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