The Damping Tail of CMB Anisotropies

arXiv:astro-ph/9609079v110Sep1996IASSNS-AST-96/47THEDAMPINGTAILOFCMBANISOTROPIESWayneHuInstituteforAdvancedStudy,SchoolofNaturalSciences,Princeton,NJ08540andMartinWhiteEnricoFermiInstitute,UniversityofChicago,Chicago,IL60637ABSTRACTBydecomposingthedampingtailofCMBanisotropiesintoaseriesoftransferfunctionsrepresentingindividualphysicaleffects,weprovideingredientsthatwillaidinthereconstructionofthecosmologicalmodelfromsmall-scaleCMBanisotropydata.Weaccuratelycalibratethemodel-independenteffectsofdiffusionandreionizationdampingwhichprovidepotentiallythemostrobustinformationonthebackgroundcosmology.Removingtheseeffects,weuncovermodel-dependentprocessessuchastheacousticpeakmodulationandgravitationalenhancementthatcanhelpdistinguishbetweenalternatemodelsofstructureformationandprovidewindowsintotheevolutionoffluctuationsatvariousstagesintheirgrowth.Subjectheadings:cosmology:theory–cosmicmicrowavebackground.Submitted:September10,1996toApJ1.IntroductionMucheffortisbeingexpendedtomeasuretheangularpowerspectrumofthecosmicmicrowavebackground(CMB)anisotropyonincreasinglysmallerangularscales.Formanytypesofmodelsforstructureformation,thespectrumcanbepredictedtoaprecisionofabout1%(Huetal.1995),raisingthehopethatthecosmologicalparametersthataretheinputtothesecalculationscanbeextractedtocomparableprecision(seee.g.Jungmanetal.1996).The“inverseproblem”ofreconstructingthemodelgivenaspectrumislesswellunderstoodthanthe“forwardproblem”ofpredictingitgiventhemodel.Forthispurpose,itisimportanttoassessthegenerationofanisotropiesinamannerthatisnottiedtoanygivenmodelforstructureformation.Fromthetheoryofanisotropyformation,weknowthatCMBfluctuationssufferedcausalprocessinganddampingoftheprimordialsignal.Inthispaper,wenumericallycalibratesucheffects,extendingandimprovinguponpriorwork(Hu&Sugiyama1995ab,1996,hereafterHSa,HSb,HScandHu&White1996b).AparticularlyfruitfulwaytovisualizetheCMBspectrum,andonethatprovidesaframeworkfortheinverseproblem,isasaproductoftransferfunctionsrepresentingindividualphysicaleffects.Thespectrumisthenconstructedoutofphysicalelementsratherthanamodel-dependentparameterization.Conceptually,–2–theevolutionofCMBanisotropiesprocessesprimordialmetricorgravitationalpotentialperturbationsintofeaturesobservableinthespectrumtoday(seee.g.Bond1996,Hu&White1996b).Sincetheevolutionobeyslinearperturbationtheory,itseffectsaredescribedbyaseriesoftransferfunctionsthatmultiplytheunderlyingperturbations.Theformofthesefunctionsdependsonthecosmologicalmodel,notonlyforthebackgroundexpansionandthermalhistory(seee.g.Bondetal.1994,Seljak1994,Hu,Sugiyama&Silk1996)butalsoforstructureformation(seee.g.Crittenden&Turok1995,Magueijoetal.1996,Durreretal.1996,Hu,Spergel,&White1996).Bydecomposingtheevolutionintofunctionsrepresentingseparatephysicaleffects,wecanisolateportionsoftheanisotropyspectrumthatarethemostsensitivetoparticularaspectsofthecosmologicalmodel.Inparticular,processesthatdampCMBanisotropies,photondiffusion(Silk1968)andrescattering(Efstathiou&Bond1987),dependmainlyonthebackgroundparametersandlittleontheperturbationsthatformstructureintheuniverse.In§2,weisolatetheseeffectsinanumericaltreatment.Fromthisdampingcalibration,weproduceconvenientfittingformulaethataccuratelydescribethebehaviorofthediffusionandreionizationdampingtransferfunctions,orenvelopes,directlyinanisotropymultipolespace.In§3,weillustratethereconstructionprocessbytestingitwithknownmodelswithinthecolddarkmatter(CDM)scenario.Byremovingthemodel-independenteffectsofdamping,oneuncoversimportantmodel-dependenteffectssuchasthebaryon-dragmodulationofthepeaks(HSa),thepotentialenvelopethatdescribesgravitationaldrivingofacousticoscillations(HSc),andtheregenerationofanisotropiesduringreionization(Sunyaev&Zel’dovich1970,Kaiser1984).Inthecontextofcurrentlypopularmodels,recoveryofthesesignatureswillhelpdistinguishbetweensuchpossibilitiesasaninflationaryorcosmologicaldefectoriginoffluctuations(Crittenden&Turok1995,Durreretal.1996,Hu&White1996b).Theeffectsofdampingarealsointrinsicallyinterestingbecausetheyprovidethemostmodel-independentprobesofthebackgroundcosmology.Wealsoconsiderhowdiffusiondampingcanbeusedtoconstrainthecurvatureoftheuniverseandreionizationdampingtodeterminetheredshiftandextentofreionizationintheuniverse.Inthisway,thestudyofeffectsinthedampingtailofCMBanisotropiespresentedherewillaidinthefuturereconstructionofthecosmologicalmodelfromtheanisotropydata.2.DampingCalculationDampingprocesseswhichaffectCMBanisotropiesprovidethemostmodel-independentinformationavailableinthespectrumandallowconstraintsoncosmologicalparameterssuchasthecurvatureandthethermalhistoryoftheuniverse.Furthermore,theseuniversaleffectsobscurethemodel-dependentsignaturesthatareusefultodeterminethemechanismforstructureformationintheuniverseandtheultimatesourceofdensityperturbations.Forboththesereasons,anaccuratecalibrationofdampingeffectsisdesirable.Inthissection,webeginwiththeformalismnecessarytodescribethem(§2.1)andsimpleapproximationstohelpunderstandtheirnature(§2.2).Wethenturntonumericalcalibrationoftheseeffects(§2.3).Finally,wegiv