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