APreprinttypesetusingLTEXstyleemulateapj
THECLUSTERINGOFGALAXIESAROUNDTHREEZ∼3DAMPEDLY-ALPHA
ABSORBERS
NicolasBouch´e
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Dept.ofAstronomy,UniversityofMassachusetts-Amherst,Amherst,MA01003USAMaxPlanckInstitutf¨urAstrophysik,Karl-Schwarzschild-Str1,D-85748Garching,GermanyEuropeanSouthernObservatory,Karl-Schwarzschild-Str2,D-85748Garching;nbouche@eso.org
arXiv:astro-ph/0403544v2 28 Jun 2004JamesD.Lowenthal
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FiveCollegeAstronomyDept.,SmithCollege,Northampton,MA01063USA;james@earth.ast.smith.edu
AcceptedforpublicationinApJ,issue10July2004
ABSTRACT
Wepresentoutresultsonthecross-correlationofLymanbreakgalaxies(LBGs)aroundthreedampedLyαabsorbers(DLAs)atzabs≃3fromdeep(µI,AB(sky)≃27.6magarcsec−2)UBVIKPNO4m/MOSAICimages.ThelargeareaoftheMOSAICimages,0.31deg2or
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∼65×65h−71Mpcco-movingatredshiftz=3,allowsustoprobetheclusteringofLBGsonscalesupto20Mpcco-moving.Oursurveycoversatotalof1deg2andcontains∼3,000LBGswithphotometricredshiftsbetween2.8and3.5.UsingtheredshiftlikelihooddistributionswithmIasaprior,weselectedLBGswithinaredshiftsliceofwidthWz=0.15(correspondingtoσz,theuncertaintyinphotometricredshifts)centeredontheredshiftoftheabsorbers.Withinthatredshiftslice,wefindthattheDLA-LBGcross-correlationwdgiswdg=(1.62±1.32)×wgg,wherewggistheLBGauto-correlation.Thiscorrespondstoacorrelationlengthofro=5±4.5h−1
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(co-moving)(orro=7±6.8h−71Mpc).Thecross-correlationismostsignificantonscales5−10Mpc.ThroughMonteCarlosimulations,wefindthatwdgissignificantlygreaterthanzeroatthe>95%level.InthreeotherredshiftslicesthatdonotcontainaDLA,wedonotfindanyevidenceofclustering.Alargersamplewillenableustodiscriminatebetweenwdg/wgg<1orwdg/wgg>1,i.etotestwhetherDLAhalosaremoreorlessmassivethanLBGhalos.Subjectheadings:cosmology:observations—galaxies:evolution—galaxies:high-redshift—
quasars:absorptionlines—quasars:individual(APM08279+5255,PC1233+4752,J0124+0044)
1.INTRODUCTION
QSOabsorptionlines,includingdampedLy-αab-sorbers(DLAs),andLymanbreakgalaxies(LBGs)arecurrentlyourtwomajorsourcesofinformationonhighredshiftgalaxies.Aftermorethantwodecadesofstudy,theexactnatureanddetailedcharacteristicsofdampedabsorbersremainunexplained.Here,weseektoconstrainthepropertiesofDLAhalosusingLBGs(Steideletal.,1999)astracersoflargescalestructure.
DLAscontainthelargestreservoirofneutralhydro-gen(Hi)athighredshifts(e.g.Lanzettaetal.,1991;Lanzetta,Wolfe,&Turnshek,1995;Ellisonetal.,2001).TheycontainmoreneutralHithanalltheabsorbersintheLy-alphaforestcombined.Mor-1
ever,theamountofHiinDLAsathighredshiftscorrespondstotheamountofHiinstarstodayatz=0:Ellisonetal.(2001)findΩHI(z=3)=10−2.6,whileBelletal.(2003)measureΩ∗(z=0)=10−2.56(bothnumbersareforh=0.65).ThesefactsledWolfeetal.(1986)toputforwardthe‘diskhypothesis’,namelythatDLAsarelargethickgaseousdiskgalaxies.Despitethenumerousob-servationsdirectedatDLAsinthepastdecade(e.g.imagingstudiessuchasMøller&Warren,1993;Lowenthaletal.,1995;Steideletal.,1994,1995;LeBrunetal.,1997;Bunkeretal.,1999;Fynbo,Møller,&Warren,1999;Kulkarnietal.,2000;Pettinietal.,2000;Rao&Turnshek,2000;Bouch´eetal.,2001;Mølleretal.,2002),thishypoth-esishasbeendebatedandtheroleofDLAsingalaxy
VisitingAstronomer,KittPeakNationalObservatory,NationalOpticalAstronomyObservatory,whichisoperatedbythe
AssociationofUniversitiesforResearchinAstronomy(AURA),Inc.,undercooperativeagreementwiththeNationalScienceFoundation.
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formationisstillnotunderstood(seethemoreex-thisisevidencethatDLAsandLBGs“donotreside
haustivesummaryofPettini,2003).inthesamepartsoftheuniverse”.ItisimportanttoHintstothenatureofDLAsaregivenbynumericalnotethatbothofthesestudieswerenotsensitiveto(Katzetal.,1996;Haehnelt,Steinmetz,&Rauch,scaleslargerthan5h−1Mpcbecausebecauseofthe2000;Gardneretal.,2001;Nagamine,Springel,&Hernquist,smallfieldofviewavailable.2003b)andsemi-analytical(Kauffmann,1996;Otherstudies,however,havepointedtoanover-Mo,Mao,&White,1999;Okoshietal.,2003)sim-densityofgalaxiesnearDLAs.Wolfe(1993)com-ulationsofgalaxyformationathigh-redshifts.binedseveralstudiesofLyαemittersaroundDLAsAll,thesesimulationsindicatethatDLAsareandfoundevidenceforacorrelationbetweenemit-∗inmajorityfaint(sub-L)insmalldarkmat-tersandDLAsatameanredshift
−1terhalosVc≪100kms.Basedoncross-sectionarguments,Fynbo,Møller,&Warren(1999),
Mølleretal.(2002),andSchaye(2001)arrivedtothesameconclusions.Fromthechemi-calevolutionpointofview,(Matteuccietal.,1997;Jimenez,Bowen,&Matteucci,1999;Boissier,P´eroux,&Pettini,2003)arguedthatDLAsarecausedbygasrichlowsurfacebrightnessdwarfgalaxies,asseenlocallyinatleastonecase(Bowen,Tripp,&Jenkins,2001).
However,DLAsshowasymmetricprofilesoftheirhighionizationspecies(Prochaska&Wolfe,1997;Ledouxetal.,1998).ThishasbeenusedtoarguethatDLAsare,infact,duetothickmassiverotatingdisks(Wolfeetal.,1986,1995;Prochaska&Wolfe,1997).Butothers,e.g.Malleretal.(2000),McDonald&Miralda-Escud´e(1999)andHaehnelt,Steinmetz,&Rauch(2000),showedthatalargerangeofmorphologiescanre-producetheobservedkinematics:DLAscanarisefromthecombinedeffectofamassivecentralgalaxyandanumberofsmallersatellitesorfilaments.Infact,coldgasaccretionalongfilamentscouldbeanimportantmechanism,especiallyathighredshifts(Keresetal.,2004).
WhetherornotDLAsareindeedmassivewillleadtodifferentclusteringpropertiesofthegalax-iesaroundthem.Inhierarchicalgalaxyformationmodels(e.g.Mo&White,1996,2002),thisclusteringyieldsameasurementofthedarkmatterhalomassassociatedwithDLAsrelativetothatofthegalaxiesusedastracersofthelargescalestructure.Inpartic-ular,ifthegalaxiesareless(more)correlatedwiththeDLAsthanwiththemselves,thiswillimplythatthehalosofDLAsareless(more)massivethanthoseofthegalaxies.Here,weusez≃3LBGs(Steideletal.,1999)astracersofthelargescalestructure.
Inanalysessimilartothatpresentedhere,Gawiseretal.(2001)foundnoclusteringofgalaxiesaroundonesingleDLAatz=4towardsBR0951-04,andAdelbergeretal.(2003)foundalackofgalaxiesnearfourDLAs(theyfoundtwowithinacylinderofradiusof5.7h−1MpcanddepthWz<0.025whereas∼6wereexpectedifthecross-correlationisthesameasthegalaxyauto-correlation).Theyarguedthat
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onpartofthisdataset.Wedetectedanover-densityofΣ/Σg≃3atthe95%levelonscales2.5 Throughoutthispaper,weadoptΩM=0.3,ΩΛ=0.7andHo=100hkms−1Mpc−1;thus,atz∼3,1′′correspondsto∼21.5h−1kpcand1′to∼1.29h−1Mpc,bothco-moving.Atthatred-shift,H(z)∼4.46Ho,soδz=0.1correspondsto67h−1Mpcinco-movingcoordinates2. 2.THEDATA TheobservationswerecarriedoutwiththeMO-SAICcameraattheKittPeakNationalObservatory4-mtelescopeonUT2000February7and8(runI),andonUT2001September23–26(runII).RunIIwasphotometric,somecirruswerepresentduringrunI.Theseeingwas0.9–1′′.5forbothruns. ThewidefieldimagerMOSAICcontainseight2k×4kthinnedSITeCCD.With0′′.258perpixel,ithasafieldofviewof35′onaside.Thereadoutnoiseis∼6e−pix−1,thedarkcurrentisnegligible(∼5e−hr−1),andtheaveragegainis3e−ADU−1.EachCCDhasbeenthinnedfordetectingU-bandphotons. Weimagedourthreefieldsthroughfourbroad-bandfilters—U(Stromgren)andBV&I(Harrisset)(seeFig.1)—usingastandardditherpattern(fivepointings)toremovecosmicraysanddetectorde-fects.Thetotalintegrationtimeforeachfieldwastypically4hr(U),1hr(B&V)and4hr(I);theobser-vationsaresummarizedinTable2.Inaddition,weobservedseveralLandolt(1992)standardstarfieldsthrougheachfilter. 2.1.TheDLAfields Giventheallocatedtelescopenight,weselectedthreefieldsforthepresenceofaDLAatz∼3andwiththeadditionalconstraintthattheQSOmustbeatahigherredshiftthanthatoftheDLA,i.e.zabs< AlthoughourDLAsdonotmeetthecolumnden-sitythresholdoflogNHi>20.3oftenquoted,thelatterisarbitraryandbasedonresolutionthresh-oldofprevious-generationinstruments.Furthermore,themetallicitiesandtheHipropertiesof‘sub-DLAs’arenotdifferenttothe‘strict-DLA’population(e.gP´erouxetal.,2003).Forthepurposeofthisstudy,thehydrogencolumndensitiesarelogNHi≥20.0,whichensurethattheabsorptionisdampedandthatthegasisneutral. 2.2.Observations 23 2.3.Datareduction ThedatawerereducedwiththepackageMS-CRED(v4.1)withinIRAF3(v2.11.3),followingthereductionsguidelinesoftheNOAODeepWide-FieldSurvey(Jannuzi&Greer,2000).ThispackagewasspecificallydesignedtoreduceMOSAICdata.Thereductionprocesscontainsmorestepsthantypicalopticalobservationsandisdetailedhere. Wefirstperformedtheoverscanlevelsubtraction.Wethencorrectedforthesmallcorrection(<0.5%)duetocrosstalkbetweenadjacentchips.Foreachnight’sdata,weremovedanaveragedzeroframe,orbiasframes,fromthescienceimages.ThethinnedMOSAICchipsrequirednodarkcorrectionsincethedarkcurrentwasonly5e−1perhour. Flat-fieldingiscriticaltoachieveprecisephotome-try.However,wehadtodealwithtwonon-traditionalcomplications:(i)theMOSAICinstrumentatthe4-msuffersfromaghostimageofthepupilinallbandsduetoreflectionsintheopticsofthecamerathatneedstoberemoved;and(ii)domeflat-fieldsmaymatchthenightskytoonly1or2%(usuallylarger).Thus,sky-flatfieldinginadditiontodome-flatfieldingwasnecessaryandsincethepupilimageisanadditivelighteffect,ithastoberemovedfromtheflat-fieldsfirst. Inthedomeflats,weremovedthepupilimagebyfittinganaxiallysymmetricpatterntothedatathem- UsingthelatestcosmologicalparametersfromWMAP(ΩM=0.268,ΩΛ=0.728,h=0.71)changesthesenumbersby∼3%.IRAFisdistributedbytheNationalOpticalAstronomicalObservatories,whichareoperatedbyAURA,Inc.undercontracttotheNSF 4 selveswiththetaskMSCPUPIL.Wethenflat-fieldedallthescienceframeswithpupil-freedome-flats.Atthispoint,thepupilimagewasstillpresentinthedata.Itismoredifficulttoremovethepupilfromindividualscienceimagesthanfromthedome-flatsbecausethepupilpatternismuchfainter,andthepupilimageismixedwithallthefaintandbrightsourcesinthedata.Asimplethresholdschemetoremovetheobjectsisnotfeasiblesincethepupilisstillpresentandthedatapoorlyflat-fielded.Thus,toremovethepupilfromthescienceimagesandtomakethesky-flats,wehadtoextractthepupilimagefromthescienceimagesthemselvesthroughthefol-lowingiterativesteps:(i)wecreatedasky-flat(ver.1)fromtheaverageofthescienceframeswithame-dianrejection;(ii)weextractedthepupilimagefromthesky-flat(ver.1)usingthetaskMSCPUPIL(pa-rameter‘type’setto‘data’)andremoveditfromthescienceframeswithRMPUPILtoproducea‘first-pass’pupil-freedata;(iii)wecreatedanothersky-flat(ver.2)usingthepupil-freedataandappliedittothedata.Wefoundthatlow-levellightfrombrightstarswascreatingsignalinthesky-flatevenifstrongmin-maxrejectionwasused.Tosolvethisproblem,wecreatedobjectmasksbyusinga2σthresholdoneachoftheeightCCDsandmaskedoutlargeareasaroundthebrightestobjects.Steps(i)through(iii)wererepeatedusingthemasksandthefinalsky-flatwasnormalizedandappliedtoalltheframes.FortheI-bandonly,weremovedfringingusingtheprocedurein(Jannuzi&Greer,2000)beforeapplyingthefinalsky-flat. CosmicrayremovalwasdoneusingthetaskXZAPfromthepackageDIMSUMandcustomizedroutines.Bad-pixelmasksincludingthecosmicraysandbleed-ingregionswereconstructed. De-projectingthe8CCDsonasingleimageisatwostepprocessandrequiresverygoodastrometry.First,usingthecoordinatesofseveralhundredUSNOstars,weinteractivelyderivedastrometricsolutions(RMS≤0.5′′)withMSCCMATCHforeachditheredexposure.Then,wemappedtheeightCCDsontoasingleimagebyrebinningthepixelstoatangent-planeprojection,thusproducingpixelsof4constantangularsize,withthetaskMSCIMAGE.Thispro-cessmatchestheWorldCoordinateSolution(WCS)solutionofallbandstoacommonreferenceposition.Theindividualflat-fielded,astrometricallycali-bratedimageswithauniformzero-pointwereaver-agedwithanaveragesigma-clippingrejectiontopro-ducethefinalstackedimages.Thescalingofeachin-dividualditheredimagewasperformedinteractivelyon∼300astrometriccalibrationstarscommontoall images. FortheI-bandofrunII,wewerenotabletoachieveasatisfactorysky-flatfielding(residuals∼1%).Inor-dertocorrectforthis,weappliedamedianfilteringtoablock-averagedimageofthestackedframeandappliedthenormalizedresultstotheimage. Eventhoughallbandsweredeprojectedtoatangent-planesolutionusingthesamepositionandorientationonthesky,therelativepixelpositionsofobjectsinthedifferentbandswerenotexactlyiden-ticalbecauseofditheringandeffectssuchasflexureofthetelescope,andopticaldistortionsduetofilters.Sinceitisimportanttohaveidenticalpixelpositionsforthephotometry,wehadtoregisterandrotateslightly(∼0.003deg)eachimagewithrespecttothereferenceband(U)using∼25stellarobjectswithhighS/Ninallbandsthroughoutthefieldofview.Thermsintherelativeastrometryof∼150stellarobjectswith20 Thestandardstarframes,whichcontained∼150Landolt(1992)standardstarsobservedthrougheachfilterandairmasses1.0 C 5 1996).Thisalgorithmperformssourcedetectionandphotometry(seeSimardetal.,2002,forasummaryofthispackage).Weoptimizedtheconfigurationpa-rameterstoensurethefaintestsourcesweredetectedandtooptimizeourcompleteness.Weusedthelo-calbackgroundestimatedina24-pixelwideannulus.Theimageswereconvolvedwitha2pixelFWHMGaussiankernelbeforesourcedetection.Thede-tectionthresholdwassetto1.5sigmawithamin-imumareaof5pixels.Bad-pixelmasksareusedasflagimages.SExtractorisabletoperformdeblend-ingofcloseobjects.Thenumberofdeblendingsub-thresholdswassetto32pixels,andthroughexperi-mentation,theminimumcontrastparameterwassetto0.0001.Ourcatalogcontainsapproximately40,000objectsperfield,30,000ofwhichhaveI>22.5mag. 2.6.Photometry Foreachobject,wemeasurethecolorina2×FWHMdiameteraperture,wherewetookseeingvariationsondifferentbandsintoaccount:thecolorintwobands,e.g.(U−B)=mB(2×FWHMB)−mU(2×FWHMU),andsimilarlyforothercolors.Al-thoughthisprocedureisstrictlyvalidonlyforstar-likeobjects,ithasbeenshowntobeagoodapproxi-mationforfaintandunresolvedgalaxies(Smailetal.,1995).Indeed,fromHubbleSpaceTelescopestud-ies,thehalf-lightradiusofLBGsis,onaverage,0.4′′(Lowenthaletal.,1997),muchlessthanourseeing.Forsourcesthatwerenotdetectedinoneband(i.e.flux<1σ),themagnitudeinthatbandissettothe1σfluxlimitina2×FWHMdiameterapertureandnocolortermiscomputed(Equation1). Intheremainderofthispaper,weuseaperturemagnitudes.Toconvertthosetototalmagnitudes,weestimatethetotalmagnitudecorrectionforstar-likeobjectstobemI(tot)=mI(2×FWHM)−0.35intheI-band,calibratedbyaddingsimulatedstarswithknowntotalfluxintoourimagesandmeasuringtherecoveredfluxinthechosenaperture. Inaddition,eachobjectinourcatalogswascor-rectedforGalacticextinctionbyadoptingE(B−V)valuestakenfromthemapsofSchlegeletal.(1998)assuminganRV=3.1extinctioncurve. 2.7.Completeness Inordertoestimateourcompleteness,weaddedtoourimagesfakestellarobjectswithMOFFATprofilesthatmatchedtheimagepointspreadfunction(PSF).Fluxesweremeasuredwiththesameaperture.Wefindthatweare50%completeuptomI≃24.35mag.TheexactvaluesforeachfieldareshowninTable4.UsingthetransformationIAB=mI+0.47,thiscor-respondstoIAB≃24.8mag(RAB∼25mag,Steideletal.1993)andto0.67L∗,wherem∗R≃24.5forgalaxies atz≃3(Steideletal.,1999).Our90%completeness levelisIAB≃24.4mag.Thus,wereachedadepthsufficienttoensurethatwesamplewellL∗galaxiesatz=3. 2.8.SelectingLymanbreakgalaxycandidatesFromourcatalogof∼40,000objects,werejectedobjectsclosetothefieldedgesandobjectswithaFWHM 6 3.1.PhotometricRedshifts Therearetwoapproachestophotometricred-shiftestimations:theempiricaltrainingsetmethod(e.g.Koo,1985;Connollyetal.,1995)andthespectralenergydistribution(SED)fit-ting(Lanzetta,Yahil,&Fern´andez-Soto,1996;Sawicki,Lin,&Yee,1997;Budav´arietal.,2000;Fontanaetal.,2000;Csabaietal.,2003).Theformerisanempiricalrelationshipbetweencolorsandred-shiftsdeterminedusingamulti-parametricfit.ThelatterisbasedonasetofSEDtemplates(empiricalortheoretical).Thetwomethodsarecomparableintheirperformanceatz≤1;however,thetrain-ingsetmethodisnotalwaysfeasible,especiallyathigh-redshifts(seediscussioninBen´itez,2000). Ontheotherhand,theSEDfittingmethodworksbestwhenthereisastrongfeatureintheSED,suchasthe4000˚Abreak,orthe912˚ALymanbreak.Thus,SEDfittingmethodswererapidlydevelopedfortheHubbledeepfield(HDF)(e.g.Budav´arietal.,2000;Fernandez-Sotoetal.,2001)withanaccuracyoftyp-ically∆z∼0.06(1+z).Inourcase,weusedthecodeHyperzfromBolzonella,Miralles,&Pell´o(2000),whichincludesintergalacticabsorptionduetotheLyαforestandinternalextinctionAtheintergalacticabsorptionprescriptionV.Weupdatedfol-lowingMassarottietal.(2001)andweusedtheex-tinctioncurveofCalzettietal.(2000)withAfrom0to1.2. Vvary-ingWeusedthetemplatesetmadeofthefourempiricalSEDsofColeman,Wu,&Weedman(1980),extendedintheUV(λ<1400˚A)byBolzonella,Miralles,&Pell´o(2000)usingthesyn-theticmodelsofBruzual&Charlot(1993)withpa-rameters(SFRandage)thatmatchedthespectraatz=0.NotethatFernandez-Sotoetal.(2001)extendedtheCWWtemplatesusingthepowerlawsofKinneyetal.(1993),andBudav´arietal.(2000)usedtheextensionsofKinneyetal.(1996).TheSEDtemplatesareconvolvedwiththeMOSAICfilterresponsecurves(includingtheCCDresponse),andzphotisfoundfromthemaximumofthelikelihooddistributionL(z)derivedfromtheχ2distribution. 3.2.SimpletestsontheHDF Weperformedseveraltestsofthetechniqueonthesampleof150spectroscopicallyconfirmedgalaxiesatredshiftsz≤6intheHubbledeepfieldnorth(HDF-N)(Cohenetal.,2000;Fernandez-Sotoetal.,2001).Weexperimentedwith5templatesetsthatincludedthe4CWWtemplatesandvariousstarbursttem-platesfromStarburst99(Leithereretal.,1999).Ofthe18galaxieswith2.75 3.3.Usingpriors SEDfittingmethodsgivethemostlikelyredshiftgiventheobservedsetofcolors.However,informa-tionsuchassize,orflux,canbeincludedinpho-tometricredshifttechniques´usingBayesianproba-bilities(followingBenitez,2000).WecoupledtheSEDfittingschemewiththepriorlikelihooddistri-butionforagalaxyofmagnitudembyBen´itez(2000)inthefollowingway:Iparametrizedtheproductprior×likelihoodisdecomposedovertheSEDtypesT: P(z)= pT(z|mI)·LT(z),(3) T wherepT(z|mI)isthepriorprobabilitygiventhegalaxymagnitudemI,andLT(z)istheprobabilityofobservingthegalaxycolorsifthegalaxyisatredshiftzandhasatypeT.ThephotometricredshiftzphotistakenfromthemaximumoftheP(z)distribution,andtheerrors,σz,arecomputedfromtheFWHMofP(z)dividedby2.35.Redshiftswithlargeσ´goodestimatorofreliabilityzmaybeunreliable.Aisthefollowing(Benitez,2000): P∆z≡P(|z−zphot|<0.2×(1+zphot)), (4) whichestimatesthe‘goodness’ofaphotometricred-shiftzphotusingEq.3,andalsohastheusefulfeaturetopicklikelyoutliers(Ben´itez,2000).Thefactor0.2isarbitrary,butsincethermsofphotometricred-shiftsσzis∼0.05(1+z),thisfactorcorrespondstoapproximately4×σz.Atz<6,theoverallrmsof∆zis0.11,and´∆z/(1+zspec)=0.06,similarto0.059foundbyBenitez(2000). 3.4.Photometricredshiftdistributions Fig.2showstheredshiftdistributionofthethreefields.ThedottedhistogramshowsthephotometricredshiftdistributionusingtheCWWtemplateswithnopriors.Thecontinuoushistogramshowsthepho-tometricredshiftdistributionusingthepriors.Fig.2showsthatusingthepriorshastheeffectofremov-inggalaxieswithzphotredshifts.Asexpected,the≃2distributionthatarelikelyofgalaxiesatloweratz∼3isnotaffectedmuch.ThisisduetothefactthatthismethodissensitivetotheshapeoftheSED,whichhasastrongbreakbetweentheUandBfiltersatthatredshift. Weusedthephotometricredshiftzphotofourgalax-iestodeterminetheirabsolutemagnitudeMTheK-correction,whichforgalaxiesatz∼3I,cor-rest.respondstotheextrapolationoftheirintrinsicfluxatλrest˚ ∼8000˚Afromtheirobservedfluxatλrest2000A,wascomputedusingaweightedsumoneach∼ SED.Eachtemplatewasweightedbythepriorprob-abilitypT(z|mI)·LT(z)sincethebest-fittedSEDwasacombinationofthespectraltypesT(seeEq.3).Atredshiftz∼3,theK-correctionis,however,small:itistypically∼0.2forblueSEDs,suchastheIrrtemplateofColeman,Wu,&Weedman(1980). Fig.3showstheabsolutemagnitudeMtionofz.EachdotrepresentonegalaxyinIasafunc-ourfields.ThetwocontinuouslinesshowourmagnitudecutsandwerecomputedusinganIrrSED.Thegalaxiesatredshiftz∼3are,asexpected,betweenthetwolinesandnearourcompletenesslimit,whichprovidesaconsistencycheckofthephotometricredshifttech-nique. AlmostallpointsthatareoutsidetherangeallowedbythecontinuouslinesinFig.3arebetweenthedot-tedlines,whichrepresentthemagnituderangeforanE/S0template,andthusarebestfittedbytheE/S0type.Thistypehasastrongbreakat4000˚AthatcreatesalargeK-correctionoffourmagnitudesandmakestheseobjectstooluminousfortheirapparentmagnitude.ThefittedSEDsarelikelytobewrong.Atthatredshift,zphottobetterconstrainthe∼SEDs. 2,IRphotometryisneeded3.5.SelectingreliablegalaxiesinslicesFromthesubsampledescribedinsection2.8,weselected∼100LBGsthatareinaredshiftslicecen-teredontheDLA.Specifically,theywerechosentohaveahighprobabilityofbeingattheredshiftoftheDLA,zabs,i.e. P(zabs±Wz/2)≡PDLA>0.5, (5) whereWfinedtwozistheredshiftslicewidth.Wealsode-additionalredshiftslicesshiftedby+0.15or−0.15fromzabs,P+andP−,respectively.WechoosearedshiftwidthofWz=0.15because,asdiscussedinBouch´e&Lowenthal(2003),itproducesthelargestsampleinthesmallestredshiftslice,giventhermsofthephotometricredshifts.Attheendof§6,weshowthatadifferentchoiceofWresults. zdoesnotchangetheMoreimportantly,thiscriterion(Eq.5)corre-spondstohighqualityphotometricredshiftsasillus-tratedinFig.4fortheAPM08279+5255field.TheleftpanelsofFig.4showtheprobabilitydistribution,andtherightpanelsshowtheprobabilitydistributionasafunctionofP∆zdefinedinEq.4,bothforthethreedifferentredshiftslices.Fig.4(a),(b),and(c) 7 showP−,PDLAandP+,respectively.Thedotsrepre-sentgalaxiesdetectedinallfourbands,UBV&I.ThefilledsquaresindicateobjectsthatarenotdetectedintheUband.SmoothingthedistributionsusingaGaussiankernel(scaledtothepeak)producedthecontinuouslinesinFig.4.Thedottedlineshowstheminimumthreshold(>0.5)usedinselectingLBGcandidatesineachoftheslices.Fromtherightpan-els,galaxiesthathaveahighprobabilityofbeinginaredshiftslicealsohavereliablephotometricred-shifts,indicatedbythefactthatP∆zredshiftslice,thenumberofgalaxies≥that0.9.FormeteachthethresholdisshowninTable5. Fig.5showsthex−ypositionsofourLBGcandi-datesthatmetthecriterionEq.5.Thesquareregionsshowthemasksusedtocoverbrightstarsanddefectssuchasstreaks. 4.CLUSTERINGANALYSIS Inthecurrenthierarchicaltheoryofgalaxyforma-tion(e.g.seeLongair,1998,andreferencetherein),smallquantumfluctuationsthatwerestretchedouttocosmologicalscalesbyinflationgrew(mainlylinearly)duringtheradiation-dominatedera,tillthepresent.Theinitialpowerspectrum(P(k)∝kn),whichchar-acterizesthesefluctuationsinFourierspace,isnearlyscaleinvariant(i.e.n≃1)onallscales.Initially,allscalesgrewatthesamerate.Smallscalesen-teredthehorizonbeforetheuniversebecamematter-dominated.Duringthattimetheirgrowthwassup-pressed.TheresultingpowerspectrumPE(k)hasn≃1(−3)onlarge(small)scales.Thesedark-matterfluctuationsformeddeepgravitationalpotentialsinwhichgalaxiesandgalaxyclustersformed.Whenthedensitycontrastreachedδρ/ρ∼1,thefluctua-tionsgrewnon-linearlyuntil∆ρ/ρ∼200. Sinceonlygravityisdrivingthisbuild-upofmatter,massivegalaxiesaremorelikelytobefoundinhigh-densityregions,whereaslow-massgalaxiesaremoreuniformlydistributed.Thisproducesanenhance-mentoftheclusteringofmassivegalaxies.There-fore,theclusteringpropertiesofgalaxiesprobetheirdark-mattermassdistribution.Theauto-correlationξ(r)isanaturaltooltostudyclusteringinthiscon-text,sinceξDMistheFouriertransformoftheevolvedpowerspectrumPcorrelationE(k)(e.g.Peacock,1999).Thegalaxyξggisrelatedtothedark-matterauto-correlationξDMviathebiasb.Atagivenred-shift, ξgg(r)=b2(M)ξDM(r).(6)ThisbiascanbecomputedinthePress-Schechterfor-malismextendedbyMo&White(2002)andrefer-encetherein. Similarlytothegalaxyauto-correlationξcandefinethecross-correlationξgg,onedgbetweenDLAs 8 andLBGsfromtheconditionalprobabilityoffindingagalaxyinavolumedVatadistancer=|r2giventhatthereisaDLAatr1: −r1|,P(LBG|DLA)=nu(1+ξdg(r))dV2, (7) wherenuistheunconditionalbackgroundgalaxyden-sity.Thus,thenumberofneighborgalaxiesinacell ofvolume∆VisgivenbyNp= ξdg(r)),whereξisthecross-correlationaveraged overthevolume∆V.Thisestimatorofξrequiresanestimateoftheunconditionalbackgroundgalaxyden-sityng.Therearetwowaystoquantifynthecross-correlation:onewayistousegalaxiesgincaseofspa-tiallyfarfromtheDLAasinBouch´e&Lowenthal(2003);theotherwayistousetheentiregalaxycat-alog.Here,weusedthelatterbecauseofthesimplic-ityofthismethodwhenrandomizingthelineofsight(seesection5.2).Naturally,largefieldswillyieldabetterestimateofncanextendtheg. Wespatialcross-correlationξtoangularcorrelationfunctionwsincetheformerisdirectlyrelatedtospatialcorrelationfunctionsξ.Namely,iftheselectionfunctionφ(z)≃1/W[−Wandzerootherwise,then zwithinz/2,Wz/2]w(r)= 2 z2+r2 z,(8) orw(rθ)≃A ro constantthatcan dβ whereβ=1−γandAisabecomputedanalytically(e.g.Adelbergeretal.,2003;Eisenstein,2003). Weusedthefollowingestimatorofthecross-correlationwdg(r), 1+ Nobs(r)Ng [1+ Nobs/NDLA,yieldsthePoissonerrorsforEq.9(e.g.Mo,Jing&Boerner,1992;Landy&Szalay,1993): σw≃ √ 1+ wgoesastheinverseofthesquarerootofthenumberdg ofDLAs,NDLA,andastheinverseofthesquarerootofthenumberofgalaxiesNg. 5.RESULTS Withtheclusteringformalismlayedoutinsec-tion4,wecanpresentourresultsontheDLA-LBGcross-correlation(§5.1)andonthecomputationoftheerrors(§5.2). 5.1.DLA-LBGcross-correlationfromthecombined fieldsFig.6showstheDLA-LBGcross-correlationwcomputedusingEq.9.IncomputingNdgobs(r)andNrandinEq.9,wetookintoaccountthemaskedregionswithbrightstarsshowninFig.5.Thedottedlineshowstheauto-correlationwetal.(2003)andthecontinuousggofAdelbergerlineshowsafittotheamplitudeofwdgusingwggastem-plate.Thefittingmethodisdescribedbelow. Itisnecessarytotakeintoaccountthedifferentse-lectionsofthedifferentfieldsinperformingthesuminEq.9indicatedbythebrackets,sowemustweighteachfieldaccordingly.Wechosetoweighteachfieldaccordingtoitserrorsateachangularscalerforeachfieldl,wecomputeNi.Thus,obs ∂f(rj) ∂wl(ri) 9 5.2.Errorcomputation BecauseeachDLAisataslightlydifferentred-shift,eachfieldhasadifferentselectionfunction,anditisnecessarytotakeintoaccountthesedifferencesbyweightingeachfieldaccordingly.Asmentioned,wechosetoweighteachfieldaccordingtoitserrorsσw(ri). Theerrorsneedtobecomputedcarefully.Severaloptionsareavailable.TheproperwaytocomputetheerrorswouldbetoresampletheDLAs(viaboot-straptechniques),butthisisimpracticalheregiventhenumberofDLAfieldsatourdisposal.Anotherwaywouldbetobootstrapthegalaxies,whichwouldreproduceonlythePoissonianerrors(Eq.11). Weusedyetanothermethod,whichistoperformMonteCarlosimulationsinwhichwerandomizethepositionoftheDLA.Thistakesintoaccounttheclus-teringvarianceduetothegalaxyauto-correlation,butmissesthevariance(andco-variance)duetothecross-correlationitself(thefactor1+wdginEq.10).However,thistermwillbesmallonscaleslargerthan5h−1Mpcbecausewdg<<1. Thus,ineachDLAfieldl,wecomputedthefullco-variancematrixCOVlfromnr=200randomizationsoftheDLAposition:COVl(ri,rj)= 1 w(ri)][wk(rj)− wis theaverageofthenrmeasurementsofthecross-correlation.Theerrorsσl(ri)towl(ri)foreachfieldlfollow. Ourerrorsareconsistentwiththeerrorsexpectedfromouranalysisofcosmologicalsimulations:inBouch´eetal.(2004,inpreparation),weconcludethatwithadatasetofthissize,wecanbesensitivetothecross-correlationonlyonscales5-10h−1Mpc,whichiswhereweseeapositivecross-correlation. 5.3.Theintegralconstraint Becausetheunconditionalgalaxydensity,nuinEq.7,isestimatedfromthetotalobservedgalaxydensity,whereasitshouldalwaysbelowerthantheobservedgalaxydensity,allestimatesofξ(orw)arebiasedlow.Thisbias∆w,oftenreferredtoasthe‘in-tegralconstraint’,canbecomputedanalytically(e.g.Landy&Szalay,1993;Saslaw,2000).Fortheangu-larcross-correlationfunction,itis: ∆w= 1 10 6.2.Isthisresultdrawnfromrandomlinesofsight?Giventhelargermstothefittedamplitudea,couldourresultsimplybealargefluctuationofthesetofpossiblevaluesforrandomlinesofsight?Totestthis,wechose100linesofsightselectedatrandom,excludingthecentral5h−1MpctoensurethatthenewlinesofsightarenotcorrelatedwiththeonescenteredontheDLAs.Wethencomputedthecross-correlationforthese100randomlinesofsightintheredshiftslicescenteredontheDLAs.Asbefore,wecomputedtheweightedmeantowdgandusedEq.13.Fig.7showsthelogarithmoftheχ2(a)forfixedamplitudesaforthe100randomlinesofsight(filledcircles).Thecontinuouslineshowsthemedianofthedistributions.Thedottedanddashedlinesarethe95%and99%levelsofthedistributions.Themedian,95%and99%levelsarefoundafteraGaus-siankernelsmoothingofthedistributionsusingtheoptimumbandwidth(Wand&Jones,1995)(There-sultsarenotsignificantlychangedusingafixedbandwidth).Theopensquareshowsthelocationofthere-sultofFig.6.Sinceitliesclosetothe95%confidencelevel,thisshowsthatthesignalmeasuredinFig.6isnotdrawnfromarandomdistributionoflinesofsight,atthe>95%confidence. 6.3.Howaboutotherredshiftslices? TheresultofFig.6shouldbecomparedwiththecross-correlationwhenthereisnoDLAinthered-shiftbin.Fromourphotometricredshiftanalysis,weselectedgalaxiesintwootherredshiftslicesthatdidNOTcontaintheDLA.WechosetheslicesthatwereintheforegroundandinthebackgroundfromtheDLA,andoffsetby+or−0.15inredshift(seeFig.4).Ineachcase,theχ2fitdoesnotfavoranyclustering:thebestamplitudeisa=−0.20±1.26anda=−0.24±2.04,respectively.Aclusteringsig-nalinthisslicewouldhavecastastrongdoubtonourresultsthatdocontaintheDLAinFig.6.Inad-dition,weperformedthesamecheckonanothersliceatredshift3.6.Thebestamplitudeforthissliceisa=−0.13±1.44. WerepeatedtheanalysiswithWwhethertheobservedclusteringdependsz=0.20totestonthechoiceoftheslicewidth.Wefoundthata=1.45±1.35inthiscase,soweconcludethattheslicewidthdoesnotstronglyaffecttheclusteringsignal. 6.4.ComparisonwithpastandfutureworkWolfe(1993)alsofoundthatLy-emittersarestronglyclusteredaroundDLAs.Incontrast,Gawiseretal.(2001)didnotfindevidenceofcluster-ingandthestudyofAdelbergeretal.(2003)foundalackofgalaxiesneartheirfourDLAs,within 5.7h−1Mpc.Sincethesetwosurveyswerenotsensi-tivetoclusteringonscaleslargerthan>5h−1Mpc,andoursisnotsensitiveto<3−5h−1Mpc,ourresultsarenotinconsistentwiththeirs.Thelackofgalaxiesonsmallscalescould,however,beduetomorelocalenvironmentaleffects,suchasstronggalacticwindsfromstarforminggalaxies. AlthoughsimulationsofDLApropertiesexist(e.g.Katzetal.(1996);Gardneretal.(2001);Nagamine,Springel,&Hernquist(2003b)),nopre-dictionoftheDLA-LBGcross-correlationhasbeenpublished.InBouch´eetal.(2004,inprepara-tion),weusetheTree-SmoothedParticleHydro-dynamical(TreeSPH)cosmologicalsimulationsofKatz,Weinberg,&Hernquist(1996b)tomeasurethe‘theoretical’DLA-LBGcross-correlation.Thesesim-ulationscontain1283darkmatterparticlesandasmanygasorstarparticles.Eachgalaxy(≡>64SPHboundparticles)isabletoformstars.Withasim-ilarnumberofDLA-LBGpairsandredshiftdepth(Wz=111h−1Mpc),wefindwsignaltonoise.Furthermore,dg>0withthesamewithamuchlargersampleof200simulatedDLAs,wefindw0.75±0.1,orrdg≃arelessmassiveothan≃3.5theh−1Mpc.Thus,DLAhaloshalosofLBGs,whichare1012M⊙(Porciani&Giavalisco,2002;Ouchietal.,2003).GiventhepresentsampleofthreeDLAs,ourobservedconstraintonwdgwithitsuncertaintyisconsistentwiththesesimulationresults. 7.SUMMARYANDCONCLUSIONS Basedondeep(µI,AB(sky)≃27.6magarcsec−2) wide-fieldimages(0.31deg2or∼65×65h−1 z=3)aroundthree71Mpcco-movingatredshiftDLAs,weidentifyLBGcandidatesbrighterthanI.80magusingphotometricredshifttechniquesAB=24thatincludedtheImagnitudeasapriorestimateinad-ditiontothecolors. Fromtheredshiftlikelihooddistributions,wese-lectedLBGgalaxieswithinaredshiftsliceofwidthWz=0.15(≃σzz)centeredontheredshiftoftheDLAsabs.Withinthatslice,wecross-correlatedtheLBGswiththepositionoftheDLAsandfoundthat•thecorrelationamplitudewdgrelativeofthetotheDLA-LBGauto-correlationcross-wspondingggwaswtodg/wrggo=5≡±4a.5h=−11.Mpc62±(co-moving),1.32,corre-•thecorrelationamplitudeisa>of0,thewhichDLA-LBGissignificantcross-atthe>95%confidencelevelbasedonMonteCarlosimulations,•theredshiftclusteringslicesthatsignaldidwasnotnotcontainpresenttheinDLAs. three11 Giventheuncertaintyofourresults,wecannotputconstraintsonthehalomassesofDLAsanddiscriminatebetweenthelargediskhypothesis(e.gWolfeetal.,1986),andsmallsub-L∗hypothesis(e.gMalleretal.,2000;Haehnelt,Steinmetz,&Rauch,2000;Mølleretal.,2002).Ourobservationoftheclusteringonlargescales(>4h−1Mpc)isnotinconsistentwithpreviousclusteringstudies(Gawiseretal.,2001;Adelbergeretal.,2003)sincethesewerelimitedtosmallscales.Inordertobeabletodirectlycomparethesestudieswithourpresentresultsonscales<4h−1Mpc,alargersampleofDLAsandmulti-objectspectroscopyofourLBGcan-didatesareneeded.Thiswillenabletotestwhetherthecross-correlationisstrongerorweakerthantheauto-correlation. N.B.acknowledgesapost-docfellowshipfromtheEuropeanCommunityResearchandTrainingNet-work“ThePhysicsoftheIntergalacticMedium”.J.D.L.acknowledgessupportfromNSFgrantAST-0206016.Wethanktheanonymousrefereeforacare-fulreadingofthemanuscriptthatimprovedthequal-ityofthepaper.WealsothankH.Mo,N.KatzandB.M´enardforhelpfuldiscussions,andJ.Fynboforreadingaearlierdraft. 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APM08279+525 PC1233+4752 J0124+0044 QSOProperties DLAproperties aGalactic extinctionfromSchlegeletal.(1998),averagedoverthefield. References.—(1)V´eron-Cetty&V´eron(2001);(2)McMahonetal.(2002)(3)Schneider,Schmidt,&Gunn(1991)(4)Carillietal.(2001)(5)White,Kinney,&Becker(1993);(6)Petitjeanetal.(2000);(7)P´eroux,C.,2003,privatecommunication. Table2 Summaryoftheobservations.Uband BbandVbandIbandAPM08279+52553.75hr35min50min2.08hrFeb.7,8,2000PC1233+47523.50hr40min50min1.92hrFeb.7,8,2000J0124+0044 3.72hr 47min 52min 2.08hr Sept.23–26,2001 16 Table3 Photometricsolution. RunIZP a FilterBI aFor ZP23.52(0.02) RunIIα-0.421(0.02)-0.072(0.01) β0.018(0.007)-0.025(0.009) 25.085(0.03) 25.25(0.02) 24.58(0.05) runI,weassumedtheairmasscoefficientαandthecolorterm βtobethesameasforrunII. Table4 Depthoftheobservations Exp./Frames(sec./#) AirmassXa(min-max) FWHM(arcsec) SBlim(1σ)b(mag/mAB) SBlim(5σ)b(mag/mAB) mlim(3σ)c(mag/mAB) FieldsFilter PC1233+4752 UBVI12600/142400/87590/106900/151.04-1.161.05-1.071.07-1.111.07-1.451.051.00.91.127.82/28.5228.59/28.5128.18/28.2027.19/27.6426.07/26.7826.84/26.7626.43/26.4525.44/25.9025.94/26.6526.75/26.6826.45/26.4725.30/25.76 cosζ bLimiting whereζisthezenithangleofthetelescope. surfacebrightnessinmagnitudespersquarearcsecond.insidea2×FWHMdiameteraperture. cMeasured Table5 Numberofgalaxiesinthedifferentredshiftslices. Field P− PDLA P+ 17 Fig.1.—ThesolidlinesshowthetransmissioncurvesforourfourfiltersU,B,V,andI.ThedashedlineshowstheCCDresponsefunction.ThedottedlinesshowthefiltertransmissionconvolvedwiththeCCDresponsefunction. 18 Fig.2.—Redshiftdistributionforeachofourfields.ThedottedhistogramshowsthephotometricredshiftdistributionusingnopriorsandthetemplatesetA.Thecontinuoushistogramshowsthephotometricredshiftdistributionusingthepriors.Usingthepriorshastheeffectofeliminatingthelargenumberofgalaxiesthathavebeenassignedzphot≃2wrongly,butdoesnotaffectthedistributionatz∼3significantly.TheverticaldashedlineshowstheredshiftoftheDLAzDLA.ThisplotshowstheeffectofthepriorsandthatourselectionpeaksataredshiftclosetothatoftheDLA. 19 Fig.3.—Absolutemagnitudevs.photometricredshiftforeachfield.Eachdotrepresentsonegalaxyinourfields.Therest-frameabsolutemagnitudeMIwascomputedusingthedistancemodulusandtheK-correction(seetextfordetails).Thecontinuouslinesshowourmagnitudeselection22 Fig.4.—Redshiftslicescentered(a)infrontof,(b)on,and(c)behindtheDLAfortheAPM08279+5255field.Thevaluezabs=2.974isindicatedbytheverticaldashedline.EachdotrepresentagalaxythatwasdetectedinthefourUBV&Ibands.ThefilledsquaresindicateobjectsthatarenotdetectedintheUband.Theleftcolumnshowstheprobabilitydistributionasafunctionofphotometricredshift.Thecontinuouslineshowsthesmootheddistribution(arbitrarilyscaledtothepeak).Therightcolumnshowstheprobabilitytobeinthatparticularsliceasafunctionofthe‘goodness’ofthephotometricredshiftP∆zdefinedinEq.4.Thedottedlineshowstheminimumthreshold(50%)usedinselectingLBGcandidatesineachoftheslices. 21 Fig.5.—Forourthreefields,thexypositionofourLBGcandidatesrelativetotheQSOlocation.Northisleft,Eastisdown. 22 APM08279+5255PC1233+4752J0124+0044Fig.6.—Thecross-correlationwdgbetweenDLAsandLymanbreakgalaxiesinaredshiftsliceofwidth(Wz=0.15)thatcontainstheDLAs.Thefilledsquaresshowthecross-correlationforthecombinedfields.ThedottedlineistheLBGauto-correlationwgg(fromAdelbergeretal.,2003,usingEq.8toaccountforthevolumeofourredshiftslice).Thecontinuouslineisafittotheamplitudeofthecross-correlationusingwˆdg=a×wgg,i.e.weassumethatbothwggandwdghavethesameslope. 2 Thesmallpanelshowstheχdistributionasafunctionoftheamplitudeaandthe1σrange. 23 Fig.7.—Thepointsshowthelogarithmofχ2(a)asafunctionoftheamplitudeafor100randomlinesofsight(excludingthecentral5h−1Mpc)intheredshiftslicecenteredontheDLAs.Thecontinuouslineshowsthemedianofthedistributions.Thedottedlineandthedashedlinearethe95%and99%confidencelevels,respectively.TheopensquareshowsthelocationofthefittedamplitudeshowninFig.6,whichshowsthatthesignalmeasuredinFig.6isnotdrawnfromarandomdistributionoflinesofsightatthe>95%confidencelevel. 因篇幅问题不能全部显示，请点此查看更多更全内容