What is the best way to measure baryonic acoustic

arXiv:0804.0233v1[astro-ph]2Apr2008Mon.Not.R.Astron.Soc.000,000–000(0000)Printed2April2008(MNLATEXstylefilev2.2)Whatisthebestwaytomeasurebaryonicacousticoscillations?ArielG.S´anchez1⋆,C.M.Baugh2,R.Angulo2.1Max-Planck-Institutf¨urExtraterrestrischePhysik,Giessenbachstrasse,85748Garching,Germany.2TheInstituteforComputationalCosmology,DepartmentofPhysics,UniversityofDurham,SouthRoad,DurhamDH13LE,UK.SubmittedtoMNRASABSTRACTOscillationsinthebaryon-photonfluidpriortorecombinationimprintdifferentsig-naturesonthepowerspectrumandcorrelationfunctionofmatterfluctuations.Themeasurementofthesefeaturesusinggalaxysurveyshasbeenproposedasmeanstodeterminetheequationofstateofthedarkenergy.Theaccuracyrequiredtoachievecompetitiveconstraintsdemandsanextremelygoodunderstandingofsystematicef-fectswhichchangethebaryonicacousticoscillation(BAO)imprint.Weuse50verylargevolumeN-bodysimulationstoinvestigatetheBAOsignatureinthetwo-pointcorrelationfunction.ThelocationoftheBAObumpdoesnotcorrespondtothesoundhorizonscaleatthelevelofaccuracyrequiredbyfuturemeasurements,evenbeforeanydynamicalorstatisticaleffectsareconsidered.Carefulmodellingofthecorrelationfunctionisthereforerequiredtoextractthecosmologicalinformationencodedonlargescales.Wefindthatthecorrelationfunctionislessaffectedbyscaledependenteffectsthanthepowerspectrum.Thismeansthatinformationfromthelargescaleshapeofthecorrelationfunction,inadditiontotheformoftheBAOpeak,canbeusedtoproviderobustconstraintsoncosmologicalparameters.Thecorrelationfunctionthereforeprovidesabetterconstraintonthedistancescale(∼50%smallererrors)thanthemoreconservativeapproachrequiredwhenusingthepowerspectrum.Keywords:methods:N-bodysimulationscosmology:theorylarge-scalestructureofUniverse.1INTRODUCTIONPriortorecombination,theionisedplasmaofelectronsandprotonswascoupledtotheradiationintheUniversethroughtheelectromagneticinteraction.Thepressureexertedbythephotonsworkedagainstthegravitationalcollapseofpertur-bationsinthedensityofbaryons.Thisledtooscillationsinthephoton-baryonfluid.Theseripplesareimprintedonthetemperaturepowerspectrumofthecosmicmicrowavebackground(CMB),asdetectedconvincinglyforthefirsttimearoundtheturnofthemillennium(deBernardisetal.2000;Hananyetal.2000).AseriesofacousticpeakshasnowbeenmeasuredwithimpressiveprecisionbytheWMAPsatel-lite(Bennetetal.2003;Hinshawetal.2003,2007,2008)andtheArcminuteCosmologyBolometerArrayReceiver(ACBAR,Reichardtetal.2008).Thepositionsandrelativeheightsofthesepeakscanbeusedtoplacetightcon-straintsonthevaluesofthefundamentalcosmologicalpa-rameters,particularlywhentheCMBmeasurementsarecom-⋆E-mail:[e-mail]fthegalaxypowerspectrum(Efstathiouetal.2002;Percivaletal.2002;Spergeletal.2003;Tegmarketal.2004;Seljaketal.2005;S´anchezetal.2006;Seljaketal.2006;Spergeletal.2007).Theacousticoscillationsarealsoimprintedonthematterpowerspectrum,albeitwithdifferentphasesfromthefeaturesseenintheCMBspectrumandwithare-ducedamplitude,duetothesmallfractionoftheto-talmassintheUniversebelievedtobeintheformofbaryons(Meiksinetal.1999).Recently,thesefeatureshaveattractedagreatdealofinterestasapotentialroutetomeasuringtheequationofstateofthedarkenergy,wDE=PDE/ρDE,wherePDEisthepressureofthedarkenergyandρDEisitsdensity(Blake&Glazebrook2003;Hu&Haiman2003;Linder2000;Seo&Eisenstein2003;Wang2006).Theacousticoscillationsinthematterpowerspectrumarerelatedtothesoundhorizonscale.IfweknowthesizeofthesoundhorizonthroughmeasurementsoftheCMBtemperaturefluctuations,wecanusethisscaleasastandardruler.Theapparentsizeofthisrulerdependsupon2ArielG.S´anchezetal.theparameterwDE,asthisinfluencestheangulardiameterdistanceouttoagivenredshift.Inthispaper,wefocusourattentiononthetwo-pointcorrelationfunctionwhichistheFouriertransformofthepowerspectrum.Theseriesofacousticoscillationsseeninthepowerspectrumtranslatesintoabumporbroadspikeinthecorrelationfunction.SuchafeaturewasdetectedforthefirsttimeinthecorrelationfunctionofluminousredgalaxiesbyEisensteinetal.(2005).Evidencehasalsobeenfoundforbaryonoscillationsinthepowerspectrumofgalaxycluster-ing(Coleetal.2005;H¨utsi2006;Padmanabhanetal.2007;Percivaletal.2007b).Theappearanceoftheacousticoscil-lationsinthepowerspectrumwasconsideredinanearliercompanionpapertothisonebyAnguloetal.(2008).Whilstthebulkoftheliteratureonacousticoscilla-tionshasfocusedonthepowerspectrum,therehasbeenrenewedinterestrecentlyintheuseofthecorrelationfunc-tiontoextractthesoundhorizonscale.Anguloetal.(2005)showedthatcorrelationfunctionofasampleofclustersatz∼1,asanticipatedfromtheSunyaev-Zeldovichsur-veyproposedbytheSouthPoleTelescope(Ruhletal.2004)oraredsequencephotometricsurveywithVISTA(),couldpotentiallyconstrainthesoundhorizonscaletoanaccuracyof∼2%,inturnfix-ingthedarkenergyequationofstatetobetterthan10%.Fortheacousticoscillationapproachtoprovidecompet-itiveestimatesofthevalueofwDE,oneneedstoextractthesoundhorizonscalefromthemeasuredcorrelationfunctiontosub-percentaccuracy.Toachievethisgoalitisessentialtoquantifyanysystematicdeviationsofthescalerecoveredfromthesizeoftheso