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Gravitational lensing and the Sunyaev-Zel'dovich effect in the millimetre/submillimetre waveband PDF

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Preview Gravitational lensing and the Sunyaev-Zel'dovich effect in the millimetre/submillimetre waveband

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed1February2008 (MNLATEXstylefilev1.4) Gravitational lensing and the Sunyaev–Zel’dovich effect in the millimetre/submillimetre waveband A. W. Blain Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE. 1February2008 8 9 9 ABSTRACT 1 The intensity of the cosmic microwave background radiation in the fields of clusters n ofgalaxiesis modified byinverseComptonscatteringinthe hot intraclustergas– the a Sunyaev–Zel’dovich(SZ)effect.Theeffectisexpectedtobemostpronouncedatafre- J quencyofabout350GHz(awavelengthofabout800µm),andhasbeendetectedinthe 2 centimetre andmillimetre wavebands.In the millimetre/submillimetre waveband,the 1 gravitationally-lensedimagesofdistantdustystar-forminggalaxiesinthebackground of the cluster are predicted to dominate the appearance of clusters on scales of sev- 1 eralarcseconds,and couldconfuse observationsof the SZ effect at frequencies greater v thanabout200GHz(wavelengthsshorterthanabout1.5mm).Recentobservationsby 9 Smail,Ivison&Blain(1997)confirmthatasignificantpopulationofconfusingsources 9 are present in this waveband. Previous estimates of source confusion in observations 0 1 ofthemillimetre/submillimetre-waveSZeffectdidnotincludetheeffectsoflensingby 0 the cluster, and so the accuracy of such measurements could be lower than expected. 8 Source subtraction may be required in order to measure the SZ effect accurately,and 9 a careful analysis of the results of an ensemble of SZ measurements could be used to / impose limits to the form of evolution of distant dusty star-forming galaxies. h p Keywords: galaxies:clustering–galaxies:evolution–cosmicmicrowavebackground - o – cosmology: observations – gravitationallensing – radio continuum: galaxies r t s a : v 1 INTRODUCTION source confusion in the absence of gravitational lensing are i X discussed byBlain, Ivison & Smail (submitted – BIS). Theprincipalsourcesofmillimetre/submillimetre-wave r a Gravitational lensing can have a more significant effect radiation from clusters are the SZ effect and thelensed im- on the population of galaxies detected in the millime- agesofdistantdustybackgroundgalaxies.Othersourcesare tre/submillimetre waveband as compared with other wave- star-formingoractivegalaxieswithinthecluster,theRees– bands;Blain(1996a,b;1997a,b–Paper1;1997c,1998)gives Sciama (RS) effect (Rees & Sciama 1968; Quilis, Ib´an˜ez & details of the effects of lensing by both galaxies and clus- Saez 1995) and primordial CMBR anisotropies. We discuss ters. Here we consider the effects of the lensed images of the properties and relative importance of all five sources background galaxies in millimetre/submillimetre-wave ob- in Section 2, and estimate the source confusion noise ex- servations of clusters on arcminute angular scales that are pected due to the lensed images of distant galaxies in Sec- suitable to detect the modifications to the intensity of the tion 3. In Section 4 the consequences of this confusion for cosmicmicrowavebackgroundradiation(CMBR)duetothe millimetre/submillimetre-wave observationsoftheSZeffect Sunyaev–Zel’dovich(SZ)effect(Sunyaev&Zel’dovich1980; are discussed, and the prospects for using the same obser- Rephaeli 1995b). Lensed images are not expected to be re- vations to detect the signature of galaxy evolution in the solved on these scales, but they could produce significant population of lensed images are assessed. Throughout this source confusion because of their uncertain spatial distri- paper we assume that the density parameter Ω0 = 1 and bution in the observing beam. Accurate estimates of this that Hubble’sconstant H0 =50kms−1Mpc−1. confusion could be necessary in order to interpret the re- sults of observations of the SZ effect. The importance of source confusion in this waveband has recently been con- firmed by the 850-µm observations of lensed images in the 2 SOURCES OF MILLIMETRE/SUBMILLI- clusters ABell370 and Cl2244−02 (Smail, Ivison & Blain METRE-WAVE RADIATION IN CLUSTERS 1997 – SIB). The effects of millimetre/submillimetre-wave (cid:13)c 0000RAS 2 A. W. Blain 2.1 The Sunyaev–Zel’dovich effect The SZ effect describes the modifications to the spectrum of theCMBR duetoinverseCompton scattering in thehot X-ray emitting gas bound to clusters of galaxies. It is usu- allyseparated intotwocomponents:athermaleffect,which describes the net energy gain of CMBR photons scattered by hot gas moving with the Hubble flow; and a kinematic effect, which describes the net Doppler shift of the photons scattered in a cluster with a non-zeropeculiar velocity. If the scattering gas is non-relativistic, then the ther- malSZeffectproducesacharacteristicincrementanddecre- ment to the CMBR intensity above and below a fre- quency of 217GHz respectively. The magnitude of this ef- fect is independent of the redshift of the scattering gas and is determined by a single dimensionless parameter y = τσTkBTe/(mec2),in which τ is thescattering optical depth Figure 1.Predictions of the spectrum of the thermal andkine- of the cluster and σT, Te and me are the electron scatter- matic SZ effects in a typical rich cluster. The frequency of the ing cross section, temperature and mass respectively. The y-parameteris typically several times 10−4 in a rich cluster peakinthe CMBRspectrum is160GHz. Observedlimitstothe intensity of diffuse extragalactic background radiation and the of galaxies (Rephaeli 1995b), and |y|<1.5×10−5 over the frequenciesofimportantobservingbandsarealsoshown. whole sky (Fixsen et al. 1996). The magnitude of the kine- matic SZ effect, which is expected to be smaller than the thermalSZeffectinatypicalcluster,isproportionaltoτvr, 2.2 Lensed images of background galaxies wherevr isthepeculiarvelocityofthescatteringgas. Ifthe The properties of the lensed images of distant dusty star- scattering gas is relativistic, then the form of the thermal forming galaxies lensed by a rich cluster at a redshift zc = effectisnolongerdescribedcompletelybythey-parameter, 0.17werediscussedinPaper1,andareexpectedtohaveflux and the values of both τ and Te affect the spectrum of the densitiesintherange1to10mJyat850µm,comparableto CMBR independently(Rephaeli 1995a). orlargerthanthefluxdensitiesofanystar-forminggalaxies ThespectrumofboththethermalandkinematicSZef- within the lensing cluster. Distant galaxies are expected to fects expected for two clusters, both with τ = 10−2 and be relatively bright in the millimetre/submillimetre wave- vr = 1000kms−1, are shown in Fig.1. One cluster con- band because the K-corrections due to redshifting the dust tains non-relativistic electrons with kBTe < 5keV and has emissionspectraofdistantgalaxiesareexpectedtobelarge y=1.4×10−4;theothercontainsrelativisticelectronswith and negative as compared with other wavebands (Blain & kBTe =10keV. Limits to the intensity of the diffuse extra- Longair 1993a). Hence, faint galaxies detected in the mil- galactic background radiation from the FIRAS instrument limetre/submillimetre waveband are typically expected to ontheCOBEsatellite(Pugetetal.1996;Fixsenetal.1996) haveredshiftsmuchlargerthanzc,andso,evenifzcwerein- are also shown. creased substantially, a large surface density of background The centimetre-wave SZ effect has been detected by galaxies and lensed images would still be expected. Birkinshaw (1990), Uyaniker et al. (1997) and Myers et al. SIB have recently detected examples of such distant (1997) atfrequenciesof20.3, 10.55and32GHzrespectively dusty galaxies in the fields of the clusters A370 and using single-antenna telescopes, and by Jones et al. (1993) Cl2244−02 at zc = 0.37 and 0.33 respectively. The surface andCarlstrom,Joy&Grego(1996)usinginterferometersat density of these objects is larger than that predicted pre- 15 and 30GHz respectively. Recently, Grainge et al. (1996) viously (Blain & Longair 1996), but is consistent with the produced the first image of the SZ effect at 15GHz. In the observed background radiation intensity in the far-infrared millimetre waveband, the SZ decrement has been detected waveband (Puget et al. 1996) and with recent observations nearthepeakoftheCMBR spectrumat2.2mm(Wilbanks oftheHubbleDeepFieldatawavelengthof2.8mm(Wilner etal.1994),usingtheSuZIEbolometerarrayreceiveratthe & Wright 1997). Even in the absence of gravitational lens- Caltech Submillimeter Observatory (Holzapfel et al. 1997), ing these sources are expected to contribute a significant and Andreani et al. (1996) have detected the SZ increment amount of confusion noise to some observations in the mil- at 1.2mm. Silverberg et al. (1997) recently detected the limetre/submillimetre waveband (BIS). submillimetre-wave SZ effect in the direction of the Coma cluster at four frequencies but low significance using the MSAM balloon-borne experiment. 2.3 Other sources of radiation CurrentobservationsoftheSZeffectareconsistentwith The far-infrared radiation emitted by dust in star-forming acoredisothermalsurfacebrightnessdistribution,whichde- pends on angular radius θ as [1 + (θ/θc)2]−1/2. The rich galaxies within a cluster could produce a detectable flux densityinthesubmillimetrewaveband.Thefractionofblue clusters Abell 2218 and Abell 2163 at redshifts zc = 0.171 star-forming galaxies in clusters tends to increase with in- and0.201 havecore radiiθc ≃50and 70arcsec respectively creasingredshift,describedastheButcher–Oemler(BO)ef- (Squireset al. 1996; Elbaz, Arnaud& B¨ohringer 1995). fect(Butcher1978,Lavery&Henry1994,Couchetal.1994), and would correspond to an increase in the luminosity of thesegalaxies in the far-infrared waveband. (cid:13)c 0000RAS,MNRAS000,000–000 Lensing and the SZ effect 3 The Rees–Sciama (RS) effect is expected to produce Lange (1993) discussed the effects of unlensed source con- a signal with a spectrum similar to that of the CMBR. If fusion on observations of the SZ effect, and estimated that the density of the core of a cluster evolves during its light theconfusionnoiseatawavelengthof850µmina1-arcmin crossing time, then the gravitational blueshift imposed on observing beam should be about 20 times smaller than the a CMBR photon as it falls into the cluster is not matched signal of the SZ effect from a cluster with y = 10−4. BIS by the gravitational redshift imposed as it climbs out, and estimate that source confusion at 850µm is actually about sothespectrumoftheCMBR ismodified.Quilis, Ib´an˜ez& a factor of 7 times more severe than this earlier value. Saez (1995) have calculated the largest possible signal due Confusion noise in the field of a cluster should be in- to this effect. creasedbygravitationallensing,becauseboththemeansep- Gravitational lensing of primordial anisotropies in the arationandfluxdensityofbrightlensedimagesareexpected CMBR would lead to tobe larger than those of unlensed background galaxies. In a spatially-correlated millimetre/submillimetre-wave back- the following sections we estimate the size of this increase groundsignal on scales similar totheEinstein radiusof the and discuss its effects on observations of the SZ effect. In lensing cluster (Paper1). order to make an accurate measurement of the SZ effect, the flux densities of confusing sources may need to be sub- tracted from the observed signal. This is usually achieved 2.4 The relative importance of these sources by observing the cluster to the same limiting flux density butatafinerangularresolution,inordertodetectthecon- The frequency-dependent surface brightness of the SZ in- fusing galaxies while resolving out the SZ signal. Loeb & crement to the CMBR intensity in the core of a cluster with y=1.4×10−4 shouldpeak at about 6µJyarcsec−2 at Refregier (1997) have shown that this procedure could in- troduce a subtle bias into measurements of the SZ effect. a wavelength of about 850µm (Fig.1). In comparison, the Because lensed images are typically brighter than unlensed largestvaluesofsurfacebrightnessofresolvedlensedimages galaxies, a larger fraction of their total number can be de- andgalaxiesintheclusteratzc =0.171thatwasmodeledin Paper1 were about 60 and 6µJyarcsec−2 respectively. The tected at any flux density limit as compared with unlensed galaxies.Theimagesareexpectedtobemorestronglymag- RS effect and primordial CMBR anisotropies are expected nified in the inner few arcminutes of the field of a cluster, to produce much smaller surface brightnesses of order 300 and 30nJyarcsec−2 respectively at their maximum intensi- and so source subtraction is expected to be more efficient there as compared with the outer regions of the field. It ties (Paper1). is this difference in efficiencies that introduces the system- Themillimetre/submillimetre-wavefluxdensitiesofany atic error into the SZ measurement. However, this effect is dustystar-forming galaxies withinaclusterareexpectedto not of immediate concern in the millimetre/submillimetre be considerably smaller than those of the lensed images of waveband, because accurate source subtraction will be im- distant galaxies unless thegalaxies are in acluster at alow possible in this waveband until large interferometer arrays redshift, that is if zc is significantly less than 0.1 (Paper1). areavailable(Brown1996;Downes1994,1996).Thecurrent The spectral energy distributions of distant lensed images accuracy of millimetre-wave observations of the SZ effect is should be flatter than those of cluster galaxies, and so at limited by the uncertain flux densities of all the confusing higher frequencies the cluster galaxies should be relatively galaxies and not just by theirincomplete subtraction. brighter as compared with the lensed images; however, the lensedimagesarestillexpectedtobebrighterthantheclus- ter galaxies throughout themillimetre/submillimetre wave- 3.2 The procedure band.Thetypicalfluxdensitiesofthelensedimagesshould approximately follow theenvelopetotheobserved limits to The effects of gravitational lensing on source confusion was thebackground radiation intensity shown in Fig. 2. estimated by combining several different models of galaxy Lensedimagesareexpectedtodominatetheappearance evolution (Blain & Longair 1996) with a model of lensing of clusters on arcsecond scales; however, on larger angular byclusters(Paper1).Alargesetofrandomdistributionsof scales the surface brightness distribution of the SZ effect background galaxies and their lensed images were derived, becomes more significant, and the SZ signal is expected to and their surface brightness distributions were convolved dominate in observations on arcminutescales at 850µm. with Gaussian beams on various scales in order to produce distributions of the flux densities due to both lensed and unlensed sources in the beams. The widths of these distri- butionswerethenusedtopredictthesourceconfusionnoise 3 ESTIMATING SOURCE CONFUSION expected with and without gravitational lensing. 3.1 Introduction Source confusion is the uncertainty introduced into the re- 3.2.1 Modeling galaxy formation and evolution sults of an observation by the flux densities of unresolved sourcesthatlieatunknownpositionsintheobservingbeam. Three models of the evolution of the population of dusty Source confusion due to extrapolated and inferred popu- star-forming galaxies are included in this paper; models I1 lations of distant dusty galaxies has been estimated by and I2 are based on pure luminosity evolution of the IRAS Franceschini et al. (1989, 1991), Helou & Beichman (1990), luminosity function (Saunders et al. 1990), and model H is Toffolatti et al. (1995) and Gawiser & Smoot (1997). BIS based on a model of mergers in an hierarchical clustering have recently made the first estimates to be based on the scheme (Blain & Longair 1993a,b) that is derived from the resultsofdirectsubmillimetre-waveobservations.Fischer& Press–Schechter formalism (Press & Schechter 1974). The (cid:13)c 0000RAS,MNRAS000,000–000 4 A. W. Blain Figure 2. Thepredicteddiffusebackgroundintensitiesinthree Figure 3. The relative amplitude of the 1σ confusion noise ex- models of galaxy formation (Table1), limits to the intensity of pectedwithandwithoutlensinginabeam-switchedobservation diffuse background emission and the spectrum of the SZ effect of the SZ effect due to distant dusty star-forming galaxies as a (Fig.1). Note that the diffuse background intensities are much function of beam-width. The predicted amplitudes are different largerthantheexpected levelofsourceconfusionnoise. in model H as compared with models I1 and I2. An arbitrarily- normalisedSZsignalisalsoshown. models are described in more detail by Blain & Longair (1996),inwhichmodelI1waslabelledmodel3.InmodelI1 uesofthefluxdensityofunresolvedsourcesoneachangular pureluminosityevolutionisbyafactor(1+z)3 whenz≤2 scale. After repeating this process many times thewidth of andbyafactor27when2<z ≤5.InmodelI2,the(1+z)3 theresultingdistributionsoffluxdensityvalues, σI(θb)and form of evolution extends to a larger redshift z = 2.6, and σS(θb) for lensed and unlensed sources respectively, were theevolution factor is 46.7 when 2.6<z≤7. Model I2was determinedandusedtoestimatetheconfusion noise.These usedtodescribetheobservedcountsofSIB.Thebackground widths were defined as half the range of flux density that radiation intensities predicted by each model are shown in included 60 per cent of the simulated flux densities. Any Fig.2 and are consistent with the observed limits to the difference in the mean flux density in the simulated lensed diffuse background radiation intensity (Puget et al. 1996; and unlensed fields gives an estimate of the residual signal Fixsen et al. 1996). expectedduetolensing;thisdifferencewasalwaysfoundto besmaller than σI and σS. TheSZeffectcanbedetectedbyeithermakingafully- 3.2.2 Modeling the effects of lensing sampled image of the field of a cluster or in a ‘beam- A ray-tracing method for determining the distribution and switched’ observation that measures the differential signal properties of the lensed images of galaxies behind a cluster between a beam that is centred on the core of the cluster was demonstrated in Paper 1. A spherical model of a lens- anda referencebeam thatis offset byseveral beam-widths. ing cluster with properties similar to those of Abell 2218 The confusion noise expected in a beam-switched observa- was used (Natarajan & Kneib 1996); that is, with a veloc- tion is given by the quadrature sum of the values of confu- ity dispersion σV = 1360kms−1 at a redshift zc = 0.171 sion noise in each beam, which are both given by σS if the (Kneib et al. 1996). The effects that different values of σV effectsoflensingareneglected,andbyσIandσSiflensingis andzc haveonthepredictedsourceconfusion arediscussed included. In an imaging observation, estimates of confusion in Section3.4. noise with and without lensing are given directly by σI and σS respectively. 3.2.3 Combining the models 3.3 The results The source confusion with and without gravitational lens- ing was estimated from a large number of surface bright- The estimates of confusion noise presented here were de- ness distributions at chosen frequencies in the millime- rived from simulations in 240 random fields at wavelengths tre/submillimetre waveband, which were set up in 10- of 2mm, 1.2mm, 850µm and 450µm. The dependence of arcmin-wide fields using galaxies drawn at random from confusion noise on beam-width was found to be very simi- the luminosity functions describing the galaxy distribution larat each wavelength;Fig.3shows thecombinedprofileof expected in models I1, I2 and H above. The correspond- theresultsatallfourwavelengths,withandwithoutlensing ing surface brightness distribution of the lensed images of for model H and for models I1 and I2. A typical predicted these galaxies in each field were then determined using the profileoftheSZsignalisalsoshown.Theincreaseinsource lensing model. Each lensed and unlensed surface bright- confusion due to gravitational lensing is most pronounced ness distribution was then convolved with a set of Gaus- when the beam-width θb is matched to the Einstein radius sianbeams,withfull-width-half-maximum(FWHM)beam- of the lensing cluster θE, that is when θb ∼ 2θE. In these widthsθb between5and300arcsecinordertoproduceval- calculations θE ≃16arcsec (Paper 1), and so source confu- (cid:13)c 0000RAS,MNRAS000,000–000 Lensing and the SZ effect 5 sion is predicted to increase most significantly, by a factor ofabout3,atθb ≃32arcsec.Thepredictedincreaseincon- fusion is smaller inlarger beams, andtendsgradually toits unlensed value when θb ≫θE. The modifications to the confusion noise due to lens- ing take this form because the most strongly magnified im- ages are formed at angular radii close to θE; most images at smaller radii are demagnified, and images at larger radii are magnified by progressively smaller amounts. In a beam smallerthantheEinsteinradius,lensingmodifiestheconfu- sionnoiseslightly,butasθbincreasestowards2θE,asteadily increasing fraction of the flux density from strongly magni- fied images at θE is included in the observing beam, and so the confusion noise increases. As θb increases above θE, the less strongly magnified images at radii larger than θE contributeasteadilyincreasingfractionofthedetectedflux density; therefore, the contribution of the strongly magni- Figure 4.The1-σ confusionnoiseexpected inabeam-switched fied images at radii near θE is steadily diluted, and so the observationoftheSZeffectwithandwithoutlensingina1-arcmin confusion noise tendsgradually toits unlensed value. beam. The confusion estimates of Franceschini et al. (1991) and The confusion noise expected in each observing band Fischer&Lange(1993; dotted lines)arealsoshown.CC andCI andmodelofgalaxyevolutionisshowninTable1andFig.4. areestimatesoftheconfusionduetogalacticcirrusemissionand Theresultsforbeam-widthsof1and2arcminarepresented IRAS galaxies respectively. CI is very similar to the estimate of confusionnoiseinHelou&Beichman(1990). in Table1, while in Fig.4 the results in a 1-arcmin beam are compared with earlier estimates. The estimates of un- lHenelsoeud&coBnfeuicsihomnannoi(s1e99a0re) asingdniFfiicsacnhtelry&larLgaenrgteh(a1n99th3)o,sebuotf (1+zc)σV10/3/D(0,zc)2. A beam correction can be added to calculate the SZ signal expected from clusters that are aremoresimilartothoseofFranceschinietal.(1991).They resolved in smaller observing beams. areingood agreementwithobservationally-basedestimates The expected dependence of both the confusion noise (BIS). Confusion noise is expected to dominate the SZ sig- and the SZ signal at a wavelength of 850µm for clusters nal at a wavelength of 450µm and to be very significant at with 0.05 ≤ zc ≤ 1 and 800kms−1 ≤ σv ≤ 2000kms−1 wavelengthsof850µmand1.2mm.Ina1-arcminbeam the is shown in Figs5(a) & 5(b) for model I1. The results are lensed confusion noise is always predicted to be at least 20 normalised to match the predictions for the model lensing percentoftheSZsignalinallthreemodels.Onlyatawave- cluster in the previous sections, which had zc = 0.171 and length of 2mm is the SZ signal expected to be much larger σV = 1360kms−1. The confusion noise is expected to be thantheconfusionnoise.Theseresultssuggestboththatthe smaller and larger by a factor of a few in models H and I2 kinematicSZeffectwouldbedifficulttodetect,andthatthe respectively. Confusion noise is expected to be less signifi- thermal SZ effect would be difficult to measure accurately, cantascomparedwiththeSZsignalinobservationsofmore inanobservationofasinglecluster,unlessthepopulationof massive and more distant clusters that are made in larger distantdustystar-forming galaxies isverysparseorevolves beams,asshownbythesignal-to-noiseratiosinFigs5(c)& veryweakly.Inthelight of recentobservations (SIB)either 5(d). of these scenarios appears veryunlikely. 4 CONFUSION NOISE AND OBSERVATIONS 3.4 The mass and redshift of the lensing cluster 4.1 Existing observations The key parameter that determines the effects of gravita- tional lensing on the confusion noise in an observation is Threeground-baseddetectionsofthemillimetre-waveSZef- the Einstein radius of the lensing cluster θE, which in turn fect havebeen published;for Abell 2163 at a wavelength of depends on the redshift zc, velocity dispersion σV and in- 2.2mm in a 1.4-arcmin-wide beam (Wilbanks et al. 1994), ternal structure of the cluster. If the cluster is assumed to and for Abell 2744 and S1077 at wavelengths of 2 and be an isothermal sphere, and D(z,zs) is the angular diam- 1.2mm in 46- and 44-arcsec-wide beams respectively (An- eter distance between a redshift z and a source at redshift dreanietal.1996).Thedetectedfluxdensitiesandestimates zs, then θE ∝ D(zc,zs)σV2 (Paper 1). Note that because zs ofthesourceconfusionnoiseintheseobservationsarelisted is typically much larger than unity for faint submillimetre- in Table2. wavesources,increasingzc doesnotsignificantlyreducethe Silverberg et al. (1997) observed the Coma cluster at surfacedensityofbackgroundsources,andsotheonlysignif- four frequencies using MSAM, a balloon-borne experiment, icanteffect ofchangingzc ontheexpectedconfusion dueto to search for the submillimetre-wave SZ effect. Because of lensed images isintroducedthroughtheresulting changein the 28-arcmin beamwidth in this experiment, gravitational θE.ThedependenceoftheSZsignalfromanunresolvedclus- lensingwillhaveaninsignificanteffectontheconfusionnoise teronσV andzc wasdiscussedbyDeLuca,D´esert&Puget in thisobservation. They estimate that CMBR fluctuations (1995),usingmodelsofclusterevolutionfromKaiser(1986) at an intensity ∆T/T ≃ 2×10−5 would be a significant and Bartlett & Silk (1994), and found to take the form sourceofconfusioninthisobservation.Distantdustygalax- (cid:13)c 0000RAS,MNRAS000,000–000 6 A. W. Blain Table 1. Estimates of the 1σ confusion noise expected for SZ measurements due to lensed and unlensed background galaxies. The y-parameter and core radius of the cluster are assumed to be 1.4×10−4 and 50arcsec respectively. The estimates are uncertain to withinabout10percent. Frequency/ FWHM SZ 1-σ confusionnoise: RatioofSZsignaltoconfusion GHz(Wave- beam signal lensed(unlensed)/mJy noise:lensed(unlensed) length/µm) /arcsec /mJy ModeII1 ModelI2 ModelH ModeII1 ModelI2 ModelH 150(2000) 60 -11.7 0.54(0.24) 0.77(0.46) 0.46(0.17) 22 (49) 15 (25) 25 (69) 120 -36.3 0.93(0.54) 1.48(0.90) 0.78(0.36) 39 (68) 25 (40) 47 (100) 250(1200) 60 7.32 3.24(1.42) 4.51(2.57) 1.42(0.55) 2.3 (5.2) 1.6 (2.9) 5.2 (13) 120 22.7 5.58(3.13) 8.79(5.23) 2.42(1.14) 4.1 (7.3) 2.6 (4.3) 9.4 (20) 350(850) 60 20.5 9.39(3.89) 12.4(6.88) 2.26(0.93) 2.2 (5.3) 1.7 (3.0) 9.1 (22) 120 63.6 16.0(8.56) 24.6(14.3) 3.94(1.98) 4.0 (7.4) 2.6 (4.4) 16 (32) 670(450) 60 3.61 41.3(14.3) 44.0(23.2) 4.22(2.46) 0.09(0.25) 0.08(0.16) 0.86(1.5) 120 11.2 66.6(31.9) 90.5(49.1) 7.96(5.76) 0.17(0.35) 0.12(0.23) 1.4 (1.9) (a) (b) (c) (d) Figure5.Theeffectsoftheredshiftzc andvelocitydispersionσV ofaclusterontheSZsignalandsourceconfusionnoiseexpectedat 850µminmodelI1.ThepropertiesoftheclustersarenormalisedtomatchthemodeldescribedinSection3.2.2,whichwassimilarto A2218withσV=1360kms−1 andzc=0.171.TheSZsignalandconfusionnoiseasafunctionofbeam-widthforaclusteratzc=0.1, 0.2, 0.5 and 1 are shown in (a); in (b) the same quantities are shown for a cluster with σV =800, 1200, 1500 and 2000kms−1. The ratiooftheSZsignaltotheconfusionnoiseexpected forarangeofvaluesofzc andσV areshownin(c)and(d)respectively. iesareexpectedtocontributeasignificantamountofconfu- mass profile of A2163 is assumed to be scaled from that sion noise in only thehighest frequency channel,equivalent of A2218, then these observations indicate an Einstein ra- to ∆T/T ≃4×10−5 at 678GHz (BIS). dius θE ≃ 24arcsec, which leads to the estimates of con- fusion noise listed in Table2. Hence, although we expect A2163 lies at a redshift zc = 0.201, has a core ra- lensingtoincreasethelevelofsourceconfusionnoiseinthis dius θc ≃ 70arcsec (Elbaz, Arnaud & B¨ohringer 1995), and σV = 1680kms−1 (Markevitch et al. 1996). If the observation, it should not exceed about 1 per cent of the (cid:13)c 0000RAS,MNRAS000,000–000 Lensing and the SZ effect 7 detected SZ signal in this cluster. Upgraded versions of the Table2.Estimatesofsourceconfusionnoiseinexistingobserva- SuZIEinstrument used in this observation (Holzapfel et al. tionsoftheSZeffect(Wilbanksetal.1994;Andreanietal.1996). 1997) continue to offer excellent performance for detecting TheresultsarederivedinSection4.1.Theobservingwavelength themillimetre/submillimetre-wave SZ effect. λandreportedSZsignalSSZ arealsolisted. TheSZsignalslistedinTable2forA2744andS1077,at Cluster λ/ SSZ / 1-σ confusionnoise: redshiftszc=0.308and0.312respectively,arederivedfrom mm mJy lensed(unlensed) /mJy they-parametersquotedbyAndreaniet al. (1996), andde- ModelI1 ModelI2 ModelH pendonlyweaklyontheassumedcoreradiioftheseclusters. A2163 2.2 -68 0.75(0.36) 1.04(0.60) 0.65(0.25) Thedifferential signal from thisbeam-switched observation A2744 2.0 -19 0.33(0.18) 0.41(0.32) 0.34(0.13) would besmaller byabout30 to40percentduetothesig- 1.2 13 1.80(0.96) 2.27(1.75) 1.00(0.38) nal from the SZ effect that remains in the reference beams S1077 2.0 -26 0.41(0.18) 0.58(0.32) 0.36(0.13) 135arcsec away on the sky. Estimates of the Einstein radii 1.2 18 2.34(0.96) 3.16(1.75) 1.06(0.38) of A2744 and S1077 are required in order to determine the confusion noise expected in these observations. The tem- peratures of 7keV quoted for the intracluster gas in both ever, these instruments have beamwidths of order several A2744andS1077matchthatofA2218(Squiresetal.1996). tensofarcminutesandsotheeffectsofgravitationallensing Hence,ifself-similarclusterevolutionisvalid(Kaiser1986), are unimportant. Applicable estimates of unlensed source then θE ≃ 13arcsec for both clusters. However, the tem- confusion for these experimentscan befound in BIS. perature of 12keV has recently been determined for A2744 (Mushotzky & Scharf 1997), in which case θE ≃ 26arcsec. The values of confusion noise that are predicted assuming 4.2.1 FIRST valuesofθE ≃13and26arcsecforS1077andA2744respec- tively are listed in Table2. These values are greater than At present, the longest observing wavelength of FIRST’s about 1 and 10 per cent of the SZ signal at wavelengths of bolometer instrument is 500µm (Griffin 1997), and so the 2and1.2mmrespectivelyinallthreemodelsofgalaxyevo- instrument’s spectral range is not optimized to detect the lution. In models I1 and I2 the unlensed source confusion peak of the signal due to the SZ effect at a wavelength of at a wavelength of 1.2mm is expected to be several times about 800µm (Fig.1). FIRST’s angular resolution is finer largerthanthevalueof0.4mJysuggestedbyAndreanietal. than about 40arcsec at 500µm, and so any observations (1996). A further increase in confusion noise due to bright of the SZ effect are likely to be affected by source confu- lensed images in the reference beam is very unlikely, be- sion. The expected flux density from the core of a cluster cause thereference beams are separated by 135arcsec from with y =10−4 in a 40-arcsec beam is about 4mJy, as com- thecluster core. pared with estimated lensed and unlensed 1σ source confu- We expect the confusion noise in existing observations sion noise values of at least 6 and 2mJybeam−1 in model of the millimetre-wave SZ effect to be about 1 and 10 per I1, Fig.5(a). FIRST should reach a 1σ sensitivity limit of cent of the SZ signal at wavelengths of about 2mm and about 1mJybeam−1 at 500µm in a 25-arcmin2 field in a 1.2mm respectively, and so these detections are unlikely to 6-hour integration (Griffin 1997), and so a detection would be artifacts of confusion noise. If a large number of detec- be possible in a reasonable integration time in the absence tions of the SZ effect could be obtained at 1.2mm then a of source confusion. However, without resolving and sub- careful analysis of the sources of noise could be used to es- tracting the flux density from confusing sources obtaining timatetheamountofsourceconfusion present,andsolimit a reliable detection for an individual cluster using FIRST theformofevolutionofdistantdustygalaxies.Observations would bedifficult. atseveralwavelengthswouldassistthisanalysis,astheam- plitudeoftheconfusingsignalateachwavelengthshouldbe correlated for each cluster. 4.2.2 Planck Surveyor Ina1-yearall-skysurveyPlanckSurveyorshoulddetectthe 4.2 Future observations SZ effect in about 1.5× 104 clusters with y > 8× 10−5 A range of new instruments and telescopes could detect and core radii subtending about 1arcmin (Bersanelli et al. themillimetre/submillimetre-waveSZeffect.Suitablespace- 1996). The kinematic SZ signal of the brighter clusters in borne instruments includeESA’s Far InfraRed and Submil- thesamplecouldbeusedtodeterminetheirpeculiarveloci- limetreTelescope(FIRST),a3.5-msubmillimetre-wave/far- tiestoan accuracy of about100 to300kms−1 (Haehnelt & infraredtelescope(Pilbratt1997),andPlanckSurveyor(for- Tegmark1996).Similarpredictionshaverecentlybeenmade merly COBRAS/SAMBA; Bersanelli et al. 1996), a CMBR by Aghanim et al. (1997). A 1.5m×1.292m aperture corre- imaging satellite with a 1.5m×1.292m aperture. Suitable spondstoabeam-widthofabout3arcminat850µm,andso ground-basedinstrumentsincludetheSCUBAcameraatthe gravitationallylensedsourceconfusionisnotexpectedtode- James Clerk Maxwell Telescope (Cunningham et al. 1994), gradetheperformanceofPlanckSurveyorbyalargeamount the US-Mexican 50-m Large Millimetre Telescope (LMT) (Fig.5). The unlensed confusion noise expected for Planck (Cortes-Medellin & Goldsmith 1994) and large millimetre Surveyor is discussed by BIS: in the 353-GHz channel, in interferometer arrays (MIAs; Downes 1994). Observations which the thermal SZ signal is expected to be largest, a 1σ by balloon-borne experiments, such as MSAM (Silverberg noise level of about 12mJy is expected in each 19-arcmin2 1997) and BOOMERANG (Lange et al. 1995), are also ca- pixel. The nominal 1σ sensitivity of the Planck survey is pable of detecting the submillimetre-wave SZ effect. How- comparable, at 16mJypixel−1 (Bersanelli et al. 1996). (cid:13)c 0000RAS,MNRAS000,000–000 8 A. W. Blain 4.2.3 SCUBA Southern Array (Downes 1996) should be able to map a 9- arcmin2 fielddowntoa3-σ sensitivityofabout0.13mJyin Ina30-hourintegrationina10-arcmin2fieldSCUBAshould each10-arcsec2 synthesisedbeamatawavelengthof1.3mm be able to detect point sources with flux densities of about ina4-hourintegration.TheMillimeterArray(Brown1996) 7and 40mJy at asignal to noiseratio of 3σ,given thecur- and Large Millimetre and Submillimetre Array (Ishiguro et rentlyattainablesensitivities(SIB,JCMTwebpage).These al. 1992) should offera similar performance. AnMIA could sensitivities match the thermal SZ signal from the core of hence detect the brightest lensed images in a rich cluster clusters with y-parameters of 8.4×10−4 and 0.12 at 850 in a matter of hours, and would be ideal for carrying out and450µm respectively.SCUBAcouldhencedetectaclus- sensitivesourcesubtractioninthemillimetre/submillimetre ter with y = 1.4×10−4 at a signal to noise ratio of about waveband. If an MIA is assumed to have a constant point 0.5σbeam−1 at the centre of the field at 850µm; however, source sensitivity, then the flux density limit at any wave- the cluster could not be detected at 450µm. The resulting lengthcanbeestimated byscaling thevaluegivenaboveat 850-µm map with an angular resolution of about 13arcsec 1.3mm by the areas of the primary and synthesized beams would contain about 200 resolution elements. The surface atotherwavelengths.Inthiscase,thethermalSZeffectfrom brightness of the SZ signal would still have 40 per cent of a cluster with y = 1.4×10−4 and θc = 50arcsec could be its central value at the edge of the field if θc ≃ 50arcsec, detectedbyan MIAwith signal-to-noise ratios ofabout 40, and so the signal to noise ratio for the thermal SZ effect 15, 2 and 6σ in 1-hour integrations at wavelengths of 3, 2, in the observation would be about 3σ. The corresponding 1.3and0.85mmrespectively.AnMIAcouldhenceobtaina kinematic effect would not bedetectable, reaching asignal- very significant detection of the millimetre-wave SZ effect. to-noise ratio of only 0.5 if τvr = 10kms−1. In general, an Confusing sources could besubtracted accurately using ob- observation of a 10-arcmin2 field lasting thours should de- servationson longer baselines, and soa verydetailed image tectthethermalSZeffectfromaclusterwithθc ≃50arcsec of themillimetre-wave SZ effect could be produced. atasignaltonoiseratioofabout0.4[y/10−4]t1/2.Inafixed integrationtime,thesignaltonoiseratioforanobservation of the SZ effect in a circular field centred on the cluster is maximized when the radius of the field is twice that of the 5 CONCLUSIONS cluster core. SCUBA will allow limited source subtraction of the Theeffectsofthelensedimagesofdistantdustystar-forming brightest lensed images in the field, as discussed in Paper1 galaxies on observations of the SZ effect in the millime- and recently confirmed by SIB. However, confusion noise tre/submillimetre waveband, in which distant sources are from fainter images could still be significant. In order to intrinsically bright have been discussed. Such images have subtract a larger fraction of lensed images and reduce the recently been detected bySmail et al. (1997). confusionnoise,observationsusingeithertheLMT,withan (i) Gravitationallensingofdistantgalaxiesisexpectedto angularresolutionlimitofabout5arcsecatawavelengthof increasesourceconfusionnoiseinmillimetre/submillimetre- 1mm,oralargeMIA,withsub-arcsecondresolution,would wave observations of the SZ effect. The most pronounced berequired. increase, by a factor of about 3, is expected in observing beams that are matched to the Einstein radius of the lens- ing cluster. This increased estimate of confusion noise is 4.2.4 Millimetre interferometer arrays not sufficiently large to affect the interpretation of exist- The performance of large MIAs (Downes 1994) was dis- ing millimetre-wave observations of the SZ effect; however, cussed in Paper 1 in thecontext of detecting lensed images itcouldprovideasignificantsourceofnoiseinfutureobser- in the fields of clusters. The large collecting areas and very vations on arcminute scales, and the brightest sources may sensitive receivers of these instrumentswill allow very faint need to be subtracted in order to measure the SZ effect ac- images to be detected at sub-arcsecond angular resolution. curately. However, the instantaneous field-of-view of a large interfer- (ii) The effect of gravitational lensing on confusion noise ometerislimitedtotheprimarybeamareaofitsindividual inthefieldsofclustersdependsonboththeformofthepop- antennas, which is about 0.4arcmin2 for an array of 8-m ulation and evolution of distant star-forming galaxies, and antennasat a wavelength of 1.3mm,and so observations of thesurfacedensityofthelensingcluster.Ingeneral,alarger fields that are several arcminutes in extent would require signal-to-noise ratiowouldbeobtained from anobservation the accurate mosaicing (Cornwell 1992) of many different of a more massive cluster, at a larger redshift, in an ob- fields. A mosaic of about 25 primary beam areas would be serving beam that is several times larger than the Einstein required in order to make the most sensitive detection of radius of thecluster. theSZeffectat850µmfromaclusterwithθc≃50arcsecin (iii) Future millimetre/submillimetre-wave observations a 9-arcmin2 field. Fewer mosaiced fields would be required oftheSZeffectusingground-basedandspace-borneinstru- at longer wavelengths, for which the primary beam area is mentswillbeaffectedbyconfusionindifferentways.Thean- larger. At a wavelength of 3mm the primary beam area of gular resolution of Planck Surveyor is probably sufficiently an array of 8-m antenna would be about 2arcmin2, and so coarse to avoid significantly increased source confusion due a mosaic of only 5 beams would be required to map the to lensing in clusters. Observations using telescopes with cluster. Hence, the most efficient strategy to detect the SZ smaller beams, such as FIRST and ground-based single- effect using an MIA would probably be to observe in the antenna telescopes, will be more seriously affected. Large millimetre rather than thesubmillimetre waveband. millimetreinterferometerarrayswillbeveryvaluableinstru- In a compact array configuration, the proposed Large ments for carrying out source subtraction and will be able (cid:13)c 0000RAS,MNRAS000,000–000 Lensing and the SZ effect 9 todetecttheSZeffectdirectly,mosteasilyinthemillimetre Grainge K., Jones M., Pooley G., Saunders R., Baker J., waveband. 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