2 0 0 3MNRAS.345. .2 6 9H _1- 2 12 -1-1 1 -1 * E-mail:[email protected] previously acceptedvaluewasaround 18.50.However,thishasbeen is usuallycalibratedviathedistance modulustotheLMCand The well-studiedPLrelationintheLargeMagellanicCloud(LMC) tween thehotlyarguedvaluesof50kmsMpc(Sandage)and in 1927.Itissometimesarguedthatwearenowatthefine-tuning lenge toastronomerssincethediscoveryofUniversalexpansion Determining thevalueofHubble’sconstant,H,hasbeenachal- Accepted 2003June20.Received20;inoriginalform1999December29 DepartmentofAstrophysicalSciences,UniversityHertfordshire,CollegeLane,HatfieldALIO9AB Mon. Not.R.Astron.Soc.345,269-291(2003) which inturnaredependentontheaccuracyofprimaryindicators © 2003RAS of distance,suchastheCepheidperiod-luminosity(PL)relation. of thesemeasurementsarebasedonsecondaryindicatormethods Fiona Hoyle,*TomShanksandN.R.Tanvir Distances toCepheidopenclustersviaopticalandA^-bandimaging (1999) calculatedH=67±7kmsMpc.However,many stage andmanymeasurementsgivevaluesforHwhichliebe- 1 INTRODUCTION DepartmentofPhysics,ScienceLaboratories,SouthRoad,DurhamDH13LE 100 kmsMpc(deVaucouleurs),e.g.Tanvir,Ferguson&Shanks 0 0 0 © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem We investigatethereddeningandmain-sequence-fitteddistancesto11young,Galacticopen to suggestthattheeffectsarenotduemetallicityvariations.Otherpossibleexplanations Previous spectroscopicestimatesofthemetallicityCepheidsintheseclustersappear F starsshowaUVexcessandinthesecondcase,NGC6664,theyaretooredU—B. not wellfittedbythestandardmain-sequenceline.Inonecase,NGC7790,wefindthat metallicity. Laney &Stobieat/xq=18.51zb0.09andwiththeHipparcosparallax-calibratedCepheidPL the L-bandand18.48±0.10from/GbandgivinganoveralldistancemodulustoLMC main sequenceofAllenappliesuniversallytoalltheopenclusters,althoughthispointis diagrams.Ourmain-sequencefittingassumesthatthesolar-metallicityzero-age ABSTRACT Key words:Cepheids-openclustersandassociations:generalMagellanicCloudsdistance foreground orbackgroundstars. for theseanomaliesarepositionalvariationsinthedustreddeninglawandcontaminationby estimate ofFeast&Catchpoleat/¿o=18.66±0.10whennoaccountistakentheLMC 0.10 andabsolutedistancemodulitotheLargeMagellanicCloud(LMC)of18.54zbfrom controversial atpresent.InthiswayweproceedtocalibratetheCepheidperiod-luminosity variable .Reddeningtotheclustersisestimatedusing\htU—B\BVcoloursofOB clusters thatcontainCepheids.EachclustercontainsorisassociatedwithatleastoneCepheid of /jLq=18.51zb0.10.ThisisingoodagreementwiththepreviousCepheidŸL-Kresult scale. (PL) relationandfindM=—2.87xlogP—1.243zb0.09,—3.442.21± andthedistancemodulustoclusterisestimatedviaB—V:VVK:Vcolour- vK We alsofindthatthetwo-colourU—B:BVdiagramsoftwoimportantclustersare bands. Itistime-consumingtoobserve alargenumberofstars being availableforobservationduringourallocatedtelescopetime. recently challengedinapaperbyFeast&Catchpole(1997)whode- now makeitpossibletoobserve a largenumberofstarsinmany magnitudes andcolours.However, charge-coupleddevices(CCDs) individually, andphotographicdata cangiverelativelyinaccurate using photoelectricobservations as eachstarhastobeobserved ing theCepheidsCSVelandSNorarenotincludedduetotheir main-sequence (ZAMS)fitting.Unfortunately,theclusterscontain- this bycheckingthevaluesofdistancemodulusandreddening termined thedistancemodulustoLMCas18.70±0.1.Thissmall done usingphotoelectricandphotographicdatainopticalwave- vated ustochecktheGalacticzero-pointofPLrelation.Wedo estimates ofHubble’sconstant.Thisdiscrepancyhasfurthermoti- difference inthedistancemoduluscausesa10percentdecrease open clusterswhichcontainCepheidsviaZAMSfittinghasbeen a sampleof11GalacticclustersthatcontainCepheidsviazero-age Previous workonmeasuringthereddeninganddistancetoyoung 2 0 0 3MNRAS.345. .2 6 9H -1 photoelectric U.Theeffectivefull width athalfmaximum(FWHM) reddenings anddistancestotheopenclustersareobtainedin imaging detectorsarealsonowavailableandalthoughsomeofthe ing CCDt/-bandphotometrytobeincludedinthisstudy.Infrared Johnson photoelectricphotometry,havebecomeavailable,allow- tantly, withsmallerandbetter-behavedcolourtermsrespectto Recently CCDswithimprovedf/-bandsensitivityandmoreimpor- Romeo etal.(1989),thesehavemainlybeencarriedoutinBVRL the effectofatmosphericextinction improvesitsagreementwith The RGOUandHarrisB,Vfilterswereused.filter 2.1.1 JKT meant thatmanydifferenttelescopeswererequired. lination oftheclustersandmultiwavelengthnaturestudy Herschel Telescope(WHT)overa2-yrperiod.Thespreadindec- American Observatory(CTIO),atCalarAltoandontheWilliam United KingdomInfraredTelescope(UKIRT),atCerroTololoInter- ing fiveobservingrunsontheJacobusKapetynTelescope(JKT), The observationsoftheGalacticopenclustersweretakendur- 2.1 Observations 2 DATA results, particularlyfortheclusterswhoseU—B:BVdiagrams these valueswiththemagnitudesofCepheidstocalibrate the observationaldataandwetestaccuracyofphotometry in thiswork,wecheckthepreviousmeasurementsofreddening modulus andthereddeninginpreviousworkwouldcausean to theclusters,theycalibratedCepheidPLrelationinV-and number ofsouthernhemisphereGalacticCepheids.Usingdatainthe has beenprimarilycalibratedintheV-band.Laney&Stobie(1993, is apracticalproposition. different wavebandsquicklyandaccurately.AlthoughCCDshave were typically6x120sintheU-band, 6x180sintheÆ-bandand combined withtheCCDresponseproducesapassbandwhichpeaks carried outusingthe1024xTektronixCCD(Tek4)withpixel Optical imagingofeightopenclusterswasobtainedduringanob- conclusions. do notappeartofollowthecanonicallocus.InSection6wedraw Cepheid PLrelation.InSection5wediscusstheimplicationsof error inthePLrelationasdeterminedbyLaneyandStobie.Hence, literature toobtainvaluesforthedistancemodulusandreddening Cepheids themselveswerenotavailableandtheCepheidPLrelation detectors usedheredonotcoveraswideanareaopticalCCDs,ob- /Ubands. However,anyerrorsinthedeterminationofdistance already beenusedforopen-clusterstudiese.g.Walker(1985a,b), of ourUpassbandis^400Àcompared to^570Àforphotoelectric our Upassbandhasdecreasedresponsetowardshorterwavelengths, at ^3750AsimilartothetraditionalphotoelectricUband.Although Section 3.2wediscusseachclusterindividually.In4use and calibrationofthedata.InSection3.1wedescribehow and distancemodulusobtainedfromtheopenclusters. serving thefullextentofanopenclusterwithamosaicpointings 270 F.Hoyle,T.ShanksandN.R.Tanvir served forcalibrationpurposesbut themainimagingobservations scale of0.33arcsecpixel.Typicalseeingwasaround1.3arcsec. serving runduring1997September16-22.Theobservationswere U. Shortexposuresof5sinU,10 sinÆand20t/wereob- 1994) presentinfrareddataalongwithV-bandmagnitudesforalarge The layoutofthispaperisasfollows.InSection2wepresent Until fairlyrecently,good-qualityinfraredmeasurementsofthe © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem -1 -1 pixel givingafieldofview73arcsec.Tocoversufficientarea passband, correctedforatmosphericextinction,peaksat^3750A, blocked UfilterandHarrisB,Vfilterswereused.Theresulting in Table1.Forcalibrationpurposes,standardstarsfromLandolt the objects,theyhadtobeobservedathighairmass.However,these immediately andthenreadagainafter theexposurewhichreduces taken usingtheND-STAREmode, wherethearrayisresetandread lapped byhalfinboththex-andy-direction sothefinalimagehad nights 1997June16-19usingtheIRCAM3near-IRimagingcamera The infrareddataweremostlyobservedatUKIRTduringthefour 2.1.3 UKIRT in non-photometricconditionsonly. the JKTweremadeincaseswhereclustershadbeenobserved taining fourstandardstarswereobserved.Threenewclusters Table 1.StandardE-regionfieldsfromGraham(1982)andstandard The observationsweremadeusingtheCTIO0.9mduringanob- 2.1.2 CTIO throughout thenight,withmostofthesefieldscontainingseveral September 21)sixLandoltfieldswereobservedatregularintervals or duringalaterobservingrunatCTIO.Thepointingsaregiven calibration frameswereobservedataslowanairmasspossible observations werenormallyusedtoobtainrelativephotometry,and 6 x300sintheU-band.Duetosoutherlydeclinationofsome the readoutnoiseto35electrons.The exposureswere60x2sand an approximateareaof6x5arcmin. Observationsweregenerally a mosaicof9x7imageswasobserved. Eachimagewasover- of eachopenclusterwethereforehadtomosaicimages.Generally with a2560x256detector.Thepixelscaleusedwas0.286arcsec observed atCTIOandfurtherobservationsofclusters only photometricnightwas1998September28andonthis was around1.4arcsec.Approximatepointingsareagaingivenin as opposedto570A.Theaverageseeingduringtheobservations electrons) andgoodquantumefficiencyinthet/-band.ACuS0 0.384 arcsecpixel.TheTek#3CCDhaslowreadoutnoise(four carried outusingthe2048xTek#3CCDwithpixelscale (1992) wereobserved.Ontheonefullyphotometricnight(1997 six E-regionstandardfieldsandoneLandoltfieldcon- stars fromLandolt(1992)wereobservedthroughoutthenight.The similar tophotoelectricUbutwithanarrowerFWHMof^350Â serving runduring1998September24-29.Theseobservationswere standard stars. 4 WZ Sgr NGC 7790 NGC 129 NGC 6823 TR35 vdBergh 1 NGC 6067 Lynga 6 NGC 6664 M25 NGC 6649 wavebands. Cluster Table 1.Approximatepointingsfortheclustersinstudyall WZ Sgr TW Nor 5 arcsecsouthofTR35 CV Mon Star E(Romeoetal.1989) Star 113(Arpetal.1959) Star j(Guetter1992) Star 136(Thackerayetal.1962) Star 5(Arp1958) Star 95(Sandage1960) Star 19(Madore&VandenBergh1975) e 2003RAS,MNRAS 345,269-291 Pointing 2 0 0 3MNRAS.345. .2 6 9H -1 -1 mass aregivenincolumns2,5and6respectively.Column7gives faint standardswereobservedforcalibration. The WHIRCAMdetectorwastheIRCAMpreviouslyused used fortheobservations,withoutMARTINItip-tiltinoperation. NGC 7790alsoliesfurthernorththantheUKIRTdeclinationlimit 2.1.5 WHT tred onstar113inArp,Sandage&Stephens(1959).Observations mosaicing techniqueusedatUKIRT.Theexposuretimewas10x k x1Hawaiidetectorwithpixelscale0.396arcsec.This infrared observationswereinsteadtakenatCalarAltoduringan- NGC 129liesfurthernorththanthedeclinationlimitofUKIRTso 2.1.4 CalarAlto the night.Theseeingthroughoutrunwastypically0.6arcsec. the centreofmosaicisapproximatelyinsamepositionas view wastherefore64arcsec.TheKfilterusedandUKIRT were madeinthe/f-band.UKIRTfaintstandardsand gives a6.6arcminsquarefieldofviewsotherewasnoneedforthe Observations werealsotakenintheJ-and//-bands. were observedonthethreephotometricnights,someofwhich dards listwereobservedthroughoutthenights.Around10standards corresponding opticalframe.StandardsfromtheUKIRTfaintstan- © 2003RAS,MNRAS 345,269-291 observation, thewavebandsobservedforeachclusterandair- at UKIRT.Thepixelsizewas0.25arcsecandthefieldof ated attheNasmythfocusandbehindMARTINIinstrumentwas September 1.TheWHIRCAM256xdetectorwhichwassitu- another observingrun.Theobservationsweremadeonthe1996 and soinfraredobservationsweremadeonthe4.2mWHTduring of Huntetal.(1998)wereobservedforcalibration. other observingrun.ObservationsweredoneusingtheRockwell1 observed earlyoninthenight,half-waythroughandatendof 1.5 s,theseeingwasbetterthan1arcsecandexposurecen- short sh()rt All theobservationsaresummarizedinTable2.Thedateofeach WHT 4.2m1/9/96NGC 7790 CF,CEa,CEbCas^o1.20550x 1 Yes UKIRT 3.8m19/6/97NGC 6823 SVVulK1.0360x 2 Yes UKIRT 3.8m19/6/97NGC 6664 EVSetK1.1460x 2 Yes UKIRT 3.8m17/6/97Trumpler 35RUSetK1.6460x 2 Yes UKIRT 3.8m17/6/97M25USgrK 1.7460x2Yes UKIRT 3.8m16/6/97NGC6649V367SetK 1.4060x2Yes JKT 1.0m21/9/97NGC7790CEa,CEb,CFCasUBV 1.296x300,8180,10120Yes JKT 1.0m21/9/97Trumpler35RUSetUBV 1.221x180,190,190Yes JKT 1.0m21/9/97NGC6664EVSetUBV 1.666x300,810120Yes JKT 1.0m20/9/97NGC6649V367SetUBV 1.394x300,2180,120No JKT 1.0m18/9/97NGC129DECasUBV1.364x180,2180,1180No JKT 1.0m18/9/97M25USgrUBV1.612x150,1150No JKT 1.0m17/9/97WZSgrUB1.713x150,2150No JKT 1.0m17/9/97NGC6823SVVulUBV1.222x150,150No Telescope Calar Alto3.5m18/8/97NGC 129DECas/Grt1.2510x1.5 Yes CTIO 0.9m28/9/98M25USgrUBV 1.271x60,5,5Yes CTIO 0.9m28/9/98NGC6649V367SCTUBV 1.261x300,60,30Yes CTIO 0.9m28/9/98vdBergh1CVMonUBV 1.26lx300,1x90,90Yes CTIO 0.9m28/9/98NGC6067V340Nor,QZNorUBV 1.363x300,190,90Yes CTIO 0.9m28/9/98Lynga6TWNorUBV 1.514x300,190,90Yes CTIO 0.9m27/9/98NGC6649V367SCTUBV 1.265x600,160,60No CTIO 0.9m27/9/98NGC6067V340Nor,QZNorUBV 1.363x300,190,90No CTIO 0.9m24/9/98WZSgrUBV 1.125x300,4150,490No the wavebandsincolumn5. Table 2.Detailsoftheobservations.Theairmassisaverageexposureandtimegiveninsecondsforeach shrt h0 © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem Date Cluster Cepheid Wavebands Airmass the taskimshift.Generallytheseshiftsweresmall(afewpixels task CCDPROCthenappliestheflatfieldstoallimages.Thesame The residualgradientintheflatfieldsisonlyaround1percent. CCDPROC. Atleasteightt/-bandskyflatsandsixB-U-band Removal ofthebiasandtrimmingframestoremove 2.2.1 JKT 2.2 Datareduction hence whereanindependentzero-pointwasobtained. indicates whereaclusterwasobservedonphotometricnightand the exposuretimeofframesusedforimaging.Forsome in thedomeflatfieldssoskyflatswereused.Atleastthree ferent biaslevelsinthefourquadrantsofCCD.Theframeswere mode. Apackagecalledquadprocwithinirafcorrectsforthedif- The datawereobtainedatCTIOusingthefour-amplifierreadout 2.2.2 CTIO using Imcombineandwereaveragedtogethera5crclipping. in somecasesnoshiftswererequired.Theimagescombined either way)astheobservationweredoneoneaftereachotherand combined togetherbyaligningtheimageswithlinearshiftsusing flat fieldswereusedinthereductionofstandardstarframes. combining algorithmanda3crclippingtoremoveanycosmicrays. was createdforeverynightusingacombinationofduskanddawn flats wereobservedoneachofthenights,soaseparateflatfield clusters acalibrationframewasobservedatCTIOandtheexpo- et al.(1998)hadfoundthattherewasaresidualgradientof5percent overscan regionwasdoneonalltheframesusingiraftask also trimmedusingquadproc.Inapreviousobservingrun,Croom sky flats.Thiswascreatedwithinflatcombineusingamedian- sure timesoftheseclustersarealsogivenincolumn7.Column8 Many imagesofthesameclusterwereobserved.Theseall Distances toCepheidopenclusters271 Exposure time(s) Photometric 2 0 0 3MNRAS.345. .2 6 9H positions acrosstheframesusing domeflatsshowednoevidence before imcombinewasusedagaintocombineallthedataframes, reduce theCalarAltodata.Aflatfieldwascreatedbymedian- been determined,alltheotheroffsetsinx-andv-directionfrom pixels andfinallycreatesamosaic.Allthedataframesweremedian- TMCOMBTNE withthesamesettingsasforJKTdataandwhere Landolt standardswereagainreducedinthesamemanner. using a3aclipping.TheE-regionstandardsandobservationsof in theQUADpackagewasusedtomedian-combineflatfields from thescienceframeusingimarith. locally intimetothescienceframe andthiswasthensubtracted frame wascreatedbycombining dedicatedskyframesobserved is dividedintothescienceframeusingimarith,resultingdata The KdatafromtheWHTwasobservedandreducedforusaspartof 2.2.5 WHT forming onefinalimageframe. that werelocalintimetotheimageframecreateaskyfor using imcombinewitha5crclippingtomedian-filterfourdataframes image, asfollows.Askyframeforeachindividualimagewascreated the bestresultswereobtainedbysubtractingaskyframefromeach Basic IRAFroutinessuchasimcombineandimarithwereusedto 2.2.4 CalarAlto frame towerethesame.Theoffsetsforstandardstars however, theseoffsetswerenotaccurateenough.Bycreatingasep- mosaiced together.Stredreadsintheoffsetfromdataheader; in thedataframes,subtractsoffdarkcountandcreatesaflat the packagetrcamdr.Thisisafairlyautomatedroutinewhichreads The UKIRTdatawerereducedusingaprogramcalledstredwithin 2.2.3 UKIRT fields wereflatto1percent.Theequivalentversionofflatcombine flats wereobservedoneachnightinthe£/-band.Theresultingflat were observedoneachnightintheBandV-bandatleastfivesky frames appearfairlyflat.Alsostandard starscalibratedinvarious flat framebymedian-combiningthedataframes.Howeverwhenthis flats wereavailableandnotenoughdataframestakentocreatea each dataframe.Theskyframewasthensubtractedofftheimage data reductioncanbefoundinMcCracken(1999).Wethat combining allthedataframes.Amoredetaileddescriptionof were moreaccurateandcouldbeusedtocreatethemosaic. was builtupoverthewholeframe.However,onceoneoffsethad create theoffsetsfile,oneofcornerframeswasfixedand fields. combined tocreateaflatfieldforeachnight.Therewasnoevidence flat-fields thedark-subtractedobjectimages,correctsforanybad field framebymedian-filteringtheimageframes.Thenprogram corrected forusingimshift. any offsetshiftsappearedbetweenthedataframestheywereagain of anysystematicerrors.Skysubtraction wasalsorequired.Asky another project.Domeflatswereusedtoflat-fieldthedataasnosky offsets requiredfortheneighbourframewerefoundbyeye.This arate offsetsfilethemosaicingcouldbedonemoreaccurately.To of alarge-scalegradientgreaterthanabout1percentintheflat 272 F.Hoyle,T.ShanksandN.R.Tanvir To createthefinalimage,allindividualframeshavetobe Multiple imagesofthesameclusterwereagaincombinedusing © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem — — regular intervalsoneachofthesixnightsatJKT.TheCCD resampled images. band. Ratherthanalteringthedata,alignmentwasjustdoneby tion 2.2.1.Theaperturesizeusedtomeasurethemagnitudeof the dataframeswithsameflatfields,etc.asdiscussedinSec- frames ofthestandardstarswerereducedinsamemanneras 2.4.1 JKT 2.4 Photometriccalibration to transformcoordinatesandwedidnotperformphotometryonthe transformation functionbetweenanytwoimages,thusallowingthe frames. Weusedtheirafroutinegeomaptocalculatebestspatial Aligning theopticaldatawithK-bandwasmorecompli- frames waseasyastherewereonlylinearshiftsbetweeneachwave- To dothis,alltheframesneedtobealigned.Aligningoptical the magnitudeofeachstarinalldifferentwavebandsisrequired. In ordertobeableproducecolour-magnitudediagrams(CMDs), 2.3 Imagealignment The Ældt—UandI/dt7?ldtcoloursaregivenby the colourtermhastobetranslatedintoinstrumentalmagnitudes. tively, andthermserrorsoncolourequationare±0.0007 nitude andthesubscriptJKTstandsforinstrumentalmagnitude, ric andthezero-point,airmasscoefficientcolourequationare methods. to 5arcsecbasedontheprofilesofbright,isolatedstarsin measuring standardsusingabigger15-arcsecaperturetoobtain frame duetocrowdingconsiderations.Wealsoexperimentedwith the magnitudeofstandardstarswas5arcsec,samesize Observations ofstandardstarsfromLandolt(1992)weretakenat optical andÆf-banddatatobealigned.Themappingwasonlyused cated, though,astherewereshifts,shearsandrotationsbetweenthe applying smallcorrectionstothex-andy-positionsofstars. calibration oftheB-bmdisnegligible whendeterminingtheU where weassumethatthecontribution fromthecolourtermin 0.0005 intheU-andÆ-bands,respectively. are ±0.0025,0.0012and0.0008intheU-,B-U-bands,respec- and zrepresentsthezenithdistance.Thermserrorsonairmass where thesubscriptLDTstandsforLandoltstandardstarmag- airmass termswerefoundtobeverysimilarbetweenthesetwo data frames.Theresultsforthezero-point,colourequationsand a near-totalmagnitudeandthenmakinganaperturecorrection aperture asthatusedtomeasurethemagnitudeofstarsindata any problemswithcrowding.Theaperturesizeusedtomeasure ^ldt Lldt=1-035[(/?jktLjkt) —0.030.06secz] 7?jkt —7?ldt+2.170.23sec(z) shown inFig.1andgivenbelowwiththermsscatter. suring themagnitudesofstarsondataframestominimize standard starswas5arcsecasthisthesizerequiredwhenmea- Uldt —#ldt=1.067[(t/jKT7?jkt) —1.860.19secz] f'jKT —f'LDT+4.030.42sec(z) — 5ldtcolourascomparedtothe offsetandairmassterms.Fora kjKT ~^ldtT2.14+0.17sec(z)0.029 LDT LDT There arenoLandoltmagnitudesavailableforthedataframesso Only thesixthnight(1997September21)wasfullyphotomet- —0.034(Z? -V)±0.037 -0.062(t/ -£)±0.039 ldtLDT LD1ldt e 2003RAS,MNRAS 345,269-291 2 0 0 3MNRAS.345. .2 6 9H — ibration. ForNGC6823thephotoelectricobservationsfromtable1 Table 3)withonlysmalloffsetsineachcase. this methodandprevious,photoelectriccalibrationsisgood(see the JKTdataandfromCTIOtoanaccuracyofafewhundredths than V~15),fairlyuncrowded,unsaturatedstarsweretakenas included isassmall0.004mag.Thesecolourtermsareusedto in thet/-bandmagnitudewithandwithoutZ?ldt^ldtterm the datafromJKT. Figure 1.Theairmasscoefficient,colourequationandzero-point,withthecorrectionapplied,forU,BVwavebands work andfindsgoodagreement.Two sourcesofphotoelectricdata Guetter (1992)compareshisphotoelectric datawiththatofprevious was notidentical,but13starswere suitableforcalibrationpurposes. conditions only,sopreviousworkhadtoberelieduponforthecal- dependent zero-pointfortheseframes.Around20bright(brighter colour andcolour-magnitudediagrams. correct theinstrumentalmagnitudesinordertomakecolour- © 2003RAS,MNRAS 345,269-291 are availablefortheclusterNGC129: Arpetal.(1959)andTurner, on theCCDframeandareaof overlapbetweenthetwoimages of Guetter(1992)wereused.Somethesestarssaturated of amagnitude.Theagreementbetweenthezero-pointfoundvia of NGC6649andM25weremadeatCTTOinordertoobtainanin- standard starstoidentifytherelationbetweenzero-pointfrom served ontheonephotometricnight.Short-exposureobservations star withacolourevenasred2?jt—^jkt~2,thedifference K The remainingthreeclusterswereobservedinnon-photometric The clustersNGC7790,6664andTrumpler35wereob- WZSgr 0.00±0.01±0.011±0.00712Turner(1984) NGC 1290.00±0.03-0.005±0.01-0.00813Turneretal.(1992) NGC 68230.00±0.01±0.0050.00413Guetter(1992) NGC 7790-0.01±0.010.0150.008-0.0150.00722Sandage(1958) Trumpler 35-0.02±0.02-0.010.015-0.00515Hoagetal.(1961) vdBergh 1-0.01±0.0150.000.02-0.0050.00824Arp(1960) NGC 60670.07±0.08*0.03±0.020.0250.0120Walker&Coulson(1984) Lynga 6-0.015±0.02-0.010.01517vandenBergh&Harris(1976) NGC 6664-0.01±0.012-0.02±0.01-0.0150.01515Arp(1958) M25 0.01±0.03-0.020.02-0.00521Sandage(1960) NGC 66490.02±0.0250.010.000.01220Madore&vandenBergh(1975) were usedforcalibration. was relieduponforcalibration.Thereisasmalloffsetbetweenthezero-pointofNGC129andTurneretal.(1992)asonlybrighteststars NGC 6067ismadewithThackerayetal.(1962).Thelastthreeclusterswereobservedonnon-photometricnightsonly,sothepreviouswork Cluster Table 3.Comparisonofthephotometrythisstudywithpreviousphotoelectricdata.Notethatcomparisoni/-band © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem Cobs -u, previous Bobs —B previous Fobs -V by thestarsinsamplewithVfainterthan14mag.Wethere- E-region standardsfromGraham(1982)andLandolt(1992)stan- 2.4.2 CTIO WZ Sgr. to calibrateNGC129.Finally,thephotoelectricworkofTurner fore usetheaverageofbrightesttwostarsfromArpandTurner the samesenseinF-band.Thesedifferencesaremainlycaused is brighterthanTurnerandthere0.01±magdifferencein In the5-banddifferenceis0.02±0.01maginsensethatArp Arp photometryand13starsincommonwiththeTurnerphotom- Forbes &Pedreros(1992).Thereareninestarsincommonwiththe quoted error.Asbefore,thesestandard frameswerereducedinthe 0.0095 offsetinthesenseofE-regions-Landolt andsimilarsized colour differencesfoundfromusing thetwodifferentstandardstar CTIO data.Menziesetal.(1991)comparedthezero-pointsand dards wereobservedforthephotometriccalibrationofoptical etry. Forthesesamplesofstars,wefindthatthet/-bandzero-point offsets inthet/—5andBVcolours. Anyoffsetsarewithinthe obtained fromArpis0.04±0.03magbrighterthanthatofTurner. studies andfoundtheoffsetsbetween thetwotobesmall,0.004± (1984) wasusedtocalibratetheclustercontainingCepheid previous Distances toCepheidopenclusters273 iV(stars) Previous work 2 0 0 3MNRAS.345. .2 6 9H =- — B andVthermserrorsoncolourequationare±0.0006, B andV,areshowninFig.2givenbelowagainwiththerms rms errorsontheairmassare±0.003,0.0011and0.0009int/, The standardstarsobservedatUKIRT weretakenfromthefaint 2.4.3 UKIRT tudes whichareusedinthecolour-colourandcolour-magnitude Again thesecoloursareusedtocalculatetheinstrumentalmagni- The colourterminthe5-bandisthiscasenon-negligibleso found intermsofCCDmagnitudesratherthanstandardmagnitudes. is generallygoodagreementbetweenthevaluesforairmass magnitude andCTIOstandsfortheinstrumentalmagnitude.The to determinethemagnitude.Again,onlyonenightwasphotometric the datafromCTIO. Figure 2.Theairmasscoefficient,colourequationandzero-point,withthecorrectionapplied,forU,BVwavebands with anoverlappingframeineach direction.A5-arcsecaperture diagrams. et al.(1998).Again,forthedataframescolourtermshavetobe coefficients andcolourequationsfoundinthisworkCroom 0.0007 and0.001intheU-,B-V-bands,respectively.There where thesubscriptstdstandsforE-fieldorLandoltstandard observed innon-photometricconditionsattheJKT. also providedazero-pointforNGC6649andM25,whichwereonly 6067, Lynga6andvdBerghl,whichwerenotobservedatJKT, airmass coefficientsandcolourequationsforeachwaveband,U, and thiswasthelastnight(1998September28).Thezero-points, 274 stars wereobservedasamosaic of fiveframes,acentralframe standards listavailablefromtheUKIRT Webpage.Thestandard B -Vstd=0.78[(5tioVctio)0.250.09secz](1) standard coloursaregivenby scatter. same mannerasthedataframesanda5arcsecaperturewasused £ctio =£td+3.340.21secz0.099(ß-y)±0.021 Uqtio £^stdH4.74+0.47secz—0.036(C/td^std)0.037 Utd —5=1•037[(í/ctio#ctio)-400.26secz V-band magnitudeshavetobeusedinthet/-bandcalibration.The Vctio =V+3.090.12secz-0.018(Z?y)±0.009 stdC sstd S s std This nightprovidedindependentzero-pointsfortheclustersNGC F. Hoyle,T.ShanksandN.R.Tanvir © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem + 0.099{0.78[(5tio-Vtio)~0.250.09secz]}]. C airmass bstandardStandard (2) the zero-point.Thermserroron airmasscoefficientiszb0.002 ference betweeneachofthecalibrations isjustasmallchangein the airmasscoefficientandcolourequationareshowninFig.4 nights, night1,2and4(1997June16,17,19),werephotometric, tre fornight2(1997June17,opencircles)andthelowerpanel4 UKIRT. Thetoppanelisfornight1,(1997June16,filledcircles),cen- Figure 3.TheK-bandzero-pointsforthethreephotometricnightsat ficient agreeswellwiththevalues given inKrisciunasetal.(1987) and thermserroroncolourterm is±0.0003.Theairmasscoef- where againthesubscriptstdrefers tothestandardstars.Thedif- given belowforeachnight. was usedtodeterminethemagnitudeofstandard.Three (1997 June19,filledtriangles). so alltheclusterswereobservedinphotometricconditions. Ku =K+7.27-0.082secz0.005(/)±0.038 Ku =K+7.26—0.082sec^0.005(/t)±0.035 Ku =K+7.17-0.082secz0.005(/)±0.026 1997 June18: 1997 June17: 1997 June16: std stdsd std The zero-pointsforeachofthenightsareshowninFig.3and 1 e 2003RAS,MNRAS 345,269-291 ^standard T/ 2 0 0 3MNRAS.345. .2 6 9H photometry tophotoelectricobservationsintheliterature.Table3 project (seeMcCracken,Metcalfe&Shanks,inpreparation,for mean magnitudefromthetruemagnitude. Thisplotshowsthetotal magnitude ofthestarsandy-axis showsthedeviationof the magnitudesfoundfrompreviousphotoelectricstudies.Inall from thecalibrateddataframes(seeSection2.4)arecomparedto The depthoftheJKTdatais19.9magfora1200sU-bandexposure, limiting depthoftheobservationstobewherePoissonerrorin magnitudes ofthestandardstars.Themagnitudeeach minimize anycrowdingproblems.Photwasalsousedtoobtainthe IRAF DAOPHOTpackage.Asmall,5-arcsec,aperturewasusedto 2.5 Photometry more details). ibration wasprovidedforusbyNigelMetcalfeaspartofanother UKIRT faintstandardsandHuntetal.(1998)wereob- 2.4.4 CalarAltoandWHT taken atUKTRT.ThesymbolsarethesameasinFig.3. Figure 4.Theairmasscorrectionandcolourequationforthe/f-banddata error (Poissonerrors,readnoiseand alsoerrorsduetocrowding) ered. ShowninFig.5aretheresults. Thex-axisshowsthetrue was usedtodeterminehowwell the magnitudescouldberecov- were placedina300st/-bandimageoftheclusterM25thenphot etry. Twenty‘simulatedstars’ofeachmagnitudeshowninFig.5 cases theresidualsaresmallwithbiggestinBandVbeing depth ofatypical/f-bandexposure120sobservedwasaround electron countsis5percent,i.e.when-\jN^+A^ky/Nobj=0.05. © 2003RAS,MNRAS 345,269-291 at eachmagnitude(fullerrorbar) andthePoissonerror,foundas Automated aperturephotometrywasdoneusingPHOTwithinthe and thosefoundontheUKIRTwebpage.Ascolourtermisvery ^0.03 mag. shows theresidualwhenourmagnitudesfortypically10stars star wasmeasuredindividuallyusinga5-arcsecaperture. served inordertocalibratetheCalarAltoandWHTdata.Thecal- small, itwasassumednegligibleintheV—K\VCMDs. V-band exposure.ThedepthsoftheCTIOdataaresimilar. 19.2 mag. 19.7 magfora360sZ?-bandexposureand20.4240 oh Finally, wetesthowthecrowdingoffieldaffectsphotom- The accuracyofthezero-pointswastestedbycomparingour First weestablishthedepthofphotometry.Wedefine « I -O s o © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem d standard^standard J —K results forsimulatedstars(seetextdetails).Thelargeerrorbarindicates bourg Cataloguetogiveanindicationoftheacceptablespreadin rors remainthesameandcorrectingerrorshowninFig.5for the totalerror(Poissonerrors,crowdingerrorsandalsoreadnoise).The Figure 5.AnindicationoftheaccuracyU-bandphotometrybasedon have alsobeentestedandwouldgivethesameresultsasZAMS the ZAMS.TheZAMSofTurner(1979b)andMermilliod(1981) for theK-banddataandnearbylocalstarstakenfromStras- near IR-bandstarsfromtheUKIRTWebpage(Tokunaga1998) nation ofAllen(1973)fortheopticaldata,intrinsiccolours these parametersisdoneviaZAMSfittingtocolour-magnitudeand In ordertoworkouttheCepheidperiod-luminosity(PL)relation, 3.1 Method 3 REDDENINGANDDISTANCE there isnosystematictrend. the reducedPoissonerror,totalerrorisestimatedtobe±0.17at For a£/-bandexposureof1800s,assumingthatthecrowdinger- this exposureof300sislessthan0.03magdowntot/=17mag. down to18magtheerrorislessthan±0.1mag. the reddening;however,previously, theaccuracyofreddening which isindependentofthedistance tothecluster.TheU—B:B colour-colour diagrams.TheZAMSusedinthisstudyisacombi- which mustbecorrectedfor.Themethodfordeterminingbothof erally significantdustabsorptionalongthelineofsighttocluster the distancetoclusterneedsbeknown.However,thereisgen- described above,asthesmaller,wider,errorbar.Thetotalfor Section 2.5,paragraph2.Thetotalerrorat17magisonly±0.036and smaller, widererrorbarindicatesthePoissonfoundasdescribedin of Allen.ThereddeninglawassumedinthisworkisfromSharpless also showsthatalthoughtheerrorsincreaseforfaintermagnitudes (1963): — Vdiagramhasalwaysbeenthe favouredmethodforestimating U =20,reducingto±0.08at18thmagand±0.0317mag.Fig.5 — ^= 0.72±0.05£(ß-V).(3) E(U -B) E(B —V) The reddeningisobtainedusing the U—B:BVdiagram Distances toCepheidopenclusters275 true magnitude 2 0 0 3MNRAS.345. .2 6 9H possibly allowingmoreaccuratedistanceestimates,butV—K:V photometry. TheimprovedUsensitivityofthecurrentgeneration Romeo etal.(1989).Thedistance moduluswhichbestfitstheB— feasibility ofthisproject.TheV-banddatathereforecomesfrom the IRCAMdetector.Thisdiagramwasalsomadeforusbefore K framesduetoashiftinthetelescopepositionhalf-waythrough in thecaseofNGC6664asthereweredifficultiesaligningVand in thesediagramsisgreaterthantheB—V:VCMDs,particularly the advantagethatslopeofZAMSisflatterthanforB—V:V, that theCepheidcouldhaveadifferentreddeningfromcluster, ror inthecalibration.Inquiteafewcases,ZAMSdoesnot the averagereddeningforclusterwhichwecanthenapplyto Fig. 6)asthemainsequenceincolour-colourdiagramissub- the routewehaveadoptedhere. the reddeningestimatedfromU—B:BVdiagramsandthisis each clusterassuming cluster. FollowingLaney&Stobie (1994),thisvalueisfoundfor creating the/f-bandmosaicforthiscluster.Therearealsofewpoints diagrams areavailableforonlysevenoftheclustersandscatter diagrams todeterminetheclusterdistance.V—K:Vhave caused bydifferentialreddeningacrosstheclusterorlocation cases arediscussedbelowinSection3.2.Thereisalsotheproblem colours. Thisisparticularlyproblematicinsomecasesandthese fit thecolour-colourdatawelloverwholerangeofB—V deviation oftheO-andB-typestarsfromZAMSvialeast- colour-magnitude diagramswhichareuncorrectedfordifferential evidence fordifferentialreddeninginNGC6823andTR35(see determination waslimitedbythedepthofU-bandphotoelectric of leastsquares,istakentobethe distancemodulus,/xq,ofthe on theV—K\VdiagramforNGC7790duetosmallsizeof Section 4. of theCepheidawayfromcluster.Thisisdiscussedfurtherin absorption toobtaindistances. account ofdifferentialreddeninginsometheclusters.Thereis of CCD’sshouldallowapotentialimprovementintheaccuracy 276 (see Table4)aretypicallylessthan0.1magandincludeanyer- squares fitting.Theerrorsquotedonthevaluesforreddening stantially broadened.Byfittingtothecentreofdatawemeasure stars ratherthantheleastreddenedenvelope,becauseithelpstake V-band observationsforthisclusterwereavailable,asatestofthe V :CMDaroundthepositionof the A0Vstars,usingmethod We useboththeB—V:VandVK:Vcolour-magnitude To determinetheerrorinreddening,wemeasurestandard We choosetofittheZAMSridge-lineofOandB F. Hoyle,T.ShanksandN.R.Tanvir © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem WZ Sgr NGC 6823 Trumpler 35 vdBerghl NGC 6067 Lynga 6 NGC 6664 M25 NGC 6649 The valuesmarked*eithercomefromorareinferredFeast&Walker(1987)astheclustersNGC129and7790 NGC 7790 NGC 129 Cluster are notincludedinthestudiesofLaneyandStobie. Table 4.Thereddenings,apparentandabsolutedistancemodulitakenfromtheworkhereLaney&Stobie(1993). E(B -FW 0.59 ±0.05 0.57 ±0.05 0.85 ±0.07 0.90 ±0.09 0.37 ±0.03 0.56 ±0.08 0.66 ±0.06 0.49 ±0.04 1.19 ±0.07 1.36 ±0.08 1.37 ±0.06 0.64* 0.53* 0.75 0.92 0.77 0.35 0.57 0.64 0.48 1.34 1.35 14.37 12.67 13.52 15.00 14.09 12.30 15.50 12.88 12.80 10.57 15.52 previous valuesbelowinSection3.2.Theerrorsonthedistance between thephotometryofthisstudyandphotoelectricdata pointed attheclustercentresocontaminationmaynotbeasmuchof recipe forhowtoremovethecontaminatingstarsfromcolour- taken fromTable4. The apparentdistancemodulusß from Madore&vandenBerghis Madore &vandenBerghisgood(seeTable3),withonlysmall Van denBergh(1975)andWalker&Laney(1986).Theagreement NGC 6649.hasbeenstudiedpreviouslyby,forexample,Madore& 3.2 Discussionofindividualclusters the reddeninganddistancesobtainedaregiveninTable4,together NGC 7790inSection3.2. in thisstudyonlycoverafieldofview~6-13arcminandare magnitude andcolour-colourdiagrams.ThedatashowninFigs6,7 found fromthe5—V:diagramwasconsistentwithTC is thencheckedagainsttheV—ÄLCMDforsevenclusters 4 maginV.Thedistancemodulusfoundfromthe7?—V:CMD in thedereddenedZAMSwhichcoversarangeofapproximately the ZAMSofA0V-typestarsoverrange—0.1° -0.2^ > 0.1^ n° -0.2^ ^ -0.2 I 0.1^ I o i oh- I o- i -0.2 ï 0.2rn ï 0.2 $ -0.1r i 0.2F1 » -0.1^ » -0.1^ r -0.2 ^ -0.1 ^ -0.2 -0.1 ^ 0.1 r 0.1 h 0.2 ^ 0.2 0.1 i- 0.1 r 0 i- 0 o i- 10 10 Provided bytheNASA Astrophysics Data System

1 —-ÿ 'J'''- I ^Walker andCoulsen v Walker andCoulsen V NGC7790 ^Thackery ^Sandage Sandage 14 14 14 12 12

e 2003RAS,MNRAS 345,269-291 vdBergh 1 NGC6664 2 0 0 3MNRAS.345. .2 6 9H 1 1 ¿ 0.1H is giveninTable3.Onlytheclusterswhere anindependentzero-pointwasobtainedareshown. Figure 10.Acheckforanycolour-dependentrelationshipbetweenthework in thisstudyandpreviousphotoelectricwork.Thefullreferenceforthecomparison ¿ -1 Jc., © 2003RAS,MNRAS 345,269-291 > 0.1^ i 0.1^ i ob- 1 0^- 1 ob L -0.1^ í -0-1I 2 “O-^ 2 -0.1I I -0.2^ I 0.2ft I -0.2^ 3 0.2ft L L S 0.2 S 0.2F~r S 0.2 i 0.1j- ’ -0.2 r -0.2 ^ -0.2 -0.2 ^- -0.1 ^ -0.2 ^- -0.1 ^ -0.2 E -0.1 I -o.i I- -0.2 ^ -0.1 r 0.1 ^ 0.2 ft 0.1 ^ 0.2 F-r 0.1 0.2 0 =- 0 0 o I— -1 -1 -1 -1 © Royal Astronomical Society r uv 0 1 0 1 I ! ~KT van denBergh 1 b - madore TR35 Lynga 6 •».•k V i 3 > L 3 1 1 1 1 1 02 2 £ -1 £ -1 ¿ -0.2^ ^ o.l- 3 -1 0 > -1 > 0 3 -1 0 >° -0.2 > o.i^ 3° -0.2 3 0.1^ 0 -0.1 -0.1 -0.1 -0.1 -0.1 I o5 I 04- I 0 1 0.1 1 0-2 I -0.2 3 0.2 I -0.2 ! -0.2 3 0.2 ! -0.2 I 0.1 ■S 0.2 Î -0.2 & 0.1 Î - i -0.2 S 0.1 I 0.1 5 -o.ib i °-r * 0.2F-r j-0.1 3 0.2 " -0-1r -0.1 0.1 0.2 0 0 -1 -1 Provided bytheNASA Astrophysics Data System 1 4f^— i*ft*{* 0 1 0 1 0 1 0 1 0 12 0 1

i ; -Tî- u 1 b, b, Sandage bnan/fana ^ bgan/lllO« Sandage Sandage b, ^Walker andCoulsen 'Walker andCoulsen NGC6067 NGC7790 ^Thackerj 1 Distances toCepheidopenclusters281 L £ -0.2^ st -0.2^ ¿ 0.1^ 1 -0.2 3 0.1 > -0.2^ > 0.1h 3 -0.2^ 3 0.1^ > -0.2^ > 0.1^ 1 0 1 0i- 1 0 1 0 1 0 1 0 2 -0.1^ 2 -0.1^ 2 -0.1^ 2 -0.1 2 -0.1^ 2 -0.1^ & 0.2 & 0.2ft i 0.2ft S 0-2FT i 0.2rr Í 0.2ft 0.1 ^ -1 -1 -1 -1 -1 9 1 -Vtt- 'Vi'.* * I vdBergh 1

nr 2 0 0 3MNRAS.345. .2 6 9H by Laney&Stobie(1994)at12.95 agreesmorewithTurner(1984) reddening inthiscluster. to ß=10.58asÆ3wasassumedandvandenBerghfound that ofvandenBergh&Harris(1976), showninFig.9and10) implying ß=12.90.Turner(1993a)obtained/x11.26with Laney &Stobie(1994)andsomewhatlowerthantheE(B—V)= ter membership.BymeasuringthereddeningofO-andB-type tors couldpossiblyexplaintheslightlyoddshapeoft/—B:B ulated withonlyaround35membersbrighterthanB^16(Turner WZ Sgrtobeaclustermember. main sequence.ThisessentiallymeansthattheageofCepheidis to anopenclustercomesfromthefactthatoftenCepheidina membership ofWZSgrtotheclusterC1814-190insomedetailand Walker (1987)ofthedifferencebetweenresultArp(1958) used byLaney&Stobie(1994)whoquoteareddeningof0.64but to theincreasedvalueforreddeningestimatedhere. in thiscasenootherzero-pointcomparisonsarepossible. is slightlylargerthanE(B—V)=0.6obtainedbyArp.Noerror B-type starsratherthantryingtofittheF-andG-typeas with Turner(1984)whoobtainedßo=11.16±0.1Æ3.1 distance modulusof=12.88±0.14whichisagaininagreement 0.61 ±0.01reportedbyTurner(1993a). cause differentialreddening(Turner1984;1993a).Thesetwofac- consistent withtheageofcluster.Feast&Walker(1987)assume cluster isaround4magmoreluminousthantheB-typestarson concludes thatthestrongestevidenceformembershipofWZSgr value ofß=12.25(withnoerror).Feast&Walker(1987)use who obtainedß=10.8±0.2assumingR3.Thisismostlydue 0.14 whichislargerthanß=12.6±0.2,inferredfromArp(1958), were notdeepenoughtoseeiftheanomalousshapeofU— was quotedbyArp.InthepreviousworkArp,observations contamination. ThevalueforE(B—V)isthen0.66±0.06which and G-typestarsmaybemoreaffectedbymetallicityorbackground offsets betweenthetwodatasetsasgiveninTable3. agreement betweenhisphotometryandoursisgood,withonlysmall agreement betweenourvaluesandthoseusedbyLaney&Stobie and alsoagainstthatofMoffat& Vogt(1975).Offsetsbetween and thevalueobtainedhere. agreement withTurner,consistentE(B—V)=0.57usedby also bethesourceofunusualU—B:BVdiagramandmore ß =12.7. and thevalueofBecker&Fenkert(1971)whoquoteanevenlower an apparentdistancemodulusof12.35,basedonarediscussionby B:B —Vdiagram.ThisisaclearcasewherewefittheO-and (1994), asgiveninTable4.Weseelittleevidencefordifferential 282 F.Hoyle,T.ShanksandN.R.Tanvir stars weobtainavalueforE(B—V)=0.56±0.08whichisin spectroscopic andproper-motionstudiesarerequiredtocheckclus- ship ofanopenclusterisquestionable.Turner(1984)discussesthe B\B —Vdiagramwouldhavebeendetectedornot.Unfortunately, — Vcolour-colourdiagramparticularlyintherange0.50.5 mag. V) =0.49takenfromFeast&Walker(1987)andtheotherisE(B A 0 NGC 6823suffersfromdifferentialreddening(Turner1979a),to NGC 6823.wasonlyobservedinnon-photometricconditions. The associationofRUSetandTr35isdiscussedbyTurner(1980) The dataintheU—B:BVdiagramforclusterTrum- Our fittedapparentdistancemodulusis13.52±0.20which, Trumpier 35.Thereislittlephotoelectricdataavailableforthis © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem previous values.Turneretal.(1992)obtainedE(B—V)0.47but previous workhadtoberelieduponforthecalibration,asdiscussed bership andreducetheerrorondistancetoNGC6823. points fortheU—BandVcolours.Withourownzero-points by +0.075and+0.025mag,respectively,althoughfewdetailswere NGC 129. Laney &Stobie(1994)duetothenortherlylatitudeofcluster the cluster,whichwithR=3impliesß12.59,againinagreement Arp etal.(1959)findßo=11.0±0.15forthedistancemodulusof This valueissimilartotheofß=12.60inferredfrom the valuefoundhere. they fittedtotheleastreddenededgeofOandBstarsratherthan in detailSection2.4.1,andseeFig.11.Thereddeningforthis that derivedhere.Again,furtherspectroscopicandproper-motion Turner (1979a)andagainthedistanceisconsiderablylargerthan for thisclustertoV=20.Inthe absence ofÍ7,theironlyrouteto for thecolourswefindill-fittingZAMSandevenifapply that theproblemmightlieinSandage’sphotometrywhichPedreros to givethesamesortofill-fittingZAMSthroughoutrange the U—ßandBVcolours. table 1ofPedrerosetal.1984)impliesthatthedifferencesin to confirmthatSandage’sU—BandVcoloursweretooblue Freedman (1984).Acheckof16starswiththeKPNOCCDseemed for theOBstars.ThispoorfitofZAMStot/—B:B imply E(B—V)=0.43.Mostpreviousestimatesareclosertothat line. WeshowoneZAMSshiftedtofittheOBstarswhichimplies has siU—B:BVdiagramwherethedatapoorlyfitZAMS with thevaluefoundhere.DLCasisnotincludedinstudyby values of/x)=11.11andR3.2obtainedbyTurneretal.(1992). 0.53 (withnoerror)forthereddeningwhichisinagreementwith to thecentreofthesestars.Arpetal.(1959)foundE(B—V)= cluster isE(B—V)=0.57±0.05.Thisvalueslightlylargerthan find anill-fittingZAMS. our photometryandthephotographic dataofPedrerosetal.westill corrections suggestedbyPedrerosetal.totheoffsetsfoundbetween et al.hadusedforcalibration.However,wehavetestedvariouszero- 0.3 17andV15 Christian etal.(1985).Theytested thefaintphotographicphotom- checked againsttheB,Vphotoelectric photometryof10starsby © 2003RAS,MNRAS 345,269-291 Figure 12.ComparisonofallthedifferentsourcesphotometryforNGC 7790. NotethereisnoU-banddatainthestudybyRomeoetal.(1989). © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem V NGC7790 NGC7790 ^ pedreros u pedreros NGC7790 NGC7790 too red.Acomparisonofourphotometry andthatofRomeoetal. they claimedbetteragreement,with B—VPedrerosbeing~0.1mag in thesensethatPedrerosetal.were toobright.In2?—V,however, suggests thatthereisascaleerror forZ?>17andV16butthe Distances toCepheidopenclusters NGC7790 NGC7790 NGC7790 V romeo 285 2 0 0 3MNRAS.345. .2 6 9H remain. Thesearethestarsmostcertaintobeclustermembers.The been trimmedsothatonlythestarslieveryclosetoZAMS photometry ofSandage(1958)andisinbetteragreementwiththe brighter by0.2magandsimilardifferencesarefoundintheBdata. in Fig.6,whenallthestars field areused,appearsinFig.13 the ill-fittingZAMS.Fig.13showsB—V:VandUB:B for moredetails). We concludethatthephotometryinthisstudyagreeswellwith than Romeoetal.by0.1magwhereasthePedrerosdataare the starsthataremostlikelytobemembersofcluster. for theclusterNGC7790butwithonlystarsthatfitzero-agemain Figure 13.Thetoppanelshowsthetí—V:Vcolour-magnitudediagram with theworkofSandage(filled triangles), Pedrerosetal.(filled diagram. ThesameUVdeficitaroundtheF-typestarsthatappears CCD dataofRomeoetal.thanthatPedreros(seeFig.12 et al.withthedataofRomeoal.;atV=17ourarebrighter extent ofthisislessthaninthecomparisondataPedreros sequence shown.Thelowerpanelshowsthesamestarsastheyappearon 286 F.Hoyle,T.ShanksandN.R.Tanvir squares) andphotometryobtained byFryandCarney(opentrian- shape oftheU—B:BVdiagram. suggesting thatcontaminationis not thecauseofanomalous same starsarethenusedtoproducetheU—B:BVcolour-colour — VdiagramsfortheclusterNGC7790.TheBV:Vdiagramhas U —B:BVdiagram.Thedeficitisstillclearlyapparentamong Fig. 14comparesthecolour-colour diagramfoundfromthiswork We havealsoattemptedtocheckseeifcontaminationiscausing © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem presented two-colourdiagramsforNGC7790butbothrelyonthe relation inNGC7790. enough totesttheZAMSfit.TheresultsofPedrerosetal.(1984,filled The solidtrianglesshowtheresultsofSandagewhichdoesnotgodeep Figure 14.Theopencirclesshowourtwo-colourdiagramforNGC7790. therefore avalueof¡i=14.40isinferred fromtheirvalueof/x= from thevalueof/xq=12.8±0.15withR3foundbySandage the E(B-V)=0.52±0.04ofSandage(1958)and the CassiopeiaregionofPerseusspiralarm. in NGC7790mayalsoaffectotherneighbouringopenclusters Phelps andJanessuggestthatwhateverisaffectingtheUBVcolours NGC 103,129)clearlyalsoshowUVexcesses.Thedataof tometry for22otheropenclustersinthevicinityofNGC7790.Their We furthernotethatPhelpsandJanesalsoobtainedCCDUBVpho- to theoriginalphotometryofSandage(1958).Asalreadyde- Pedreros etal.(1984)correctionofA(U—B)+0.075mag the datatoZAMS.ThussameanomalousshapeofU— found inthisworkandconfirmsthepoorfitofZAMSU—B:BV ßo —12.65±0.15.Pedrerosetal. (1984)assumeR—3.28and and thereforegiveadistancemodulus ofß~14.3,astheymeasure which givesR=3.09withE(B — V)=0.54and(BV)q0 fi =14.37±0.13,whichisclosetothevalueof14.35,inferred 0.63 ±0.05ofPedrerosetal.(1984)whousedsimilartechniques. data (Be7,NGC663,637,TrI,581,457,Be62, graphs showthat10outofthe11clusterswithsufficientlygoodU with Sandage’sU—Bphotometrywithouttheabovecorrection. other datasetswhichareindependentofthepresentedhere. and FryCarneypointsdo,showthesamepoormatchof go deepenoughtotesttheshapeofdatabutPedrerosetal. gles, B.Carney,privatecommunication).TheSandagepointsdonot squares) andFry&Carney(1997,opentriangles)showthesameeffectas (1958). Romeoetal.(1989)assume aformulaforthevalueofR, stars, theapparentdistancemoduluswhichfitsV:R—Visthen B :B—VcoloursofOBstars,E(BV)=0.59±0.05,isbetween scribed, ourindependentlyzero-pointedphotometryagreesbetter B:B —VdiagraminNGC7790appearstobereproducedthese 12.3. 0 Assuming theestimateofE(B—V)=0.59±0.05fromOB Thus ourestimateoftheNGC7790reddeningbasedonU— We notethatPhelps&Janes(1994)andGuptaetal.(2000)have e 2003RAS,MNRAS 345,269-291 2 0 0 3MNRAS.345. .2 6 9H / periods. TheclustersassociatedwithRUSetandSVVulsufferboth Laney &Stobie(1994).Thethreesolid circlesinaboxareQZNor,RUSet Figure 15.TheGalacticCepheidsare shownbythesolidcircles,LMC from thepresenceofdifferentialreddeningandfactthat third, QZNor,seemtohavethewrongM—coloursfortheir using equation(3).ThetrianglesshowthesamerelationforLMC The valuesforE(B—V)ceharegiveninTable5. taken intoaccount, these CepheidsaretakenfromFeast&Walker(1987). the meanofobservationsat2-3epochsWelchetal.(1985) these Cepheids.TheTGbanddataforDLCasandCFcomefrom The clustersNGC7790and129lieatnortherlylatitudesso magnitude ofeachtheCepheidsisrequired.Wherepossiblethese the reddeninganddistancemodulusofcluster,apparent the cluster,weproceedtodeterminePLrelation.Aswellas 4 PLRELATION given inLaney&Stobie(1993),indicated herebytheboxedopencircles. and SVVul.Thereddeningsofthese Cepheids arecorrectedtothevalues Cepheids bythetrianglesandSMC Cepheidsbythesquares,takenfrom Cloud (SMC).Thesearetakenfromtables2and3inLaney& Cepheids andthesquaresareforinSmallMagellanic with theCepheidreddeningsobtainedfromcluster Cepheids. Thisiscalculatedvia gives agoodapproximationtothereddeningofCepheid.The cluster OBstars.Schmidt-Kaler(1982)foundthatwhentheeffect come fromLaney&Stobie(1993,1994)whohavehigh-qualityV- © 2003RAS,MNRAS 345,269-291 Stobie (1994).TwooftheCepheids,RUSet,SVVulandpossiblya M —=VK0.91XRc^E{B-V)^(6) of thecolourdifferencebetweenOBstarsandCepheidis and arethereforeapproximate.TheV-banddatatheperiodsfor are unobservablefromSouthAfricanAstronomicalObservatory and /0-bandmeasurementsformostoftheCepheidsinthisstudy. values for((Æo)—(lo)cephcomefromFeast&Walker(1987). (SAAO) andsotherearenomagnitudesfromLaney&Stobiefor Using thevaluesfordistancemodulusandreddeningtowards E(B -V)ceh=V)[0.980.09«ß>