The Canada-France Deep Fields III Photometric Reds

arXiv:astro-ph/0310038v221Jul2006TheAstrophysicalJournalSupplementSeries,162:20–37,2006JanuaryPreprinttypesetusingLATEXstyleemulateapjv.5/14/03THECANADA–FRANCEDEEPFIELDSIII:PHOTOMETRICREDSHIFTDISTRIBUTIONTOIAB=24M.Brodwin1DepartmentofAstronomy&Astrophysics,UniversityofToronto,ONM5S3H8,CanadaandJetPropulsionLaboratory,CaliforniaInstituteofTechnology,MailStop169-506,Pasadena,CA91109S.J.Lilly1,2andC.PorcianiDepartmentofPhysics,SwissFederalInstituteofTechnology(ETH–Z¨urich),ETHH¨oenggerberg,CH–8093,Z¨urich,SwitzerlandH.J.McCrackenandY.MellierInstitutd’AstrophysiquedeParis,98bis,bdArago,75014Paris,FranceO.LeF`evre1andS.FoucaudLaboratoired’AstrophysiquedeMarseille,TraverseduSiphon,13376MarseilleCedex12,FranceD.CramptonHerzbergInstituteofAstrophysics,WestSaanichRoad,Victoria,BCV9E2E7,Canada(Received2003October2)TheAstrophysicalJournalSupplementSeries,162:20–37,2006JanuaryABSTRACTWecomputeaccurateredshiftdistributionstoIAB=24andRAB=24.5usingphotometricredshiftsestimatedfromsix–bandUBVRIZphotometryintheCanada–FranceDeepFields–PhotometricRed-shiftSurvey(CFDF–PRS).OurphotometricredshiftalgorithmiscalibratedusinghundredsofCFRSspectroscopicredshiftsinthesamefields.Thedispersioninredshiftisσ/(1+z).0.04totheCFRSdepthofIAB=22.5,risingtoσ/(1+z).0.06atournominalmagnitudeandredshiftlimitsofIAB=24andz≤1.3,respectively.WedescribeanewmethodtocomputeN(z)thatincorporatesthefullredshiftlikelihoodfunctionsinaBayesianiterativeanalysisandwedemonstrateinexten-siveMonteCarlosimulationsthatitissuperiortodistributionscalculatedusingsimplemaximumlikelihoodredshifts.Thefield–to–fielddifferencesintheredshiftdistributions,whilenotunexpectedtheoretically,aresubstantialevenon30′scales.WeprovideIABandRABredshiftdistributions,medianredshifts,andparametrizedfitsofourresultsinvariousmagnituderanges,accountingforbothrandomandsystematicerrorsintheanalysis.Subjectheadings:Galaxies:DistancesandRedshifts—Galaxies:Photometry—Methods:Statistical—Methods:DataAnalysis1.INTRODUCTIONThelastdecadehasseengreatadvancesinourun-derstandingoftheevolutionoftheUniverse,primar-ilyduetogroundbreakingstudiesoftheintermediate(Lillyetal.1995b)andhighredshift(Steideletal.1996)Universe.These”pencilbeam”surveysprobedtocos-mologicaldepthsoverquitemodestareas,revealingthestrongluminosity,morphological,andclusteringevolu-tionofthegalaxypopulationoverthelast12Gyr.Itwas,however,recognizedatthetimethatthesmallwin-dowsontheUniverseprovidedbythesesurveysweresubjecttosubstantialsample,or“cosmic”variance,inparticularformeasurementsonthescaleofthesurveyfieldsizes.Recentlythe2dF(Collessetal.2001)andSDSS(Yorketal.2000)surveysprovidedthefirstprecise”lo-cal”(z∼0.1)measurementsofthegalaxyluminos-ityfunction(Norbergetal.2002b;Blantonetal.2003),providingacrucialbaselinereferenceforevolution-arystudies.Inaddition,measurementsofthegalaxycorrelationfunctioninthesesurveys(Norbergetal.2002a;Zehavietal.2002)haveconvincinglydemon-stratedluminosity–dependentclusteringlongseenatlowersignificanceinsmallersamples.Thesesurveysfinallyovercamethecosmicvarianceissuesthathadplaguedpreviouslocalsurveysbysamplingover103squaredegrees.WiththeadventoflargeformatmosaicCCDs,weun-dertooktheCanada–FranceDeepFields(CFDF)survey,adeepUBVIimagingsurveyinfour30′×30′fields.PublishedresultsfromtheCFDFincludeastudyofthegalaxyangularcorrelationfunctiontoIAB=25(McCrackenetal.2001),andameasurementoftheclus-teringpropertiesofLyman–breakgalaxiesatz∼3(Foucaudetal.2003).InthispaperweintroducetheCFDFPhotometricRedshiftSurvey(CFDF–PRS),de-rivedfromahighlyuniformUBVRIZsub–sampleofthemainsurvey,whichformsthebasisofseveralevolution-arymeasurementsofthegalaxypopulationasafunctionofredshift.Futurepapers(Brodwinetal,inprepara-tion)willpresentstudiesofthegalaxyluminosityandcorrelationfunctions.Inthispaperwefocusonanaccuratemeasurementofthegalaxyredshiftdistributionfrom0z1.3.We2Brodwinetal.introduceanoveliterativetechniquetoextracttheopti-malredshiftdistributionusingthefullredshiftlikelihoodfunctionsforeachgalaxy.Wepresentbinnedredshiftdistributionsalongwithparametrizedfitstoourresults.Theoutlineofthispaperisasfollows.Section§2brieflydescribestheCFDF–PRSdata.Section§3de-scribesthecalculationandcalibrationofthephotomet-ricredshifts.Section§4introducestheiterativeBayesianmethodofrecoveringtheredshiftdistributionusingthefullredshiftprobabilityfunctionforeachgalaxy.InSec-tions§5and§6wepresentthephotometricredshiftdistri-butions,obtainedusingtheiterativemethod,asafunc-tionofsamplelimitingmagnitudeintheCFDFdowntoIAB=24andRAB=24.5,bothinhalfmagnitudebinsandviaparametrizedfits.Finally,inSection§7wesummarizeourresults.Mostofourresultsareindependentofcosmology.Wherenecessarywehaveassumedaconcordancecosmol-ogyinagreementwiththerecentWMAP(Spergeletal.2003)results{ΩM,ΩΛ}={0.27,0.73}andaHubblecon-stanth=0.71whereH0=100h.AlldistancesareexpressedincomovingMpc.2.CANADA–FRANCEDEEPFIELDSTheCanada–FranceDeepFields(CFDF)isadeep,multi–colorimagingsurveycovering1deg2(McCrackenetal.2001;Foucaudetal.2003,hereafterCFDF1andCFDF2,respectively).Theacquisition,re-duction,andverifica