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1、Mon.Not.R.Astron.Soc.000,000–000(0000)Printed5February2008(MNLATEXstylefilev1.4)Scalarstatisticsonthesphere:applicationtotheCMBC.Monteser´ın1,2,R.B.Barreiro1,J.L.Sanz1andE.Mart´ınez-Gonz´alez11InstitutodeF´ısicadeCantabria,CSIC-Univ.deCantabria,Avda.delos
2、Castross/n,39005Santander,Spain2Dpto.deF´ısicaModerna,Univ.deCantabria,Avda.delosCastross/n,39005Santander,SpainAcceptedReceived;inoriginalformABSTRACTAmethodtocomputeseveralscalarquantitiesofCosmicMicrowaveBackgroundmapsonthesphereispresented.Weconsider
3、herefourtypeofscalars:theHessianmatrixscalars,thedistortionscalars,thegradientrelatedscalarsandthecurvaturescalars.Suchquantitiesareobtaineddirectlyfromthesphericalharmoniccoefficientsaℓmofthemap.Wealsostudytheprobabilitydensityfunctionofthesequantitiesfor
4、thecaseofahomogeneousandisotropicGaussianfield,whicharefunctionsofthepowerspectrumoftheinitialfield.Fromthesescalarsitisposibletoconstructanewsetofscalarswhichareindependentofthepowerspectrumofthefield.Wetestourresultsusingsimulationsandfindagoodagreementbet
5、weenthetheoreticalprobabilitydensityfunctionsandthoseobtainedfromsimulations.Therefore,thesequantitiesareproposedtoinvestigatethepresenceofnon-GaussianfeaturesinCMBmaps.Finally,weshowhowtocomputethescalarsinpresenceofanisotropicnoiseandrealisticmasks.Key
6、words:methods:analytical-methods:statistical-cosmicmicrowaveback-ground1INTRODUCTIONetal.2004,Larson&Wandelt2004,McEwenetal.2004,Cruzetal.2005).AlthoughsomeoftheseresultscouldbeTheCosmicMicrowaveBackground(CMB)iscurrentlyoneexplainedbythepresenceofforegr
7、oundcontamination,inofthemostvaluabletoolsofcosmology,providingwithaothercasestheoriginofthedetectionisuncertainandagreatwealthofinformationabouttheuniverse.Aparticu-primordialorigincannotbediscarded.Theseresultsmo-larlyinterestingsubjectiswhethertheCMBt
8、emperaturetivates,evenmore,thedevelopmentofnoveltechniquestoarXiv:astro-ph/0511308v110Nov2005fluctuationsfollowornotaGaussiandistribution.ThisisperformfurtherGaussianityanalysesoftheCMB.akeyissuesinceGaussianfluctuationsarep
