Predicting the CIB-$\phi$ contamination in the cross-correlation of the tSZ effect and $\phi$

0.17 MB·

by  G. Hurier

Astronomy&Astrophysicsmanuscriptno.szlens_conta_cib (cid:13)c ESO2017
February1,2017
LettertotheEditor
Predicting the CIB-φ contamination in
the cross-correlation of the tSZ effect and φ
G.Hurier1
Institutd’AstrophysiqueSpatiale,CNRS(UMR8617)andUniversitéParis-Sud11,Bâtiment121,91405Orsay,France
e-mail:[email protected]
Preprintonlineversion:February1,2017
Abstract
7
1 TherecentreleaseofPlanckdatagivesaccesstoafullskycoverageofthethermalSunyaev-Zel’dovich(tSZ)effectandofthecosmic
0
microwave background (CMB) lensing potential (φ). The cross-correlation of these two probes of the large-scale structures in the
2 Universeisapowerfultoolfortestingcosmologicalmodels,especiallyinthecontextofthedifferencebetweengalaxyclustersand

n CMBforthebest-fittingcosmologicalparameters.
a However,thetSZeffectmapsarehighlycontaminatedbycosmicinfra-redbackground(CIB)fluctuations.Unlikeotherastrophysical
J components, the spatial distribution of CIB varies with frequency. Thus it cannot be completely removed from a tSZ Compton

1 parametermap,whichisconstructedfromalinearcombinationofmultiplefrequencymaps.Wehaveestimatedthecontaminationof
3 theCIB-φcorrelationinthetSZ-φpower-spectrum.WeconsideredlinearcombinationsthatreconstructthetSZComptonparameter
fromPlanckfrequencymaps.Weconcludethateveninanoptimisticcase,theCIB-φcontaminationissignificantwithrespecttothe
] tSZ-φsignalitself.
O Consequently,WestressthattSZ-φanalysesthatarebasedonComptonparametermapsarehighlylimitedbythebiasproducedby
CIB-φcontamination.
C
. Keywords.galaxyclusters,CMB,cosmology,power-spectrum,modelling
h
p
-
o 1. Introduction estimate the CIB-φ contamination in tSZ-φ cross-correlation.
r
In Sect. 4, we discuss the cleaning process proposed by Hill &
t
s Modern cosmology extensively used cosmic microwave back- Spergel (2014) and estimate the residual contamination level.
a ground (CMB) data. During their propagation along the line FinallyinSect.5,weconclude.
[ of sight, photons are affected by several physical processes
1 such as the thermal Sunyaev-Zel’dovich effect (tSZ, Sunyaev Throughoutthepaper,weconsiderH =67.1,σ =0.80and
0 8
v & Zeldovich 1969, 1972) and CMB gravitational lensing Ω =0.32asourfiducialcosmologicalmodel,unlessotherwise
m
7 (Blanchard & Schneider 1987), which trace the gravitational specified.
4 potentialintegratedalongthelineofsight,φ.
0
At microwave frequencies, foreground emissions contribute to
9 2. ModellingthetSZ,φ,andCIBcross-correlations
the total signal of the sky, for example the cosmic infra-red
0
background (CIB, Puget et al. 1996; Fixsen et al. 1998). The
. Thetotalpower-spectrumbetweentheAandBquantities(tSZ,
1 tSZ effect, gravitational lensing, and the CIB are tracers of
φorCIB)canbeexpressedas
0 the large-scale structures in the matter distribution of the
7 Universe. They have been powerful sources of cosmological C(cid:96)A×B =C(cid:96)A×B−P+C(cid:96)A×B−C, (1)
1
and astrophysical constraints (see e.g., Planck Collaboration withCA×B−PthePoissoniancontributionandCA×B−Cthecontri-
v: results. XX 2014; Planck Collaboration results. XXX 2014; bution(cid:96)fromlargeangularscalecorrelations. (cid:96)
i PlanckCollaborationresults.XVII2014).
X
r 2.1. Poissonianterm
a Alltheseprobespresentcorrelationsthroughtheirrelationto
thelarge-scaledistributionofmatterintheUniverse.TheCIB-φ ThePoissonianorone-halotermofthepower-spectrumcanbe
correlation has already been detected with high significance writtenusingahalomodelasthesumofthecontributionsfrom
(Planck Collaboration results. XVIII 2014). More recently, the each halo. The number of halos per unit of mass and redshift,
tSZ-φ correlation estimated from a Compton parameter map d2N ,isgivenbythemassfunction(seee.g.,Tinkeretal.2008).
(Hill&Spergel2014)hasbeenusedtoconstraincosmological dMdV
Usingthelimberapproximation,wecanwritetheone-haloterm
parameters.
as
(cid:90) (cid:90)
dV d2N
We discuss the contamination from the CIB-φ correlation C(cid:96)A×B−P =4π dzdzdΩ dMdMdVWAPWBP. (2)
intothetSZ-φcorrelationestimatedfromaComptonparameter
ThetSZcontributioncanbewrittenas
map.InSect.2,wepresentacoherentmodellingofthetSZ,φ,
and the CIB spectra and cross-correlation. Then in Sect. 3, we WP =Y y , (3)
tSZ 500 (cid:96)
1
G.Hurieretal.:CIB-φcontaminationinthecross-correlationofthetSZeffectandφ
withY thetSZfluxoftheclusters,relatedtothemass, M Table1.Cosmologicalandscaling-lawparametersforourfidu-
500 500
viathescalinglawpresentedinEq.4,andy theFouriertrans- cial model for both Y − M (Planck Collaboration results.
(cid:96) 500 500
form on the sphere of the cluster pressure profile from Planck XX2014)andtheL −M relationfittedonCIBspectra.
500 500
Collaborationresults.XX(2014)perunitoftSZflux.
We used the M − Y scaling law presented in Planck Fiducialcosmo M −Y M −L
500 500 500 500 500 500
Collaborationresults.XX(2014), Ωm 0.32 logY(cid:63) -0.19±0.02 T0 24.42
E−βsz(z)D102an−g4(Mz)Yp5c020=Y(cid:63)(cid:34)0h.7(cid:35)−2+αsz(cid:34)6(1×−1b0)1M4M50(cid:12)0(cid:35)αsz, (4) Hσ80 06.870 αβsszz 10..7696±±00..058 αγβccciiibbb 011..37.765222
δ 3.22
with E(z) = Ωm(1+z)3 +ΩΛ.ThecoefficientsY(cid:63),αsz andβsz, (cid:15)cciibb 1.1±0.2
taken from Planck Collaboration results. XX (2014), are given
in Table 1. The mean bias, (1 − b), between X-ray mass and
the true mass was estimated from numerical simulations, b (cid:39) 2.2. Large-scalecorrelationterms
0.2 (see Planck Collaboration results. XX 2014, for a detailed
We now focuss on the contribution from large angular scale
discussionofthisbias).
correlations in the matter distribution to the tSZ-φ-CIB cross-
correlationpower-spectramatrix.Weexpresthiscontributionas
Thelensingcontributioncanbewrittenas
(cid:90)
(χ(cid:48)−χ)χ dV
WP = −2ψ , (5) CA×B−C =4π dz WCWCP , (10)
φ (cid:96) χ(cid:48) (cid:96) dzdΩ A B k
with χ the comoving distance, χ(cid:48) the comoving distance of the withP ,thematterpower-spectrum.
k
CMB,andψ(cid:96) the3DlensingpotentialFouriertransformonthe In the following subsections we present the window functions,
sky. W,relatedtoeachcontribution.
Wecanexpressthepotentialψasafunctionofthedensitycon-
trast, For the tSZ effect, we considered the two-halo large-scale
∆ψ= 3Ω H2δ, (6) correlation. We neglected the contribution produced by diffuse
2 m 0a tSZemissionfromthewarmhotinterstellarmedium.Thetwo-
withatheuniversescalefactorandδthedensitycontrast.Then, halocontributionreads
thelensingcontributionreads (cid:90)
d2N
WP = 3ΩmH02(1+z)(χ(cid:48)−χ)χδ , (7) WtCSZ = dMdMdVY500y(cid:96)blin, (11)
φ (cid:96)((cid:96)+1) χ(cid:48) (cid:96)
where b is the bias relating the halo distribution to the over-
whereδ istheFouriertransformofthedensitycontrastprofile. lin
(cid:96) density distribution. We considered the bias from Mo & White
(1996) and Komatsu & Kitayama (1999), which is realistic at
TheCIBcontributioncanbewrittenas
galaxyclusterscale.
WP (ν)=S (ν)c , (8)
CIB 500 (cid:96)
with S (ν) = aL500(ν), the infra-red flux at frequency ν of the For the lensing potential, we accounted for the large-scale
500 4πχ2(z) correlationbyconsideringstructuresinthelineargrowthregime
hosthaloandc theFouriertransformoftheinfra-redprofile.
(cid:96) as
TtioonmdoedrievletdhefroLm500th−eMre5l0a0tiorenlaptrioonpowseeduisnedShaanpgareatmaelt.ri(c20r1e2la)-. WC = 3ΩmH02 (1+z)(χ(cid:48)−χ). (12)
φ c2(cid:96)((cid:96)+1) χ(cid:48)χ
TocomputethetSZ-CIBcorrelation,weneedtorelatetSZhalos
withCIBemissions.Consequently,wecannotuseaparametriza-
tionthatrelatesgalaxyhaloswiththeCIBflux.Weneedarela-
For the CIB at frequency ν, we considered the two-halo
tion that relates the galaxy cluster halo to the associated total
large-scalecorrelationas
CIBflux.
We chose to parametrize the CIB flux, L500, at galaxy cluster (cid:90) d2N
scalewithapowerlawofthemass1,M , WC (ν)= dM S (ν)c b . (13)
500 CIB dMdV 500 (cid:96) lin
(cid:34) M (cid:35)(cid:15)cib
L500(ν)= L0 1×1051040M (1+z)δcibΘ[(1+z)ν,Td(z)], (9) It is worth noting that the CIB-φ cross-correlation is domi-
(cid:12) natedbythetwo-haloterm3,incontrasttothetSZ-CIBandtSZ-
where L0 is a normalization parameter, Td(z) = T0(1+z)αcib is φcorrelationswhichpresentasignificantcontributionfromboth
thethermaldusttemperature,andΘ[ν,Td]isthetypicalspectral oneandtwo-haloterms.
energydistribution(SED)ofagalaxythatcontributestothetotal
CIBemission,
(cid:40) 2.3. Redshiftdistribution
Θ[ν,T ]= νβcibBν(Td) ifν<ν0
d ν−γcib ifν≥ν0, In Fig. 1, we present the redshift distribution of power for the
tSZ,CIB,andlensingpotentialauto-correlationspectra.ThetSZ
with ν0 the solution of dlog[dνlβocigb(Bνν)(Td)] = −γcib. The coefficients effectisproducedbystructuresatlowredshift(z<2).TheCIB
T ,α ,β ,γ ,δ ,and(cid:15) aregiveninTable1. andφspectraaredominatedbyobjectsathigherredshift.
0 cib cib cib cib cib
1 We consider the CIB-φ and tSZ-CIB cross-correlations, conse- 3 Thiscanbeexplainedbythehigh-zandlow-masshalosensitivity
quentlythereisnoneedtomodeloftheCIBatgalaxyscale. of this cross-correlation, which favours the two-halo, whereas low-z,
2 FixedvaluefromPlanckCollaborationresults.XXX(2014) high-massobjectsfavourtheone-haloterm.
2
G.Hurieretal.:CIB-φcontaminationinthecross-correlationofthetSZeffectandφ
reads
(cid:88)
Cconta = w Cφ×CIB(ν). (15)
(cid:96) ν (cid:96)
ν
Figure1.DistributionsofthetSZ,φ,andCIBpowerasafunc-
tionoftheredshiftat(cid:96) = 1000.Theblacksolidlinedepictsthe
lensingpotential,φ,thegreydashedlinethetSZeffect,thedark
blue,lightblue,green,yellow,orange,andreddashedlinesplot
theCIBat100,143,217,353,545,and857GHz,respectively.
Figure2. Residual contamination before cleaning in light blue
and after cleaning in dark blue. The red solid line presents the
The mean redshift of structures that dominate in the CIB is a tSZ-φcorrelationforourfiducialmodel.Thesolidbluelinesare
function of the considered frequency. These redshift windows the contamination considering the set of weights from Hill &
highlightthehighdegreeofcorrelationbetweentheCIBandφ Spergel(2014)for fsky =0.3.Thedashedbluelinesarethecon-
andthelowdegreeofcorrelationbetweentSZandtheothertwo tamination considering the set of weights from Hill & Spergel
probesoflarge-scalestructures. (2014)for fsky =0.2.
Forexample,thehighdegreeofcorrelationbetweentheCIBand
φhaverecentlybeenusedtodetectthelensingBmodesofpo-
larizationbytheSPTcollaboration(Hansonetal.2013).
InFig.2,wepresentourestimationoftheCIB-φcontamina-
Consequently,smallCIBresidualsinatSZComptonparameter
tion considering the set of weights from Hill & Spergel (2014)
mapcanleadtoasignificantbiasinthetSZ-φcorrelationanaly-
andcompareitwiththeexpectedtSZ-φcross-correlationpower-
sis.
spectrumforourfiducialmodel.
Thecontaminationishigh,withasimilaramplitudeasthetSZ-φ
3. CIB-φcontaminationintSZ-φcross-correlation correlation. Furthermore, the contamination level is highly de-
pendentonthesetofweights.Fordifferentsetsofweights,the
3.1. tSZComptonparametermap contaminationvariesanthesameorderofmagnitudeasthetSZ-
φsignal.
The recently released Planck data allow constructing full-sky
ThisvariabilityhighlightsthedifficultyofcontrollingtheCIB-φ
tSZComptonparametermap(PlanckCollaborationresults.XXI
contaminationthatcanleadtoahighbiasintSZ-φanalysis.
2014)usinginternallinearcombination(ILC)componentsepa-
However,thecontaminationlevelishighlydependentontheex-
ration methods (see e.g., Remazeilles et al. 2011; Hurier et al.
actCIBfrequencycorrelationmatrix.Consequently,thederived
2013). These methods reconstruct the tSZ signals using linear
valuehastobeconsideredasanorder-of-magnitudeestimateof
combinations
y=(cid:88)w T , (14) theeffectivecontamination.
ν ν
ν
where Tν is the intensity at the frequency ν and wν are the 4. CleaningtheCIB-φcontamination
weightsofthelinearcombination.ForILC-basedmethods,these
weightsarecomputedbyminimizingthevarianceoftherecon- In their analysis, Hill & Spergel (2014) proposed a method
structedy-mapunderconstraints. of cleaning for CIB-φ contamination in tSZ-φ spectrum. Their
ThelevelofCIB-φcontaminationinatSZ-φanalysisbasedona methodconsistsofacorrectionoftheform
tSZComptonparametermapdependsontheweights,w ,used
forthelinearcombination. ν C(cid:96)φ×y,corr =C(cid:96)φ×y−αcorrC(cid:96)φ×CIB(857), (16)
We here considered the weights provided in Table 2 of Hill &
Spergel (2014), which have been used to constrain the cosmol- whereCφ×yisthemeasuredcorrelationbetweenthetSZandpo-
(cid:96)
ogyfromthetSZ-φcross-correlationpower-spectrum. tential maps. The factor α is computed from an adjustment
corr
ofCCIB(857)×CIB(857) onthecross-correlationofthetSZCompton
(cid:96)
parameterandthe857GHzmaps.
3.2. PropagationofCIB-φspectra
Weproposetotesttheaccuracyofthisprocedureusingourmod-
We stress that the CIB is composed of different populations of ellingofthetSZ,φ,andCIBcross-correlations.Intheiranalysis
objects at different frequencies. The associated power-spectra Hill&Spergel(2014)neglectedthetSZ-CIBcorrelationcontri-
present variations of shape with respect to the frequency. The butionforcomputingα .However,attheconcernedfrequen-
corr
CIB-φ spectra present the same variations of shape with fre- cies, the tSZ-CIB correlation factor can reach about 20% and
quency.TheCIB-φcontaminationinthetSZ-φcross-correlation therefore cannot be neglected. Neglecting tSZ-CIB correlation
3
G.Hurieretal.:CIB-φcontaminationinthecross-correlationofthetSZeffectandφ
forthecleaningprocessleadstoanunderestimationoftheCIB- Acknowledgment
φcontamination.Inanoptimisticcase4,α reads
corr We are grateful to N.Aghanim and M.Douspis for usefull
(cid:42)(cid:16)(cid:80)w CCIB(ν)×CIB(857)(cid:17)+CtSZ×CIB(857)(cid:43) discutions.
α = ν (cid:96) (cid:96) . (17) WeacknowledgethesupportoftheFrenchAgenceNationalede
corr CCIB(857)×CIB(857) laRechercheundergrantANR-11-BD56-015.
(cid:96)
Wecomputedthisvalueforeachsetofweightsat(cid:96) = 600.The
valueofα variesby3%dependingonthevalueof(cid:96)usedfor
corr
the computation (300 < (cid:96)<1500), with a higher level of con- References
tamination using higher (cid:96) values. Hill & Spergel (2014) found
Blanchard,A.&Schneider,J.1987,A&A,184,1
αcorr =(6.7±1.1)×10−6KC−1MBfor fsky =0.3.Consideringtheas- Fixsen,D.J.,Dwek,E.,Mather,J.C.,Bennett,C.L.,&Shafer,R.A.1998,ApJ,
sociatedsetofweightwepredictα =(7.1±0.2)×10−6K−1 508,123
corr CMB Hanson,D.,Hoover,S.,Crites,A.,etal.2013,PhysicalReviewLetters,111,
for300<(cid:96) <1500.Withthis,weestimatetheassociatedresid-
141301
ualcontaminationinthetSZ-φspectrumas Hill,J.C.&Spergel,D.N.2014,J.CosmologyAstropart.Phys.,2,30
Hurier,G.,Macías-Pérez,J.F.,&Hildebrandt,S.2013,A&A,558,A118
 
C(cid:96)res =(cid:88)wνC(cid:96)φ×CIB(ν)−αcorrC(cid:96)φ×CIB(857). (18) KMoom,Hat.suJ.,&E.W&hKitiet,aySa.mDa.,MT..11999969,,MApNJR,5A2S6,,2L812,347
PlanckCollaborationresults.XVII.2014,A&A,571,A17
ν
PlanckCollaborationresults.XVIII.2014,A&A,571,A18
In Fig. 2, we present the obtained residuals for the set of PlanckCollaborationresults.XX.2014,A&A,571,A20
PlanckCollaborationresults.XXI.2014,A&A,571,A21
weights from Hill & Spergel (2014). The CIB-φ residual con-
PlanckCollaborationresults.XXX.2014,A&A,571,A30
tributeswith(20±10)%ofthetSZ-φsignalfor(cid:96)rangingfrom
Puget,J.-L.,Abergel,A.,Bernard,J.-P.,etal.1996,A&A,308,L5
500to2000. Remazeilles,M.,Delabrouille,J.,&Cardoso,J.-F.2011,MNRAS,410,2481
This level of contamination is dependent on the CIB luminos- Shang,C.,Haiman,Z.,Knox,L.,&Oh,S.P.2012,MNRAS,421,2832
ityfunction(seeSect.2.2).Theuncertaintylevelwasestimated Sunyaev,R.A.&Zeldovich,Y.B.1969,Nature,223,721
Sunyaev,R.A.&Zeldovich,Y.B.1972,CommentsonAstrophysicsandSpace
by propagating the CIB luminosity function uncertainties (see
Physics,4,173
PlanckCollaborationresults.XXX2014,fordetailsonestimat- Tinker,J.,Kravtsov,A.V.,Klypin,A.,etal.2008,ApJ,688,709
ing the CIB luminosity function parameters). This uncertainty
levelisdominatedbyδ and(cid:15) ,whichsettheamountofcor-
cib cib
relationbetweentheCIBmapsobservedatdifferentfrequencies.
Other parameters, such as b or CIB SED parameters, have a
lin
weakereffectontheCIB-φresidualestimation.
5. Conclusionanddiscussion
We have presented a modelling of the tSZ-φ-CIB cross-
correlations.Basedonthismodelling,wepredictedtheexpected
CIB-φcontaminationinthetSZ-φpower-spectradeducedfrom
a Compton parameter map built by linearly combining Planck
channelsfrom100to857GHz.
Wedemonstratedthattheexpectedlevelofcontaminationfrom
theCIB-φisatthesamelevelasthetSZ-φsignalitself.
We also demonstrated that the CIB-φ contamination level is
highlydependentonthesetofweightsusedforconstructingof
theComptonparametermap.Todothis,weusedrealisticvalues
deducedfromthesky,fortheweights.
We tested a cleaning method for this bias and showed that the
level of residual bias can reach about 20% of the tSZ-φ spec-
trumfortheusedsetofweights.Consequently,westressthatan
tSZ-φanalysisthatis basedonamulti-frequencyComptonpa-
rameter map may present a high level of bias. A careful CIB-φ
analysishastobeperformedsimultaneouslytoatSZ-φanalysis
toavoidhighbiasinthefinalresults.
Hill&Spergel(2014)constrainedσ (Ω /0.282)0.26 = 0.824±
8 m
0.029 and found that the tSZ-φ power-spectrum scales as σ6.1.
8
Thus,abiasof(20±10)%onthethetSZ-φamplitudeproduces
a bias of (3.3±1.7)% on the σ amplitude. As a consequence,
8
theCIB-φinducedresidualbiasinthismeasurementcontributes
about1σoftheuncertainty.Suchabiasmayexplainthediffer-
encebetweenthetSZ-φcross-correlationandcosmologicalpa-
rameterestimationmadewithatSZspectrum.Thelatterfavours
lowervaluesforσ ,withσ (Ω /0.28)0.395 =0.784±0.016.
8 8 m
4 Withoutuncertaintiesorsystematicsforthecomputationofα
corr
4