An I-band calibration of the SBF method at blue colours

An I-band calibration of the SBF method at blue colours

Astronomy&Astrophysicsmanuscriptno.mieskeFebruary5,2008

cESO2008

AnI-bandcalibrationoftheSBFmethodatbluecolours

arXiv:astro-ph/0605660v1 26 May 2006

S.Mieske1,M.Hilker2,andL.Infante3

1

2

3

EuropeanSouthernObservatory,Karl-Schwarzschild-Strasse2,85748GarchingbeiM¨unchen,Germany

e-mail:smieske@ArgelanderInstitutf¨urAstronomie-AbteilungSternwarte,AufdemH¨ugel71,53121Bonn,Germanye-mail:mhilker@astro.uni-bonn.deDepartamentodeAstronom´ ayAstrof´ sica,Ponti ciaUniversidadCat´olicadeChile,Casilla306,Santiago22,Chilee-mail:linfante@astro.puc.cl

ABSTRACT

Context.Thesurfacebrightness uctuation(SBF)methodisapowerfultooltoderivedistancestogalaxiesforwhichsinglestarscannotberesolved.Uptonow,themethodhasbeencalibratedmainlyatredcoloursduetotheintrinsicfaintnessofblueearly-typegalaxies.Aims.InthispaperweaddresstheI-bandcalibrationoftheSBFmethodatbluecolours,theregimeofdwarfellipticalgalaxies(dEs).

Methods.Wepresentdeepandwide- eldVIphotometryofthecentralFornaxclusterobtainedatLasCampanasObservatory.WiththesedataweperformanSBFanalysisof25dEsintherange 16.5<MV< 11.2mag,0.8<(V I)0<1.10mag.Ourcolourcalibrationisaccuratetobetterthan2%.ForthecalibrationanalysisweexcludeeightdEswhoseSBFmeasurementwasa ectedbypoorseeing(FWHM 1′′).Results.OurSBFdataareinconsistentatthe3σlevelwithacolourindependentabsoluteSBFmagnitude

MI (V I)plane.Weobtainthefollowingone-branchempiricalSBFcalibration:

MI,whichissigni cantlylarger

thanfoundatreddercolours.ThisisinagreementwiththosetheoreticalSBFmodelsthatpredict

indicator.ThisnormalisedamplitudeconvertedtomagnitudeisintheframeworkofSBFinvestigationsreferredtoasappar-ent uctuationmagnitude

o printrequeststo:S.Mieske

An I-band calibration of the SBF method at blue colours

2S.Mieskeetal.:SBFcalibrationatbluecolours

surveytomeasuretheapparentI-bandSBFmagnitude

MIandthedereddenedcolour

(V I)0,determinedintherange1.05<(V I)0<1.3:

MRand(B R)in

the

range

1

.

<

(

B

R)<1.3magbytargetingnearbydwarfellipticalgalaxieswithknowndistances.TheseauthorsbasedtheircalibrationonthetheoreticalpredictionsofWorthey(1994)modelsandusedtheirobservationaldatatoadjustthezero-pointofthosemod-els.InJerjenetal.(2001)theyfoundthatthemodelspredictedtoofaintSBFamplitudesby0.13mag.Furthermore,theypro-posetwoseparatebranchesinthe

MRbecomesbrighterwithyounger

andmoremetal-richstellarpopulation.Thismeansthattheage-metallicitydegeneracyof

Mz

vs.(g z)for1.0<(g z)<1.3.Theyobtainedasigni cantslopeinthatcolourrange(4.5σ),butdidnot ndevidenceforabimodalityof

MF160Wand(V I)0intherange

1.05<(V I)0<1.24mag,whichwasbasedonlyongiantgalaxiesandyieldedacomparableslopetothatinequation(1).Forgroundbasedinfraredbands,Jensenetal.(1998)andLiuetal.(2002)presentedcalibrationsbetweenKand(V I)0,alsobasedpurelyongiantgalaxies.ThesmallsampleofJensenetal.intherange1.15<(V I)0<1.27magwasconsistentwithazeroslopebetween(V I)0and

MIareplottedvs.(V I)0for

asetofoldtointermediateagestellarpopulationswithawiderangeofmetallicities,takenfromdi erentliteraturesources:Worthey(1994),whouseshisownstellarpopulationmod-elsbasedonVandenBerg(1985)andYale(Greenetal.1987)isochrones;Liuetal.(2000),whousetheupdatedmodelsbyBruzual&Charlot(1993)plustheBertellietal.(1994)Padovaisochrones;Blakesleeetal.(2001)whousethestellarpopula-tionmodelsofVazdekisetal.(1996)andtheupdatedGirardietal.(2000)Padovaisochrones;andCantielloetal.(2003),whousethestellarpopulationsynthesiscodebyBrocatoetal.(1999,2000)andtheTeramo-Pisa-Romeisochrones(e.g.Castellanietal.1991,Castellanietal.1992andBonoetal.1997a,1997b).Equation(1)isalsoshowninFig.1.TheWortheymodelpredictionsaresplitupintotheoriginalpredic-

An I-band calibration of the SBF method at blue colours

S.Mieskeetal.:SBFcalibrationatbluecolours3

tionsfromWorthey(1994)1andthosethat

use

the

alternatestel-

lar

evolutionary

isochrone

library

fromBertelliet

al.(1994)2

.Forthe

sakeofclarity,weseparatethemodelpredictionsintotwodi erentplots.

Forredcolours,allmodelstraceequation(1)reasonablywell,withtheoriginalWorthey-modelsandthoseofBlakesleeetal.beingmoredeviantfromtheempiricalcalibrationthantheothermodels.Inthebluerange,thereisanotablediscrepancybetweenthemodelpredictions:theoriginalWorthey(1994)modelsandthoseofLiuetal.(2000)predictacolourinde-pendent

MIcausedby

agedi erences.Thosemodelspredictacontinuationofequa-tion(1)forintermediateagesanda atteningoftherelationforveryoldages.At(V I)0 0.90thisleadstoanuncertaintyofupto0.5maginrelating

MI= 2.0+2.25×((V I)0 1.09)mag

(2)

ThiscaserepresentsthetheoreticalSBFmodelsplottedintheleftpanelofFig.1,whichviewedasawholesuggestanon-zerobutshallowerslopethanthatoftheempiricalcalibrationatreddercolours.SeecaseC)belowforthereasonofchoosing(V I)=1.09ascolourlimit.

CaseC:Thisisequation(1)appliedfor(V I)0>1.09andaconstantof

MI 2.0mag

ofthemodelsintherightpanelofFig.1matchesthevalueof

MI= 2.00mag,likeincase

C).Thisisappliedtoallgalaxieswith(V I)0<1.09whosedistanceincaseB)islargerthanthemeandistance.Inotherwords,galaxieswith

MI= 2.00mag,whilethosebelowareassigned

relation(1).ThemeandistanceobtainedwiththiscaseisofcourseveryclosetothatincaseB).

aa

CarnegieObservatoriesSystemforMultiObjectSpectroscopy,http://llama.lco.cl/aoemler/COSMOS.html

3

An I-band calibration of the SBF method at blue colours

4S.Mieskeetal.:SBFcalibrationatblue

colours

Fig.1.Theoretical“isochrones”inthe

a

a

M

I

=

2.00magandthecontinuationofequation(1)for(V I)0≤1.09.SeeSect.4formoredetails.

strumentalmagnitudesweremeasuredwiththeIRAFpackageAPPHOTinaperturesequaltothoseusedbyLandolt(1994).Then,asinglephotometricsolutionwasdeterminedfortheentire8k×8kimage.Chip-to-chipvariationsaroundthemeanphotometriczeropointweresmallerthan0.02mag.Tocor-rectforgalacticreddeningandabsorption,weusedtheval-uesfromSchlegeletal.(1998),whogiveAI=0.025andE(V I)=0.018forthecoordinatesoftheFornaxcluster.

3.2.SBFmeasurement

TheSBFmeasurementprocedurewassimilartothatalreadyoutlinedinMieskeetal.(2005)basedonVLTFORS1photom-etry.Somenuanceshavebeenmodi ed:the uctuationsfromtheskybackgroundwerenowderivedinthesameimageclosetotheinvestigateddEinsteadofinacomparison eld.Thosesky uctuationsconsistedofundetectedbackgroundgalaxiesandfringing.Theseeingwasnotconstantoveronechip,gen-erallyincreasingtowardstheedgesofthe eldofview.Thiscausedacorrespondinglyvaryingamountof uctuationfromundetectedbackgroundgalaxiesalongthechip.Alsothefring-ingvariedinsomecasessigni cantlyoveronechip,seeFig.2.Thesetwodependencesonpositionrequiredalocaldetermina-

tionofsky uctuations.NotethatfortheVLTFORSphotom-etrytherewasnosigni cantfringingnorstrongvariationsofseeingamongthedi erentexposures.

Inturnwedescribetherelevantmeasurementstepsfordeter-miningtheSBFmagnitude:

1.ModelmeangalaxylightwithELLIPSEusingasigmaclip-pingalgorithmtodisregardcontaminatingsources,subtractthemodel.

2.Detectandsubtractremainingcontaminatingobjectsfromoriginalimage.

3.Modelmeangalaxylightonthecleanedimage.4.Subtractmodeloforiginalimage.

5.Divideresultingimagebysquarerootofthemodel,cutoutcircularportionwithradiustypically20-25pixel(4 5′′),cor-respondingtoabout4-8seeingdiskdiameters.

6.Maskoutcontaminatingsourceslikeforegroundstarsandbackgroundgalaxies.

7.Calculatethepowerspectrum(PS)ofthecleanedimage.8.CalculatethePSoftheskybackgroundinthreedi erentblankimagesectionsclosetotheinvestigatedgalaxy.ThisskybackgroundPScontainsboth uctuationcontributionsfromundetectedbackgroundgalaxiesas uctuationscausedbyfringing,seeexplanationatbeginningofthissubsection.

An I-band calibration of the SBF method at blue colours

S.Mieskeetal.:SBFcalibrationatbluecolours5

Normalisethese uctuationsbydividingtheseblankimagesbythemeangalaxyintensityintheregionwhereSBFaremea-sured.SubtractthisnormalisedbackgroundPSBGfromthePSoftheSBFimage.

9.ObtaintheazimuthalaverageoftheresultingPS.10.FitfunctionoftheformP(k)=E(k)×P0+P1

(3)

totheresult.Here,E(k)=PSF(k) W(k)withW(k)thePSofthemaskusedtoexcisecontaminatingsourcesandrestrictthemeasurementarea.PSF(k)istheundistortedpowerspec-trumofthePSFnormalisedtounityatk=0.PSF(k)isderivedfromonetothreewellexposedstar(s)inthesameimageclosetotherespectivegalaxy.Whenmorethanonestarwasused,theaveragePSF-PSwasadoptedasPSF(k).ThevariationsinPSFFWHMbetweenstarschosenforonegalaxyweresmall,around5%.UsingE(k)insteadofPSF(k)implicitlycorrectsforthepowerspectrumdampingatlowwavenumbersthatiscausedbytheconvolutionoftheundistortedPSF

(

k

)

with

thepowerspectrumofthe

mask(seeMieskeetal.2005).Theamountofpowerspectrumdampingatwavenumberzerowasonaverage0.11magwithagalaxy-to-galaxydispersionof0.04mag.Thesignal-to-noiseratiooftheSBFmeasurementisthende nedasS/N=P0

mIfrom

10 0.4 (MV+15)

=5(Milleretal.1998).Thecalculatedval-uesfor GCarelisted

inTable1,rangingbetween0.01magand

0.42magwithameanof0.06magandmedianof0.03mag.Thecolour(V I)0ofeachgalaxywasadoptedasthemeanoftwovalues: rst,the(V I)0estimatesfromtheIMACSdataintheregionwhereSBFweremeasured;second,thecoloursde-rivedbyusforthesamegalaxiesinHilkeretal.(2003).TheselatterdatawerebasedonWFCCDphotometrywiththe2.5mduPonttelescope,alsoatLasCampanas.Thosecolourshadbeendeterminedincircularaperturesof4′′radius,whichisincloseagreementtothesizeoftheregionwhereSBFweremeasured.ForthosegalaxiesenteringourSBFdataset,thesystematicdif-ferencebetweentheIMACSandWFCCDcoloursis0.017±

0.021mag,withascatterof0.10mag.Thisshowsthatourpho-tometriccolourcalibrationisaccuratetobetterthan0.02mag.Fig.3showstheCMDoftheinvestigatedgalaxiesforthevar-iouscoloursets.Thermsdispersionincolourofalinear tis0.083magfortheIMACSdata,0.068fortheWFCCDdataand0.058magforthemean,independentofmagnitude.Weadoptthisverydispersionof0.058magascolouruncertainty.Thisistobeseenasanupperlimittotherealcolourerrorbecausethermsdispersioncertainlyincludessome“cosmic”scatter.With(V I)0athand,

mI,

thisyieldedthe“nullhypothesis”distancemodulus(m M)A,seeTable1.Fig.4showsthumbnailimagesillustratingtheSBFmeasurementprocedurefortwooutofthe28dEswithclearSBFsignal.25ofthe28investigatedgalaxieshadS/N>3andenteredoursubsequentanalysis.Theirabsolutebrightnessesareintherange 16.5<MV< 11.2mag,theircentralsurfacebrightnessescovertheregime20.3<µV<24.6mag/arcsec2.Theyoccupyacolourrange0.8<(V I)0<1.10mag,ide-allysuitedforextendingtheTonrycolourrangetotheblue.InFig.5weshowthatthenullhypothesisSBFdistancemodulusdoesnotcorrelatewiththeS/NoftheSBFmeasurementnorwiththeamountofbackground uctuationsBG.

NotethelargerangeofBGvaluesinFig.5.Thishasthreerea-sons:The rstandmainreasonisrelatedtothefactthatBGisdeterminedby ttingequation(3)tothenormalisedskyback-groundPS.Forthis ttingwehavetoexcludethesamelowwavenumberregimethatisexcludedfor ttingthegalaxySBFamplitudeP0.SinceBGisonlyafractionofP0,thisexclusionoflowwavenumbershasastrongere ectonthe ttingpreci-sionforBGthanfor ttingP0.Indeed,thenegativevalueforBGthatismeasuredforFCC215(seeTable1andFig.5)isaconsequenceofthislowwavenumberexclusion.Theback-groundPSintheremainingwavenumbersispredominantlynoisedominatedsuchthataformallynegativevalueforBGis tted.Asaconsequenceofthat,theSBFdatawithpoorseeing(FWHM>0.85′′)showascatterinBGof0.16magwhichisal-mosttwiceaslargeasthescatterof0.09magforthedatawithgoodseeing(FWHM<0.85′′),seeFig.5.ThesecondreasonforthevariationofBGisthatthegalaxiesinvestigatedspanaconsiderablerangeinsurfacebrightness(>4mag).ThisleadstovaryingrelativeamountsofBG,giventhattheSBFsignalinlowersurfacebrightnessregionsismorestronglya ectedbyskybackground uctuations.Thethirdreasonisthesomewhatvaryingfringingamplitude,bothbetweendi erentchipsanddi erentnights,seeforexampleFig.2.

We nallynotethattheskybackgroundcorrectionofthegalaxySBFdataisdonebydirectlysubtractingtheskyback-groundPSimagefromthenormalisedgalaxylightPSimage.Onlythequanti cationofthecorrectionisachievedby ttingaPS.Totaketheuncertaintyarisingfromthepower-spectrum tandfromthesky uctuationvariabilityintoaccount,weadoptthescatterofP0resultingfromthesubtractionofthreedi er-entskybackgroundPSimagesaserrorestimateoftheSBFmeasurement,seethefollowingSect.3.2.1.

An I-band calibration of the SBF method at blue colours

6S.Mieskeetal.:SBFcalibrationatblue

colours

Fig.2.TwoimageexcerptsfromthesamechipandexposureclosetotwoinvestigateddEs,illustratingthevariabledegreeoffringing.Intheleftthumbnail,FCC194isatthebottomright.Intherightthumbnail,FCC196isatthebottom.Bothimageshavethesameintensitycuts.Notethefringingpatternsintherightthumbnail,whicharenotpresentintheleft

one.

Fig.3.ColourmagnitudediagramofthegalaxiesenteringourSBFanalysis,i.e.thoseoneswithanSBFS/N>3,seealsoFig.5.SmallbluecirclesindicatecoloursderivedfromthepresentIMACSdataset.SmallredasterisksindicatecoloursfromtheWFCCDdatasetofHilkeretal.(2003).Largeencir-cledasterisksisthemeanofbothvalues.TheVmagnitudeisfromtheWFCCDdatasetforallgalaxies.

TheerrorofP0wasestimatedintwoways:

1.basedontheMonteCarlosimulationspresentedinMieskeetal.(2003a).Forthemedianseeingofourdata(0.75′′),inter-polationofthesimulationresultsfor0.5and1.0′′forFornaxdEsand1hourintegrationyieldsthefollowinguncertainties:0.37magintherange 11>MV> 13mag,0.27magintherange 13>MV> 14.5mag,and0.20magintherangeMV< 14.5mag.Notethatthesimulationerrorsarecalcu-latedforimagesofthesamepixelscalethantheoneusedhere.ThefainterVLT-FORSzeropointsassumedinthesimulationsarepracticallycompensatedbythelargerintegrationtimesofourMagellan-IMACSdata.

2.fromthescatterofthe ttedvaluesforP0whensubtractingthethreedi erentskybackgroundpowerspectra.Thiswasanimportantdouble-checkoftheerrorsadoptedfromthesimu-lations,becausethefringingoftheIMACSdatarepresentanadditionaluncertaintysource,apartfromthephotonnoiseandbackgroundgalaxy uctuationswhichhadbeenincludedinthesimulations.

ThemaximumofbotherrorestimateswasadoptedaserrorinP0.Forsevenoutofthe25dEsinvestigated,thescatterfrombackgroundsubtractionwaslargerthantheMonteCarloesti-mate,seeTable1.Theresultingmeanerrorof(m M)is0.41magwhenadoptingcalibrationcaseA).Therearefourgalax-iesintherange 16.5<MV< 11.5magwhichwereim-agedtwiceinthecourseofoursurveysincetheywerelocatedintheoverlapofadjacent elds.Thedi erencesin(m M)betweenthosedoublemeasurementsrangedbetween0.10and0.35mag.Thisisencouraginglylow,indicatingthatouruncer-taintyestimatesareontheconservativeside.

3.2.1.ErrorestimateforSBFdistances

Theerrorof(m M)hastwoequallyimportantcontributions:uncertaintyin(V I)0andP0.

Theuncertaintyin(V I)0of0.058mag(seeabove)translatesintoa0.26magdistanceuncertaintyinthecaseoftheempiri-callycalibratedslope4.5.

3.3.Correlationbetweenseeingand

mIasa

functionofseeing,seeFig.6.Thosetwoobservablesshouldbeindependentofeachother.However,wedo nda2σsig-

An I-band calibration of the SBF method at blue colours

S.Mieskeetal.:SBFcalibrationatbluecolours

NameFCC222

1.036

FCC223

1.121

FCC241

0.900

FCC156

1.012

FCC196

0.898

FCC218

0.971

FCC140

0.881

FCC168

1.013

FCC214

1.016

FCC215

0.986

FCC192

0.860

LSB6-4

0.863

LSB10-8

20.01

28.72±0.37

5.5

0.29

0.04

0.64

31.76±0.45

31.24±0.39

30.73±0.37

19.87

28.26±0.37

8.1

0.17

0.02

0.86

31.31±0.45

30.79±0.39

30.27±0.37

19.40

28.74±0.45

4.2

0.41

0.01

0.68

31.21±0.52

30.98±0.47

30.75±0.45

19.07

28.75±0.37

7.5

0.27

0.03

0.62

31.09±0.45

30.93±0.39

30.76±0.37

18.88

28.69±0.37

9.9

0.24

0.04

0.66

31.05±0.45

30.88±0.39

30.70±0.37

18.54

29.11±0.37

4.5

0.39

0.02

0.67

32.07±0.45

31.60±0.39

31.12±0.37

18.17

29.07±0.27

7.6

0.21

0.02

0.73

31.61±0.37

31.34±0.30

31.08±0.27

17.67

29.17±0.27

5.3

0.24

0.07

0.79

32.04±0.37

31.61±0.30

31.18±0.27

17.24

29.24±0.31

7.1

0.41

0.42

1.20

31.61±0.41

31.43±0.34

31.25±0.31

16.40

29.31±0.20

9.4

0.22

0.03

0.65

32.18±0.33

31.75±0.24

31.32±0.20

15.86

29.56±0.20

11.0

0.23

0.02

0.71

31.44±0.33

31.44±0.33

31.44±0.33

15.65

mI

29.44±0.20

S/N4.1

BG0.05

GC0.07

seeing[′′]

0.65

(m M)A31.69±0.33

(m M)B31.57±0.24

(m M)C31.45±0.20

7(m M)D31.45±0.2031.44±0.3331.32±0.2031.25±0.3131.18±0.2731.08±0.2731.12±0.3731.05±0.4531.09±0.4531.21±0.5231.31±0.4530.73±0.37

Table1.ResultsofSBFmeasurementsforthe25FornaxdEswithS/N>3intheSBFmeasurement.Thegalaxiesareorderedbydecreasingbrightness.Inthe rstcolumn,the

reference

number

in

theFornaxClusterCatalogFCC(Ferguson&Sandage1989)isgiven.Thelastfourgalaxieshadbeentoofaintforthiscatalog.Theyarelabelledwitha eldnumberandrunningindexaccordingtoHilkeretal.(2003).AllcolumnshavemagnitudesasunitsexceptS/Nandseeing.(V I)0isthemeancolourofthephotometryfromHilkeretal.(2003)andthispaper.VisfromHilkeretal.(2003).Theotherparametersarederivedinthispaper.BGgivestheamountofbackground uctuationpresentintheoriginal uctuationimage,comprisingboth uctuationsfromundetectedbackgroundsourcesand uctuationsarisingfromfringing.(m M)Ato(m M)Dgivethefoursetsofdistancesobtainedwhenapplyingthefourdi erentcalibrationtestcases,seeSect.2.

ni cantcorrelationinthesensethatbadseeingdatahavestronger

mIisthata ttothesameseeingpowerspectrumyieldssys-tematicallyhigherP0whenexcludingmorelowkdatapoints(whichisthecaseforbadseeingdata).Wehavetestedthisforourstellarpowerspectra:fora xedassumedwidthofthepowerspectrum,the ttedP0dependsonlyverymarginally(toafewpercent)onthelimiting twavenumberk,evenwhenthe ttedpowerspectrumdatapointsareallbelow1/3ofP0.Wehavealsodouble-checkedwhetherforsomelargeseeingdatawemayerroneouslyhaveusedmarginallyresolvedobjectsforPSF tting.However,thiswasnotthecase.

Jensen,Tonry&Luppino(1998)arguethatpoorqualitySBFdatainIRSBFmeasurementsarepronetoarti cialincreasesofthe uctuationamplitudeduetoskybackground uctuations,imperfectgalaxymodellingorundetectedbackgroundsources.Forourdata,wecanmostlikelyexcludethee ectofsky uc-tuationsandundetectedbackgroundsources,seeSect.3.2.Thesky uctuationsareindependentofseeingandderiveddistance(seeabove),andtheglobularcluster uctuationsaresmall.We

concludethattheimperfectgalaxysubtraction(seee.g.rightpanelofFig.4)isthemajorcontributortotheincreaseof uc-tuationpoweratlargeseeing.ThisisbecausethePSFscaleapproachesthatexpectedforgalaxymodelresiduals(theSBFimagesfortheworstseeingdatahaveadiameterofonlyabout8PSFFHWM)suchthatthecommonlyappliedrejectionoflowwavenumbersinthepowerspectrum tcanapparentlynotremovealltheresidualpowerforthebadseeingdata.

FortheSBFcalibration,wethereforeexcludealldatawithsee-ingworsethan0.85′′FWHM.Doingthisremovesthedepen-denceofseeingon

mIvs.(V I)0.

An I-band calibration of the SBF method at blue colours

8

Calibration

S.Mieskeetal.:SBFcalibrationatbluecolours

d(m M)

d(V I)0

31.64±0.14

Equ.(1)and(2)(caseB)

31.13±0.10

Equ.(1)andconstant(caseD)

+0.190.47 0.10+0.180.45 0.10

0.40±0.020.31±0.02

2.23±1.681.775±1.65

0.079±0.079 0.189±0.062

(m M)SBF

Equ.(1)(caseA)

31.24±0.10

Constant(caseC)

31.23±0.08

31.39±0.12

σ(m M)

+0.180.44 0.10+0.110.28 0.06

δ(m M)

0.35±0.020.37±0.02

d(m M)

dV0

0.82±1.130.57±0.71

0.102±0.051 0.037±0.033

Table3.LikeTable2,butnowincludingall25investigateddEs.

Inallplots,galaxieswithseeingworsethan0.85′′areindi-cated.Table1givestheresultsinnumbers.Table2summarises

theparametersforeachcalibrationcasewhenusingonlythose17galaxieswithseeingbetterthan0.85′′.Shownisthemean(m M),thedistancescatter,themeanmeasurementerror,andthedependenceof(m M)oncolourandmagnitude(d(m M)).Table3showsthesame,butforall25galaxies.

Asastartingpointtotestthesecases,wehavetoadopta du-cialFornaxclusterdistancemodulus.ThemeanoftheCepheid,PNLF,GCLFandI-bandSBFdistancefromtheHST-KeyprojectsummaryofFerrareseetal.(2000)is(m M)=31.52mag.Notethathere,theCepheidscaleisusedtocalibratetheothermethods.Freedmanetal.(2001)presentarevisedCepheidcalibration,whichcausesadownwardcorrectionof0.13magfortheaverageCepheiddistancetotheFornax,VirgoandLeoIclusters(Table8oftheirpaper).Theresult-ingcorrectedmeanFornaxdistancethenis31.39mag.ThiscorrespondsexactlytotherevisedCepheiddistanceforFornaxfromFreedmanetal.(2001),whichhasanerrorof0.12mag.Therefore,wede neareferencedistanceof(m M)=31.39±0.12mag.BecauseofthesameCepheidscalerevision,alsotheformalzero-pointofequation(1)becomesfainterby0.09±0.02mag,ascalculatedfromcomparingtherevisedCepheiddistanceswiththeoldonesusedbyTonryetal.(1997)fortheirgroupcalibration.However,thisisasmallchangecomparedtothezero-pointscatterofmodelsshowninFig.1.Wedidthere-forenotincludethiso setinthetestcases,alsobecausetheTonrycalibrationdidnotextendtobluecolours.

Wede nethreecontrolcriteriaforthefourdi erentsetsofdis-tancemoduli:1)wedemandthatthereisnosigni cantcorrela-tionbetweencolour(V I)0anddistance(m M).Sinceweaimatacalibrationof

dV0

MIwithsmallcosmicvariance–aspredictedbytheLiuandWortheymodels,seeFig.1–doesnot tourSBFmea-surements.ThelargescatterofcaseC)isaccompaniedbyacleartrendofVwith(m M),signi cantatthe3σlevel.ThisstrengthenstheconclusionthatcaseC)isnotthebestapprox-imationofourdata.AlsoincaseB)thereissomecorrelationbetweenVand(m M),butatslightlylowersigni cance(2σ).CaseA)showsamarginaltrendofcolourwithdistance,butonlyatthe1.3σsigni cance.FortheshallowercalibrationcasesB)andD)thenominalvalueofthetrendbecomesverysmall.ForcaseC)thenominalslopeiscomparablebutofoppo-sitesigntothatincaseA).Thisisconsistentwithaslight at-teningoftherelation

between

An I-band calibration of the SBF method at blue colours

S.Mieskeetal.:SBFcalibrationatbluecolours

9

Fig.4.ExamplethumbnailsoftheSBFmeasurementproce-durefortwoFornaxclusterdEs.LeftFCC194,rightLSB6-4.Thumbnailsizeis12.5′′.Imagesequencefromtoptobottom:1.Originalgalaxyimage.2.Galaxylightmodelsubtractedfromformerimage.3.Formerimagedividedbysquarerootofgalaxymodel,withcontaminatingsources/ tresidualsmaskedandwiththemeasurementregionrestrictedtoacirculararea.4.AzimuthallyaveragedpowerspectrumoftheformerSBFimage,withthe tindicatedbythedashedline.

Wenotethatforthefullsample,caseC)isrejectedatevenhighersigni canceduetoalowermeandistanceandstrongercorrelationbetween(m M)and(V I

).

Fig.5.DistancemodulusforcaseA)(seetext)plottedvs.S/NoftheSBFmeasurement(left)andtheamountofback-ground uctuationsBGcontributingtothemeasuredSBFsig-nal(right).ThethreesourcesmarkedwithlargecirclesintherightpanelarethosebelowS/N=3intheleftpanel.Filledcirclesareforgalaxieswithseeingbelow0.85′′,opencirclesforseeingabove0.85′′,seeFig.6and

text.

Fig.6.The uctuationmagnitude

mIisinsigni cant.

4.2.Theempiricalapproach

Wealsogivethebest tresultofapurelyempiricalcalibrationvalidinthecolourrange0.85<(V I)0<1.10mag,assuming(m M)=31.39±0.12mag:

An I-band calibration of the SBF method at blue colours

10S.Mieskeetal.:SBFcalibrationatblue

colours

Fig.7.ApparentVmagnitudeplottedvs.SBFdistancemodu-lusforthefourdi erentassumedcalibrationrelationsA)toD),asde nedinSect.2andTable2.Filledcirclesaregalaxieswithseeingbetterthan0.85′′.Theirmeandistanceandits1σerrorareindicatedbytheverticalsolidanddashedlines.Thegreenticksat(m M)=31.39magmarkthereferenceFornaxclusterdistancefromFreedmanetal.(2001)anditserror.Opencirclesaredatapointsforgalaxieswithseeingworsethan0.85′′.Theywerenotincludedincalculatingthemeandistanceandareonlyshownforthesakeof

completeness.

Fig.8.(V-I)0colourplottedvs.SBFdistancemodulusforfourdi erentassumedcalibrationrelations,seeFig.7.

Fig.9.ApparentSBFmagnitude

mIfainterthanthelineforcaseB),while

applyingthesolidandlongdashedlinetotheothergalaxies.

ThezeropointerrorincludesourstatisticalerrorsandtheerroroftheFornaxclusterreferencedistance.Thestatisticalerrorsofthezeropointandtheslopewerederivedfromthedisper-sionofthedatapointsaroundthelinearrelation,notfromthesinglemeasurementerrors(thiswouldhavedecreasedtheer-rorsby50%).TheformaldisagreementwiththeTonryslopeof4.5is1.1σ,whilethedisagreementwitha0slopeis1.3σ.Forthefullsampleofgalaxies,thezero-pointchangesto 2.31±0.15,andtheslopeto2.80±1.36.Notsurprisingly,thisagreeswiththe ndingfromthesemi-empiricalapproachthatcaseC)isrejectedathighersigni canceforthefullsample.

Toquantifytheintrinsicscatter–the“cosmicvariance”–oftheempirical“goodseeing”calibration,wesubtractinquadraturethemeansinglemeasurementuncertaintyin

MItobemoresensitivetodi erentage/metallicity

combinationsinthebluethaninthered(seeleftpanelofFig.1).NotethatthetwotheoreticalpredictionsbyLiuetal.andWortheyetal.intherightpanelofFig.1thatpredictacolourindependent

An I-band calibration of the SBF method at blue colours

S.Mieskeetal.:SBFcalibrationatbluecolours11

5.Discussion

TheresultsoftheprevioussectionsuggestanoverallshallowerslopethantheTonryslopedeterminedforredcolours,accom-paniedbyasigni cantcosmicscatter.ThequestioniswhetherthisiscreatedbyasinglerelationwithsomescatterasincaseB)(seealsoMeietal.2005),orbyatwo-branchsolutionasincaseD)(Jerjenetal.2001).CaseD)containstheimplicitas-sumptionthata)therelationbetweenMI-(V I)0plane.

Toinvestigatethis,wetestthedistancedistributioninthedif-ferentcalibrationcasesforbimodality.WeuseKMM(e.g.Ashman,Bird,&Zepf1994)inhomoscedasticmodetoquan-tifytheprobabilitywithwhichadouble-peakedGaussiandis-tancedistributionispreferredoverasingle-peakedone.Thisiscertainlyaverycrudeestimator,butthemeasurementuncer-taintiesandlownumbersdonotallowformoredetailedconsid-erations.Thecon dencelevelswithwhichabimodalGaussianispreferredoveraunimodalonearethefollowing:88%forcaseA),92%forcaseB),64%forcaseC),and27%forcaseD).Thestrongestcaseforadouble-peakeddistributioniscaseB),yieldingonemainpeakwith12galaxiesandasecondaryonewith ve.These vegalaxiesaretheonesbelowthelongdashedlineinFig.9.ThefactthattheprobabilitiesforcasesB)andD)aresodi erentisconsistentwithapropertwo-branchcalibrationasopposedtoaunimodalonewithbroadscatter.However,thecon dencelevelforcaseB)isonly1.8σ,andthereforethis ndingisstillofindicativenature.WenotethattheSBFS/Nandalsotheamountofbackground uctuationsBGisnotafunctionofdistancemodulus.Bothentitiesarein-distinguishablebetweenSBF-brightandSBF-faintsample.Arethereanyotherdi erencesbetweendEsbelongingtothebrightandfaint

mIisinthatcontextconsistentwithat

leasttwoseparatedwarfformationepisodesinFornax.

We nallynotethattheaverageprojectedradialdistancetoNGC1399isindistinguishableforbothsamples,indicatingthatbothgroupsarenotdistributedinasigni cantlydi er-entfashion.DuetotheintrinsicfaintnessoftheinvestigateddEs,onlythreeofthemhavespectroscopicmetallicitiesavail-able(Held&Mould1994andMieskeetal.2006),ofwhichonlyFCC211isbluerthan(V I)0=1.09.Thisobviouslydoesnotallowoneaspectroscopiccon rmationofbimodalityintheage-metallicitydistribution.

5.1.RevisitingtheHydraandCentaurusSBF

measurements

Attheendofthisdiscussionwerevisittherelativedistancebe-tweenHydraandCentaurus.Thepurelyempiricalcalibrationrelation(5)for0.85<(V I)0<1.10magcanbeusedtochecktheSBFdistancestothedEdominatedsampleofHydraandCentaurusclustergalaxiesfromMieske&Hilker(2003b)andMieskeetal.(2005).Thereisa0.05magoverlapofthecolourregimeforrelation(5)withthatofTonry’srelation(1).IntheHydra/Centauruspapersweassumedrelation(1)toholdfor(V I)0>1.00,anda50%smallerslopefor(V I)0<1.00.Boththezero-pointandslopeofrelation(5)areconsistentwiththatadoptedfor(V I)0<1.00inthosepapers.Thatis,theSBFdistancesremainunchangedinthecaseof(V I)0=1.00asthelimitbetweensteepandshallowslope.Ifwerestrictthevalidityofrelation(1)toHydra/Centaurusgalaxieswith(V I)0>1.10andadopttheslopeofrelation(5)forbluercolours,themeandistanceofbothsamplesbecomes0.09maglower.I.e.thereisnoconsequencefortherelativedistance.Theuncertaintyofre-lation’s(5)zero-pointislargerthanthisdi erence.ThereforewecanstatethattheblueSBFcalibrationfromthispaperdoesnotchangetherelativeHydra/Centaurusdistancenordoesitrequireachangeintheabsolutedistances.

6.Summaryandconclusions

WehavepresentedI-bandSBFmeasurementstakenwithIMACS@Magellanforasampleof25dEsintheFornaxclus-terinthecolourmagnituderange 16.5<MV< 11.2magand0.8<(V I)0<1.10mag.TheaimofthisinvestigationwastoaddresstheSBFcalibrationatbluecolours.Ourcolourcalibrationisaccuratetobetterthan0.02mag.Toavoidobser-vationalbiasestowardstoobrightSBFamplitudes,werestrictourcalibrationsampletothose17galaxieswithseeingbetterthan0.85′′.

Theseareourresults:

–OurSBFdataareinconsistentatthe3σcon dencelevelwithaconstant,colourindependentabsoluteSBFmagni-tude

MIand

(V I)0.Thereissomeevidencethatthisslopeisshallowerthanthevalueof4.5foundbyTonryetal.(1997)atreddercolours,butatlessthan2σ.–Inthe

An I-band calibration of the SBF method at blue colours

12S.Mieskeetal.:SBFcalibrationatbluecolours

asingleonewithsomeuniformscatter.We ndevidencethatthefaintergalaxiesinoursamplesexhibityoungerinte-gratedagesandhighermetallicitiesthanthebrightergalax-ies.

–FromapurelyempiricalSBFcalibration(relation

5)wede-ducea0.34±0.14magcosmicscatterof

MItobemoresensitivetodi erentage/metallicity

combinationsinbluecoloursthanatredcolours.

–ApplyingtheempiricalcalibrationtotheSBFmeasure-mentsofHydraandCentaurusclusterdEsfromMieske&Hilker(2003b)andMieskeetal.(2005)hasnoe ectontherelativeSBFdistanceofbothgalaxyclusters.Alsotheabsolutedistancesdonotrequirecorrection.

Acknowledgements.Wethanktheanonymousrefereeforhiscom-mentsandsuggestionswhichhelpedtoimprovethepaper.Weowethankstothesta atLasCampanasObservatoryfortheirassistanceincarryingouttheobservations.SMacknowledgessupportbyDFGprojectHI855/1andDAADPh.D.grantKennzi erD/01/35298.LIwassupportedbyFONDAP“CenterforAstrophysics”.

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