High significance detection of the tSZ effect relativistic corrections

0.46 MB·

by  G. Hurier

Astronomy&Astrophysicsmanuscriptno.relat_tsz_publi (cid:13)c ESO2017
February1,2017
High significance detection of the tSZ effect relativistic corrections
G.Hurier1,2
1 CentrodeEstudiosdeFísicadelCosmosdeAragón(CEFCA),PlazadeSanJuan,1,planta2,E-44001,Teruel,Spain
2 Institutd’AstrophysiqueSpatiale,CNRS(UMR8617)UniversitéParis-Sud11,Bâtiment121,Orsay,France
e-mail:[email protected]
Received/Accepted
Abstract
7
1 ThethermalSunyaev-Zel’dovich(tSZ)effectisproducedbytheinteractionofcosmicmicrowavebackground(CMB)photonswith
0 the hot (a few keV) and diffuse gas of electrons inside galaxy clusters integrated along the line of sight. This effect produces a
2 distortionofCMBblackbodyemissionlaw.Thisdistortionlawdependsontheelectronictemperatureoftheintra-clusterhotgas,Te,
throughtheso-calledtSZrelativisticcorrections.Inthiswork,wehaveperformedastatisticalanalysisofthetSZspectraldistortion
n onlargegalaxyclustersamples.Weperformedastackinganalysisforseveralelectronictemperaturebins,usingbothspectroscopic
a measurementsofX-raytemperaturesandascalingrelationbetweenX-rayluminositiesandelectronictemperatures.Wereportthe
J
firsthighsignificancedetectionoftherelativistictSZatasignificanceof5.3σ.WealsodemonstratethattheobservedtSZrelativistic

1 correctionsareconsistentwithX-raydeducedtemperatures.ThismeasurementofthetSZspectrallawdemonstratesthattSZeffect
3 spectraldistorsioncanbeusedasaprobetomeasuregalaxyclustertemperatures.

Keywords.Cosmology:Observations–Cosmicbackgroundradiation–Sunyaev-Zel’dovicheffect
]
O
C
. 1. Introduction The TCMB measurement using tSZ effect by Hurier et al.
h
(2014)hasshownthatPlanckfullskymulti-wavelengthobserva-
p
Galaxy clusters contain a hot thermal plasma that Comptonize tions of the sub-millimeter and microwave skies are tailored to
-
o the cosmic microwave background (CMB) photons when they studythepropertiesofthetSZspectraldistorsions.Inthiswork,
r are traversing the galaxy cluster. This interaction produces the we present the first high-significance detection of the tSZ rela-
t
s well known thermal Sunyaev-Zel’dovich (tSZ) effect (Sunyaev tivistic correction using a statistical analysis of a large galaxy
a & Zeldovich 1972), which induces a spectral distortion of the cluster sample. The paper is organized as follows, Section 2
[
CMB blackbody emission law. This spectral distortion can be presents the data used in this analysis, Section 3 describes the
1 considered as independent of the electron energies as long as tSZ effect, Section 4 describes the methodology, and Section 5
v the electron velocities are significantly smaller than the speed presentstheresults.
0 oflight,c.Typicalplasmainsidegalaxyclustershaveatemper-
2 ature of several keV. Thermal electrons in hot galaxy clusters
0
((cid:39) 5 keV) have velocities of the order of 0.1 c. Consequently,
9
relativistic corrections have to be applied to the tSZ spectral
0
distorsions (Wright 1979). Fitting formula have been proposed
.
1 toeasethemodelingofthetSZrelativisticcorrections(Nozawa 2. Thedata
0 etal.2000).
7
2.1. Planckintensityfull-skymaps
1
: These relativistic corrections offer the possibility of using
v thetSZeffectspectraldistorsionasaprobetomeasurethetem- This paper uses the first 15.5 month survey mission of Planck
i
X peratureofthehotplasmainsidegalaxyclusters(Pointecouteau HFI (Planck Collaboration early I 2011), corresponding to
two full-sky surveys (Planck Collaboration results I 2014). We
r et al. 1998; Ensslin & Hansen 2004). Recent works (Zemcov
a refer to Planck Collaboration results VI (2014) and Planck
etal.2010,2012)havereportedevidenceofthetSZrelativistic
CollaborationresultsVIII(2014)forthegenericschemeoftime-
correctionsupto3σusingZ-Spec.
orderedinformation(TOI)processingandmap-making,aswell
asforthetechnicalcharacteristicsofthePlanckfrequencymaps.
Galaxy clusters host galaxies, and consequently the tSZ ThePlanckchannelmapsareprovidedinHEALPix(Górskietal.
effect is spatially correlated with radio and infrared emission 2005)N =2048atfullresolution.Anerrormapisassociated
side
fromgalaxies.Radiogalaxiesandinfraredemissionshavebeen witheachchannelmapandisobtainedfromthedifferenceofthe
showntobeasignificantbiasfortSZ-basedstudies(Hurieretal. firsthalfandsecondhalfofthesurveyrings,foragivenpoint-
2013; Planck Collaboration 2015 results XXIII 2016). Thus, if ing position of the satellite spin axis. Here we approximate the
notconsideredcarefullytheseemissionscouldsignificantlybias PlanckHFIbeamsbyeffectivecircularGaussianswithFWHM
anattemptofdetectionforthetSZrelativisticcorrections. up to 5 arc minutes that can be found in Planck Collaboration
resultsVII(2014).
1
G.Hurier:HighsignificancedetectionofthetSZeffectrelativisticcorrections
Table1.Maincharacteristicsofthegalaxyclustercatalogs. N Compton parameter to CMB temperature, K , conversion
cl CMB
isthenumberofobjectsinthecatalog,T andT arethe factors for each frequency channel depend of the convolution
e,min e,max
coveredrangeoftemperature,T isthemedian,z andz of this tSZ contribution to the sky intensity with the Planck
e,med min max
arethecoveredrangeofredshiftandz isthemedianredshift frequencyresponses.
med
Catalog Ncl Te,min Te,max Te,med zmin zmax zmed This characteristic spectral signature of tSZ effect makes it
MCXC 1743 0.11 10.25 2.81 0.00 1.26 0.14 auniquetoolforthedetectionofgalaxyclustersaspresentedin
CAV08 192 2.44 19.13 6.99 0.03 1.24 0.26 Planck Collaboration2015 results XXVII(2016) and is related
ZHA08 37 3.2 11.6 6.7 0.14 0.30 0.23
toT throughrelativisticcorrections.
VIK09 85 2.13 14.72 4.4 0.03 0.89 0.09 e
The relativistic corrections on the tSZ emission law have been
PRA09 31 2.07 8.91 3.85 0.06 0.18 0.12
computedaspresentedin(Pointecouteauetal.1998).Fromthis
ECK11 26 0.62 2.99 1.61 0.01 0.05 0.02
estimation, if we assume that the relativistic corrections on the
MIT11 64 0.90 15.91 4.37 0.00 0.22 0.05
REI11 232 2.0 15.0 5.9 0.04 1.46 0.30 tSZemissionlawcanbedescribedasafirstorderapproximation
MAH13 50 3.1 12.1 6.5 0.15 0.55 0.24 (seeNozawaetal.2000,foradetailedfittingformula),
LAG13 117 2.0 15.2 5.8 0.11 1.24 0.35
∆Trelat(T )=∆Tunrelat+T ∆Tcor , (5)
CMB e CMB e CMB
2.2. Catalogs theaveragedtSZemissionfromdifferentelectronpopulationsat
varioustemperaturescanbemodeledwithasingletemperature.
Weusedtwodifferentgalaxyclustersamples.Thefirstonecon-
This approach enables the possibility to perform stacking
siders all galaxy clusters in the MCXC catalog (Piffaretti et al.
analyses of the tSZ relativistic corrections. This approximation
2011). For this sample we computed the electron temperatures
is already implicitly considered when fitting a single temper-
usingthescalingrelationfromPrattetal.(2009),
ature on the observed tSZ signal. Considering that electronic
L =(0.079±0.008)(T[keV])2.70±0.241044erg.s−1. (1) temperature varies along the line of sight. We stress that the
X quasi linear behavior of the tSZ spectral distorsion relativistic
In the second sample we considered galaxy clusters for correctionswithrespecttoTeisonlyusedtomotivateastacking
which we have a spectroscopic temperature (Cavagnolo et al. analysis.Inthefollowing,whenfittingforTeonthestackedtSZ
2008;Zhangetal.2008;Vikhlininetal.2009;Prattetal.2009; signal we use the exact tSZ spectral distorsion as a function of
Eckmiller et al. 2011; Mittal et al. 2011; Reichert et al. 2011; Te.
Mahdavietal.2013;Laganáetal.2013).
In Table. 1, we summarize the main characteristics of each
galaxyclustercatalogs,N isthenumberofobjectsinthecata-
cl
log,T andT arethecoveredrangeoftemperature,T
e,min e,max e,med
isthemedian.Westressthatthedifferentcatalogspresentover-
lapsofobjects.Thisoverlaphasbeenconsideredinthefollow-
inganalysis.
3. ThetSZeffect
The thermal Sunyaev-Zel’dovich effect (Sunyaev & Zeldovich
1972)isadistortionoftheCMBblackbodyradiationthroughin-
verseComptonscattering.CMBphotonsreceiveanaverageen-
ergyboostbycollisionwithhot(afewkeV)ionizedelectronsof
theintra-clustermedium(seee.g.,Birkinshaw1999;Carlstrom
etal.2002,forreviews).ThethermalSZComptonparameterin
agivendirection,n,ontheskyisgivenby
(cid:90)
k T
y(n)= n B eσ ds, (2) Figure1.tSZspectraldistorsionasafunctionofthefrequency
em c2 T
e forvarioustemperaturesofthehotplasmafrom0to20keV.
wheredsisthedistancealongtheline-of-sight,n,andn andT
e e
aretheelectronnumberdensityandtemperature,respectively.In
unitsofCMBtemperature,thecontributionofthetSZeffectfor Figure 1 shows the tSZ spectral dependance as a function
of the frequency for various temperatures of the hot plasma
agivenobservationfrequencyνis
ranging from 0 to 20 keV. We observe that the main conse-
∆T quence of relativistic corrections is a modification of the zero
CMB =g(ν)y. (3)
TCMB flaretiqouneνncy(cid:39),ν201,7o.f4t+heTtS/Z2.sWpeectarlaslodoisbtsoerrsvioena,sthigantiffioclalonwtisntchreearsee-
0 e
Neglectingrelativisticcorrectionswehave of the 353 to 545 GHz tSZ intensity ratio. In general, higher
(cid:20) (cid:18)x(cid:19) (cid:21) temperaturesfortheplasmawillfavorahighertSZamplitudeat
g(ν)= xcoth −4 , (4) high-frequencies,andalowertSZintensityatlowfrequencies.
2
ThePlanckexperimenthasalargefrequencycoverageatlow
with x = hν/(k T ). At z = 0, where T (z = frequency(< 217GHz)wherethetSZeffectproducesaninten-
B CMB CMB
0) = 2.726±0.001 K, the tSZeffect is negative below 217GHz sitydecrement,at217GHzwheretSZeffectisalmostnull,and
andpositiveforhigherfrequencies. athigherfrequencies(> 217GHz)wheretSZproducepositive
2
G.Hurier:HighsignificancedetectionofthetSZeffectrelativisticcorrections
anisotropies on the CMB. This makes Planck HFI a really tai- Table2.Correlationmatrixofstatisticaluncertaintiesforemis-
lored instrument for the tSZ effect detection and scientific ex- sion tSZ emission law, estimate from 1000 random positions
ploitation. acrossthesky.
4. Methodology Frequency(GHz) 100 143 353 545
100 1 0.62 -0.49 -0.48
4.1. EstimationoftSZfluxperfrequencyandstacking
143 0.62 1 -0.49 -0.56
WerefertoHurieretal.(2014)foradetaileddescriptionofthe 353 -0.49 -0.49 1 0.83
tSZ flux extraction in Planck intensity maps. We first extracted 545 -0.48 -0.56 0.83 1
2x2o patches around each galaxy clusters. We cleaned for in-
fraredemissionusingthe857GHzchannel.Wealsocomputed
secondaryanisotropiesthemselvesthroughthekSZeffect.
a tSZ y-map with the MILCA method (Hurier et al. 2013) and
we estimated the tSZ flux in each Planck frequency using the
MILCAmapasatemplatetobuildthespectralenergydistribu-
tion (SED) toward each galaxy clusters. Then, we subtract the 4.3.1. Cosmicinfraredbackground
217 GHz signal to other channels in order to clean for CMB
For the estimation of T from tSZ measurement, the 545 GHz
emission. Finally, we divided our galaxy clusters samples into e
mapisthekeyfrequencychannel,howeveritisalsoafrequency
T bins. We separated the MCXC into five temperature bins
(∆eT = 2 keV) and the spectroscopic sample into three tem- for which one the detection of the tSZ effect is the most chal-
e
perature bins (∆T = 4 keV). Then, we performed a stack of lenging.Atthisfrequency10%oftheCIBemissionisproduced
e
by objects with redshift lower than 1.0 (Lagache et al. 2005;
individualgalaxyclustermapsforeachtemperaturebin.
Addison et al. 2012). See Planck Collaboration 2015 results
Figure2showstheresultsofthestackingproceduretoward
XXIII (2016), for a measurement of the tSZ×CIB cross corre-
MCXC clusters for the lowest temperature bin (top panel) and
lation.Anexcessofemissionathighfrequencyisproducedby
for the highest temperature bin (bottom panel). We observe a
theCIBresiduals,whichthusmimictheeffectofrelativisticcor-
significantamountoftSZsignalinthe545GHzstackedmapfor
rectionsonthetSZspectraldistorsion.
thehigh-temperaturebin,whereasthelow-temperaturebindoes
ThetSZemissionscalesasM tothepowerof1.79(Planck
notpresentasignificanttSZemissionatthisfrequency. 500
CollaborationresultsXXIX2014)andtheCIBscalesasM to
500
the power of (cid:39) 1.00 (Planck Collaboration 2015 results XXIII
4.2. Backgroundandforegroundcontamination 2016).Consequently,thetSZ-CIBratiodecreasewith M and
500
thus with T as F ∝ T−1.20 assuming that T evolves as
Toestimatethecontaminationbyothersourcesofanisotropiesin 500 CIB 500 500
Planckfrequencymaps,weperformedthefluxextraction,asde- M2/3.ThisimpliesthatCIBresidualswillbemoreimportantfor
500
scribedinHurieretal.(2014),at1000randompositionsacross lowtemperaturegalaxyclusters.Consequently,CIBcontamina-
the sky. These random positions follow the same spatial repar- tioncanbeseparatedfromtSZrelativisticcorrectionsbyconsid-
tition in latitude as our sample of galaxy clusters to avoid any eringseveralbinsoftemperature.
biascomingfromthegalacticplanearea,whichdoesnotcontain We also stress that our dust-cleaning procedure using the 857
galaxyclustersintheusedsample.Inthefollowingweconsider GHzchannelwillremovemostoftheCIBcontamination,con-
thatuncertaintiesareuncorrelatedbetweentwodifferentgalaxy sideringthattheclustersinoursampleareessentiallylow-zob-
clusters. jects (Planck Collaboration 2015 results XXIII 2016). Indeed,
Consequentlywecanderivedthefullcovariancematrixforthe dusty galaxy emission in these galaxy clusters presents a very
fluxestimationinfrequencychannelsfrom100to545GHz,an similarspectralbehaviortotheMilkyWay.
example of such a correlation matrix is presented in Table. 2.
This covariance matrix has a determinant of 2.4 10−4, which
4.3.2.Radiopointsources
quantifies the volume occupied by the swarm of the data sam-
plesinourfourdimensionsubspace(HFIfrequenciesfrom100 Inordertoavoidcontaminationbyradioloudactivegalacticnu-
to545GHzexcluding217GHz). cleus(AGN),weremovedfromtheanalysisclustersthatpresent
Considering that most foreground and background emissions an emission above 0.5 mK at 100 GHz in a radius of 30’
CMB
havebeencleanedfromthemaps,thecovariancematrixisdom- fromthegalaxyclusterposition.
inatedbytheinstrumentalnoise,thatiscorrelatedbetweenfre-
quenciesduetothecleaningprocess.Thehighlevelofcorrela-
4.3.3.kSZ
tionbetween353and545GHzalsoreceivescontributionsfrom
thermaldustresidualsinthesemaps.Westressthatthiscorrela- The kSZ effect follows the same spectral dependance as the
tion matrix only accounts for uncertainties produced by uncor- CMB and thus is suppressed from our analysis by the CMB
relatedcomponentswithrespecttothetSZeffect. cleaningperformedwiththe217GHzchannel.However,some
kSZresidualsmayremainsinthemeasuredSEDduetocalibra-
tionuncertainties(PlanckCollaboration2015resultsVIII2016).
4.3. Correlatedforegroundcontamination
The inter-calibration uncertainties at 100, 143, 217, 353, and
AswediscussinSect4.2,errorsinducedbyuncorrelatedfore- 545 GHz are 0.09, 0.07, 0.16, 0.78, and 5% respectively. We
groundscanbefairlyestimatedusingrandompositionsoverthe stress that absolute calibration uncertainty does not affects the
sky. However this estimation does not account for extra-noise tSZ spectral signature, it only affects the overall Compton pa-
and bias produced by physically correlated emissions, such as rameter normalization, which did not impact the estimation of
radio sources contamination at low frequency, cosmic infrared T .
e
background (CIB) contamination at high frequency, and CMB Propagatingtheseuncertaintiesthroughourdataprocessing,we
3
G.Hurier:HighsignificancedetectionofthetSZeffectrelativisticcorrections
Figure2.Fromlefttoright:stackofPlanckintensitymapsat100,143,353,545GHzcleanedbythe857and217GHzchannel,
and MILCA tSZ map, centered on the location of Planck MCXC clusters for a low-T bin (top panel) and a high-T bin (bottom
e e
panel).Eachstackedmaprepresentsanareaof2◦×2◦.
deduced that the calibration uncertainties induce a leakage of for temperature bin j, and Async a synchrotron spectrum with
i
thekSZeffectamplitudeintotSZeffectfluxmeasurementwith spectral index -1. Adjustable parameters are Yj, T , and Fj
e sync
a standard deviation of 0.2%. The kSZ is typically one order thesynchrotronamplitude.
ofmagnitudefainterthanthetSZeffect,similarlytSZrelativis-
tic corrections modify the tSZ spectral distorsion by (cid:39) 10%. TofitthevalueofT ineachtemperaturebins,weusedapro-
Consequently,kSZeffectresidualsmayaffectthetSZrelativis- filelikelihoodapproache.Weuseaflatpriorforthesynchrotron
ticcorrectionsmeasurementat(cid:39) 0.2%forasinglegalaxyclus- contamination: 0% < Fj < 15%. For each value of T and
ter.Additionally,thekSZeffectisaveragingtozerowhenstack- sync e
Fj , we compute through an unbiased linear fit the tSZ flux,
ing galaxy clusters,the bias for agiven temperature bin is thus sync
(cid:39) 0.2%/N . Consequently, the kSZ component contamination (cid:98)Yj,ofourmeasurement.
cl
canbesafelyneglected. Inthisanalysiswehaveuncertaintiesonboththemeasurement
(mainly the CMB contamination) and the model (bandpass un-
certainties),thistwosourcesofuncertaintieshavesimilarampli-
4.4. Systematicsproducedbybandpassandcalibration
tudes.Consequentlyweusethefollowingestimator:
uncertainties
TheonlyPlanckchannelthatpresentsasignificantrelativeband- (cid:98)Yj =(cid:104)ATWA−Tr(CTW)(cid:105)−1(cid:104)ATW(cid:98)Fj(cid:105), (7)
A
pass uncertainty for the tSZ effect is the 217 GHz channel
(Planck Collaboration results IX 2014). However, as we clean WithAthetSZtransmissionvector,CAtheAcovariancematrix,
for CMB using this channel, we are not sensitive to this uncer- (cid:98)FjisthemeasuredtSZemissionlawandW =C−1istheinverse
Fj
tainty in the measurement of Te through relativistic corrections ofthenoisecovariancematrixon(cid:98)Fj.Thenwecomputetheχ2,
tothetSZeffectspectraldistorsion. foreachcoupleofparameters(T ,Fj )as
However, the relative calibration uncertainty is a major limi- CMB sync
tation, as this uncertainty is higher at high frequency (Planck χ2 =(cid:16)(cid:98)Fj−Fj(cid:17)T(cid:16)C +(cid:98)Y2C (cid:17)−1(cid:16)(cid:98)Fj−Fj(cid:17). (8)
CollaborationresultsVIII2014),wherethetSZrelativisticcor- Fj A
rectionspresentasignificantdepartureformnon-relativistictSZ.
Calibrationuncertaintiesare< 0.2%for100,143and217GHz Finally,weestimatethevalueofTe bymarginalizingoverFsjync
channels,<1%at353GHzand5%at545and857GHz.Inthe andcomputingthefirst-ordermomentumofthelikelihoodfunc-
following,weconsideruncertaintiesfromcalibrationandprop- tion,L = e−χ2/2,withrespecttoT .Wecomputetheuncertain-
e
agatethemtoouranalysis. tiesonT usingthesecond-ordermomentumofL.
e
5.2. Averagedelectronictemperatures
5. Dataanalysis
IfweassumeafirstorderapproximationofthetSZspectraldis-
5.1. Profilelikelihoodanalysis
torsion,thenthebin-averagedtemperatureisgivenby,
Todescribeourmeasurement,themostgeneralmodelreads
(cid:80)
TkYk
Fj =YjA(T )+Fj Async, (6) Tej (cid:39) (cid:80)k Yek , (9)
i i e sync i k
with Ai(Te)beingthee(cid:82)xacttSZspectraldistorsionforaplasma where Tej is the averaged temperature for the bin j, Tek is the
temperature,T ,Yj = ydΩtheintegratedComptonparameter temperatureofagivengalaxycluster,k,inthebin j,andYk the
e
4
G.Hurier:HighsignificancedetectionofthetSZeffectrelativisticcorrections
integratedComptonparameterofthegalaxyclusterk.However,
tSZrelativisticcorrectionsarenotlinearwithrespecttoT ,thus
e
TjdiffersfromtheComptonparameterweightedaverageofTk.
e e
We estimated the discrepancy between the Compton parameter
weightedtemperatureandtherealaveragebyperformingstacks
oftherealtSZspectraldistorsionsintemperaturebins,forelec-
tronic temperatures ranging from 0 to 15 keV and bin width
rangingfrom1to10keV.Then,wefitforasingletemperature
in each temperature bin using Eq. 8. We stress that the bias is
thusdependentontheexperimentalsetting(frequencycoverage
anddatacovariancematrix).WefoundthatinsmallT binsthis
e
discrepancyisnegligible,below0.05keVforbinwidth∆T <5
e
keV. This supports the first order linear assumption when per-
formingastackinganalysisofthetSZrelativisticcorrections.
Figure4.MeasuredtemperaturefromtSZrelativisticcorrection
forthegalaxyclusterswithX-rayspectroscopictemperature,as
5.3. Results afunctionofthetemperaturederivedfromX-rays.The1:1rela-
tionisshownasasolidredline.
Figure 3 shows the relation between the temperature derived
from tSZ relativistic corrections and the temperature derived
from X-ray luminosity. Fitting for the slope of this relation we
obtain T = (1.65±0.45)T , with a significance of 3.7 σ inalltemperaturebins.InFig.4,thehighesttemperaturebinis
e,tSZ e,X
dominated by calibration uncertainties, which supports the cal-
andconsistentwitha1:1relationat1.4σ.Consideringthelarge
ibration origin of the observed high-temperature overall excess
numberofgalaxyclustersinsideeachbin,theuncertaintiesover
forthetSZrelativisticcorrections.
theX-raytemperatureaverageissmallcomparedtotemperature
bin width and tSZ temperature uncertainties. Thus, we did not
displaytheseuncertainties.
6. Discussionandconclusion
Wehaveperformedthefirsthighsignal-to-noiseratiodetection
of the tSZ relativistic corrections at a significance level of 5.3
σ. We have considered potential contamination by radio and
infraredemissionandshownthatthessourcesofcontaminations
arenegligible.
In this work, the tSZ relativistic corrections detection has been
achieved through a statistical analysis of large galaxy cluster
samples. In particular, we used several temperature bins to
distinguish real tSZ relativistic corrections signature from
systematic effects such as CIB contamination or calibration
uncertainties. This analysis exhibits the complexity of the
tSZ relativistic corrections recovery from a small number of
frequencies due to the required cleaning of CMB and infrared
astrophysicalcomponents.
However, future CMB-experiments, such as COrE+1, which
Figure3. Measured temperature from tSZ relativistic correc-
willhavebettersensitivityoramorerefinedfrequencycoverage
tion for the MCXC galaxy cluster sample, as a function of the will offer the possibility of performing better measurements,
temperature derived from X-ray luminosity. The 1:1 relation is
and scientific exploitation of the tSZ relativistic corrections
shownasasolidredline.
(Hurieretal.,inprep).
The tSZ effect spectral distorsion is commonly used as a prior
forgalaxyclusterdetection,thisanalysisshowsthatwearenow
Figure4showstherelationbetweenthetemperaturederived
reachingthelevelofaccuracywheretSZrelativisticcorrections
from tSZ relativistic corrections and the temperature derived
canbedetected.Thisimpliesthatgalaxyclusterdetectionbased
from spectroscopic X-ray analyses. Fitting for the slope of this
relationweobtain,T =(1.38±0.26)T ,withasignificance onthetSZspectraldistorsionneglectingrelativisticcorrections
e,tSZ e,X
might be biased toward low-temperature objects, and then bias
of5.3σandconsistentwitha1:1relationat1.5σ.Uncertainties
thedetectionofhigh-zhigh-massgalaxyclusters.
overtheX-rayspectroscopictemperaturearesmallcomparedto
thebinwidthandtSZtemperatureuncertainties.Consequently,
theyaredisplayedonthefigure.
Inbothcases,Figs.3and4,werecovertheexpectedrelation
Acknowledgements
between tSZ estimated temperatures and X-ray temperatures.
We do not observe significant contamination produced by CIB The author thanks N.Aghanim & D.Poletti for useful discus-
residuals, that would appears as an overestimation of the tSZ sionsandcomments.WeacknowledgethesupportoftheFrench
temperatureinthelowesttemperaturebins.Weobserveinboth AgenceNationaledelaRechercheundergrantANR-11-BD56-
casesthatthetSZtemperatureforthehighestX-raytemperature 015.
bins overestimates the X-ray temperature. This bias might be
produced by calibration uncertainties leading to an overall bias 1 http://hdl.handle.net/11299/169642
5
G.Hurier:HighsignificancedetectionofthetSZeffectrelativisticcorrections
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