Blind component separation for polarized observations of the CMB

We present in this paper the PolEMICA (Polarized Expectation-Maximization Independent Component Analysis) algorithm which is an extension to polarization of the SMICA (Spectral Matching Independent Component Analysis) temperature multi-detectors multi-comp

Mon.Not.R.Astron.Soc.000,000–000(0000)Printed5February2008

A(MNLTEXstyle lev2.2)

BlindcomponentseparationforpolarizedobservationsoftheCMB

J.Aumont,J.F.Mac´ as-P´erez

LaboratoiredePhysiqueSubatomiqueetdeCosmologie,53AvenuedesMartyrs,38026GrenobleCedex,France

arXiv:astro-ph/0603044v3 9 Jan 2007

5February2008

ABSTRACT

WepresentinthispapertheP EMICA(PolarizedExpectation-MaximizationIndependent

ComponentAnalysis)algorithmwhichisanextensiontopolarizationoftheSMICA(SpectralMatchingIndependentComponentAnalysis)temperaturemulti-detectorsmulti-components(MD-MC)componentseparationmethod(Delabrouilleetal.2003).Thisalgorithmallowsustoestimateblindlyinharmonicspacemultiplephysicalcomponentsfrommulti-detectorspo-larizedskymaps.AssumingalinearnoisymixtureofcomponentsweareabletoreconstructjointlytheanisotropieselectromagneticspectraofthecomponentsforeachmodeT,EandB,aswellasthetemperatureandpolarizationspatialpowerspectra,TT,EE,BB,TE,TBandEBforeachofthephysicalcomponentsandforthenoiseoneachofthedetectors.P EM-ICAisspeciallydevelopedtoestimatetheCMBtemperatureandpolarizationpowerspectrafromskyobservationsincludingbothCMBandforegroundemissions.Thishasbeentestedintensivelyusingasa rstapproachfullskysimulationsofthePlancksatellitepolarizedchan-nelsfora14-monthsnominalmissionassumingasimpli edlinearskymodelincludingCMB,andoptionallyGalacticsynchrotronemissionandaGaussiandustemission.Finally,wehaveappliedouralgorithmtomorerealisticPlanckfullskysimulations,includingsynchrotron,realisticdustandfree-freeemissions.

Keywords:–Cosmicmicrowavebackground–Cosmology:observations–Methods:dataanalysis

1INTRODUCTION

MappingtheCosmicMicrowaveBackground(CMB)polarizationisoneofthemajorchallengesoffuturemissionsofobservationalcosmology.CMBpolarizationislinearandthereforecanbede-scribedbythe rstthreeStokesparametersI,QandUwhicharegenerallycombinedtoproducethree elds(modes),T,EandB(Zaldarriaga&Seljak1997).ThepolarizationoftheCMBphotonscarriesextraphysicalinformationsthatarenotaccessiblebythestudyofthetemperatureanisotropies.Thereforeitsmeasurementhelpsbreakingdownthedegeneraciesoncosmologicalparame-tersasencounterwithtemperatureanisotropiesmeasurementsonly(Zaldarriagaetal.1997).Furthermore,thestudyoftheCMBpo-larizationisalsoafundamentaltooltoestimatetheenergyscaleofin ationwhichhasbeenproposedtosolvetheproblemsof atness,ofisotropyandoftheseedperturbationsfortheformationofthestructuresintheUniverse.In ationarymodelspredictthepresenceoftensorperturbationsofthemetricwhichwillleadtoanuniquesignatureintheCMBpolarizationBmodes.Thedetectionofthelatterwouldbeastrongproofofsuchanepochandalsoawaytoconstraintheenergyscaleatwhichin ationoccursbymeasuringthetensortoscalarratio,r(Turner&White1996).

SincethebeginningoftheCMBanisotropiesob-servationswiththeCOsmicBackgroundExplorer(COBE)(Smootetal.1992),agreatamountofexperi-mentshavebeendesignedtodeterminetheCMBtem-

peratureangularpowerspectrum(Netter eldetal.1997;Milleretal.1999;deBernardisetal.2000;Hananyetal.2000;Leeetal.2001;Netter eldetal.2002;Halversonetal.2002;Sieversetal.2003;Rubino-Martinetal.2003;Beno tetal.2003;Hinshawetal.2006;Barkatsetal.2005;Readheadetal.2004;Leitchetal.2005;Tristrametal.2005;Jonesetal.2005).Bycontrast,thepolarizationanisotropies,whicharebetween2and5ordersofmagnitudeweakerthantemperatureonesarenotaccuratelymeasuredyet.A rstdetectionoftheCMBEmodeshasbeenperformedbyDASI(Kovacetal.2002;Leitchetal.2005),CAPMAP(Barkatsetal.2005),CBI(Readheadetal.2004)andmorerecentlybyBOOMER G(Montroyetal.2005)andWMAP(Pageetal.2006).TheTEtemperature-polarizationcrosscorrelationhasbeenmeasuredbyWMAP(Pageetal.2006)andBOOMER G(Piacentinietal.2005).NodetectionoftheCMBBmodeshasbeenreportedyet.Nevertheless,constraintsonthetensortoscalarratio,r,havebeensetbytheWMAPteam.Theysetanupperlimitofr<0.55(95%CL)(Spergeletal.2006)forthetemperatureandpolarizationanalysisandofr<2.2(95%CL)(Pageetal.2006)forapolarization-onlyanalysis.

Thedetectionofsuchlowsignalsispossiblebyimprovingtheinstrumentalsensitivity,butthisisnottheonlyissueinthedeterminationoftheCMBpolarizationpowerspectra.Otheras-trophysicalemissionsasforexamplethedi useGalacticemis-sionincludingfree-free,dustandsynchrotronandtheextragalactic-sourcesemissionsalsocontributetotheskybrightnessatthefre-

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