kravtsov
relation.
(2011).ThustheouterradiustowhichtheNFWmodelisfitted
to the measuredshear profilemayextendfurtherintothe infall
region than in their simulation study, and thus might bias our
4. Discussion
massmeasurements.Weimplementedasimpletestwherebywe
InSect.4.1wediscusstheeffectofsystematicuncertaintieson
comparedthemassobtainedfromNFWmodelsfittedtothean-
our results, and in Sect. 4.2 we compare our results with the nulus0.15−2MpctothosedescribedinSect.2.4.Themeanratio
literature.
ofthemassesderivedfromthesefitsandthoseuponwhichour
resultsarebased(0.15–3Mpc)is1.01±0.17.
4.1.Systematicuncertainties Choiceofmass-concentrationrelation – We adoptedthe Duffy
Several sources of systematic uncertainty have been discussed etal.(2008)mass-concentrationrelationforourmassmodelling
in the preceding sections. Here we describe the tests that were of the shear signal, which aids comparison with the literature
performedtoassesstheamplitudeoftheseuncertainties. (Kettulaetal.2013).Howeverobservationalstudies(e.g.Okabe
et al. 2013;Umetsu et al. 2014)indicate thatclusters are more
Fittingmethod –We testedtherobustnessofthefittingmethod concentrated than expected from simulations (e.g. Duffy et al.
mpfitexy
on the resultant scaling parameters using (Williams
2008; Bhattacharya et al. 2013). Hoekstra et al. (2012) show
idl
etal. 2010).Thisis a variationof the standard fitting tech- that a 20% change in normalisation of the mass-concentration
niquempfit(Markwardt2009)thatminimisesaχ2statisticand relation would bias NFW-based masses by ∼5–15%, although
iterativelyadjustsforintrinsicscatter.However,itdoesnotcal- recent work by Sereno et al. (2015) suggest the bias could be
mpfitexy
culate the error on the intrinsic scatter. Using the accounted for by selection effects. As a simple test, we per-
XXL+COSMOS+CCCP fit of 96 objects produces a slope of turbed the normalisation of the Duffy et al. (2008) relation by
b = 1.71± 0.11, intercept of a = 13.55± 0.09, and intrinsic a factor of 1.31 to bring it into line with the stacked weak-
scatter ofσintlnM|T = 0.38,i.e.fullyconsistentwith ourresults lensing analysis of Okabe et al. (2013). The masses that we
presentedinSect.3(Table2). computed using this perturbed relation are slightly lower than
our Duffy-based masses, although consistent within the errors:
Upper limits – To test the sensitivity of our results to the
treatment of clusters with upper limits on M we re-fitted (cid:10)MPerturbed/MDuffy(cid:11) = 0.93±0.14.Althoughitispossibletoob-
500,WL
tain a mass when allowing concentration to be a free parame-
the mass-temperature relation excluding these objects, obtain-
ing a marginally shallower slope of b = 1.63 ± 0.13 and ter ((cid:10)Mfree/MDuffy(cid:11) = 0.87 ± 0.14), we did not do this as we
an intrinsic scatter of σlnM|T = 0.39 ± 0.06 for the joint were not able to constrain concentration with this data. The
XXL+CCCP+COSMOSsampleandb = 1.84±0.38,σlnM|T = slope of the mass-temperature relation fits to the joint sam-
0.30±0.18 for the XXL-only sample – again, consistent with ple, based on our perturbed and free-concentration masses are
b =1.75±0.13andb =1.71±0.14.Withintheerrors
ourmainresults. perturbed free
both are consistent with the Duffy concentration prior results.
Centringoftheshearprofile–Clustermassesaredominatedby The XXL-only M–T relation using free-concentration masses
statisticalnoisesuchthatwhetherwecentretheshearprofileon hasregressionparametersb=1.77±0.37,a=13.54±0.21,and
the BCG or onthe X-raycentroiddoesnotlead to a large sys- σlnM|T =0.38±0.20.
tematic uncertainty. There is large scatter between the masses
derivedfromthedifferentcentres;however,thebiasisminimal Cosmic shear test – Heymans et al. (2012) compute the
((cid:10)MXray /MBCG (cid:11)= 1.00±0.16)andsodoesnothaveanim- star-galaxy cross-correlation function of objects within the
500,WL 500,WL CFHTLenS catalogue finding an amplitude much higher than
pactonourresults.TheBCGcentredfitsreturnaXXL-CCCP-
COSMOScombinedMT relationwithslopeb=1.61±0.14and expected from simulations. Approximately 25% the fields fail
anintrinsicscatterofσintlnM|T =0.43±0.06. tbhaicskcoisnmtoicasghreeaermteesnttanwditwhhesinmrueljaetcitoends.brTinhgistheaffoebcstesrv∼at4io0n%s
Source selection – The photometric redshift uncertainty of of our systems: XLSSC054, 055, 060, 056, 091, 095,
galaxies and its contributionto the mass estimation of clusters 096, 098, 099, 103, 104, 105, 107, 108, 110, and
in oursample is small (cid:10)dξ/ξ(cid:11) = 0.13and so we used all back- 111. Excluding these systems from our sample does not
groundgalaxieswithP(z)measurementsthatsatisfyourredshift significantly change our results; for example a joint fit to the
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A&A592,A4(2016)
Fig.8.Left:comparisonofourresultsontheslopeofthemass-temperaturerelationwiththoseintheliterature(Eckmilleretal.2011;Lovisari
et al.2015; Sunet al.2009; Vikhlininetal. 2009). Right:comparison of themass of aclusterof temperature T = 3keV at z = 0.3based on
mass-temperaturerelationsandthoseintheliterature.Inbothpanels,filledcirclesaresamplesthatuseweak-lensingmasses,opendiamondsare
samplesthatusehydrostaticmasses.TheCOSMOS+CCCP+160DandCOSMOS-onlyrelationsarefromKettulaetal.(2013)andtheCFHTLS
relationfromKettulaetal.(2015).BChasbeencorrectedforEddingtonbias.
remainingXXL clusters, COSMOS, and CCCP (80 systems in each of the correlation coefficients between L–T and fitted the
total)yieldsa = 13.43+−00..1039,b = 1.79+−00..1162,σint,lnM|T = 0.42−+00..0067. mass-temperaturerelationforeachofthesesamples.Comparing
Thissuggeststhatithasaninsignificanteffectonclusterlensing the bias between the scaling relation parameters measured be-
wherePSFresidualsarereducedfromtheradialaveraging.All fore and after the flux cut as a function of the correlation be-
CFHTLenS fields are used in both Velander et al. (2014) and tweenL–T showsaweakdependency.Weexpectthecorrelation
Kettulaetal.(2015). coefficientbetweenluminosityandtemperaturetobe∼0.3(e.g.
Maughan2014).Inourmodelthiscorrespondstolessthan5%
Mismatchintemperaturemeasurementapertures–Asdiscussed biasinbothslopeandnormalisation.Kettulaetal.(2015)apply
intheresultssection,ourtemperaturemeasurementaperturedif- acorrectionforEddingtonbiastobothmassesandtemperatures
fersfromthatusedbyCCCP.Thisshouldnotdramaticallyaffect toasamplesimilartooursintheirscalingrelation.Theirresults
ourresults as the temperatureprofile of clustersis shallow and indicate a 10% bias on the slope when uncorrected for; how-
forgroups0.3 Mpc is a significantfractionofr500,WL, whereas ever,thisisdetectedat0.7σsignificance.FortheCCCPclusters
for the massive clusters in CCCP the same holds at 0.5 Mpc. used in this paper, a selection function model is not possible.
Nonetheless, as a test we computed temperatures within the The CCCP sample is selected from a variety of archived data
same 0.5Mpc aperture for our clusters, finding that this mea- and various selection criteria. We note that the selection func-
surement is feasible for 36 of the 38 XXL clusters, and for tion test above only applies to the XXL-only sample, but will
all10COSMOSgroups.Thebestfitslopeparameterandintrin- be modelled comprehensivelyin a future XXL paper,when an
sicscatterforthisfullyself-consistentnon-coreexcisedrelation alternativemassiveclustersamplewithawell-definedselection
areb=1.61±0.12,andσ(lnM|T) =0.42±0.06.Themismatched functionisavailable.
apertureuncertaintyisthereforecomparabletothestatisticaler-
rors,anddoesnotalterourresult. Outliers – One particular outlier in our sample is XLSSC 110.
ThissystemhasbeenstudiedindetailbyVerdugoetal.(2011)
Selection function – The XXL-100-GC sample selection and is particularly interesting for the strong lensing features
function needs to account for the flux-limit, survey volume, caused by a merger of three galaxies. For this system the tem-
pointingsand more.In the M–T relation this calculationis not perature is particularly low for the estimated mass. If we in-
trivial.Wecreatedasimplifiedtoymodeltotestthebiasinmea- stead centre our shear profiles on the merger (corresponding
suredslope ona fluxlimitedsampleasafunctionofthecorre- to the BCG) we obtain a 25% higher mass. For this system
lation between X-ray luminosity and temperature. For this test thetemperaturemayhavebeenunderestimatedbytheexclusion
wetookapopulationof10000groupsandclusterswithmasses of the AGN contaminated emission from the merger. Verdugo
(1×1013 < M500 < 1×1015 M(cid:9)) and redshifts(0 < z < 1.5) et al. (2011) use several methods to estimate the mass of this
from the Tinker et al. (2008) mass function. We converted the systembutwithinafixedradius.Refittingthejointscalingrela-
mass simultaneously to X-ray luminosity using the scaling re- tionexcludingthissystemgivesconstraintsofb = 1.71±0.13,
lation in Maughan (2014) and temperature using a relation of a=13.54±0.09,andσlnM|T =0.41±0.06.
slope1.5,normalisation13.65.Theseweredrawnfromabivari-
ate Gaussian distribution with intrinsic scatter in log of 0.4 Mass bias on XXL-100-GC masses – To test the impact of bi-
10
and 0.3 for luminosity and temperature, respectively, and re- ases on the individually measured weak-lensing masses in the
peatedforcorrelationcoefficientsbetweenluminosityandtem- XXL sample on the masses derived from the M–T relation,
peraturefrom0to1instepsof0.05.Eachluminositywasthen we perturbed the XXL masses down by increments of 10%,
convertedtoafluxandacutat3×10−14 ergss−1 cm−2 wasap- refitted the joint M–T relation, and recomputed the masses
pliedtoreplicatetheselectionontheXXL-100-GCsample.We of XXL-100-GC. We find for offsets of 10, 20, and 30% in
drew20samplesof100clustersbeforeandafterthefluxcutfor XXL masses, the resulting M–T derivedmasses, M , will
500,MT
A4,page10of17