19 6 9ApJS. . .18. .167B line oftheprobablereasonsfordifferenceshasbeengivenpreviously(Bessell1967), independent investigationofshort-periodvariableFstarsmadeatthisobservatoryfrom The AstrophysicalJournalSupplementSeriesNo.160,Vol.18 variable ,werechosenascomparisonstars for boththeobservationalandreduction gravities, andunexpectedlylowmassesbeingderivedformanyofthesestars(Danziger old Astars. high microturbulenceandanapparentoverabundanceoftheiron-groupelements.Thesepeculiarities by Mihalas.Largeanomalouslineblanketingintheblue-violetregionwasfoundforpPupand8Set, by adoptingthesolarvalueofHe/H=0.11formodelcomposition,instead0.15used standard starsrjLepF0VandaCMiF5IV(Procyon)fortheDeltaScutipPup,5Set, fitting thecontinuumfluxtomodel-atmosphere computations. procedures andforthecurve-of-growthanalyses. Inaddition,becauseaCMihasan and additionalobservationsafullerdiscussiongivenherestrengthenboththe Del whichwerenotinagreementwiththosederivedbytheaboveauthors.Abriefout- of metallic-linestars.ThemassestheDeltaScutistarsdeterminedfromobservedtemperatures curve-of-growth analysesrelativeto77Lepshowedthatthelinestrengtheninginthesestarswasdue was derivedfromboththeHyprofileandenergydistribution.Fromafittingofcontinuum profiles werecomparedwiththemodel-atmospherecomputationsofMihalasandSearleOketo Hy profileandtocorrecttheobservedfluxesforlineblanketing.Theresultantenergydistributions and gravitiesareconsistentwithnormalleft-to-rightevolutionintheHRdiagramforstarsofabout Procyon totheMihalascomputationsitwasfoundthattruegravityofcouldonlybederived derive theeffectivetemperaturesandgravities.Foreachstarsamevalueoftemperature (c) 1969.TheUniversityofChicago.Allrightsreserved.PrintedinU.S.A. MKK standardsrjLepF0VandaCMiF5IV, havingcolorsbracketingthoseofthe conclusion madeinthatpaperandtheproposition thattheDeltaScutistarsarePopula- and Kuhi1966;Danziger1967;Dickens1967).An and thelowCa/FeSc/Feratiosalsofoundfor8Set,Del,pPuparesimilartoproperties 50-inch telescopeatMount Stromloweremadecoveringfourperiodsfor pPupandone accurate (0''288)andmass(1.8Mo), it waspossibletocompareforthefirst tion Istarsofabout1.5-2Moevolvingfromthe mainsequence. 6 Delandthenon-variablestarsr)LepaCMi arepresented.Thebright,sharp-lined time theactuallogg(whereisgravitational acceleration)withthatderivedby ô Delovercompletecycles.Coudéspectracoveringfrom3390to6700Âwereobtainedmeasurethe 1964 to1966obtainedvaluesof6andloggfortheDeltaScutistarspPup,dSet, 1.9 Afo.ThespacemotionsofalltheknownDeltaScutistarssupportinterpretationtheirbeing e In thispaper,spectrophotometricobservations of thevariablestarspPup,ôSet,and Recent investigationsofDeltaScutistarshaveresultedinlowtemperatures, Photoelectric continuumobservationsbetween3390and10400ÂhavebeenobtainedfortheMKK Continuum observations withtheCassegrainphotoelectricspectrumscanner onthe * Presentaddress:YerkesObservatory, WilfiamsBay,Wisconsin. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Mount StromloandSidingSpringObservatories,ResearchSchoolofPhysicalSciences, AN INVESTIGATIONOFSHORT-PERIODVARIABLESTARS - I.THEDELTASCUTISTARS Received Jidy24>1968;revisedSeptember301968 y Australian NationalUniversity M. S.Bessell* INTRODUCTION OBSERVATIONS ABSTRACT 167 19 6 9ApJS. . .18. .167B 1 -1 corrected fluxesatmanyphases,expressedinmagnitudesperunitfrequencyinterval, absolute scalebyusingOkestandardsmodifiedasdescribedBessell(1967).Thered were madeondifferentcyclesforpPup,butconsecutivelythesamecycle8Del. complete cyclefordSetand8Del.Blue(3390-5700Â)red(5000-10000scans and blueobservationswerecombinedbybestfittingtheoverlappingpoints.Theun- Extinction wasdeterminedeachnight,andtheenergydistributionswereplacedonan spectral range3300-6700 Â.Thedispersionsobtainedwere6.7Âmm“ intheblue,and Lep andaCMi. referring tothemidpointofscan.Table2also containstheenergydistributionofr¡ are givenforpPupinTable1andôDel8Set2.Instantaneousenergy laE plateswere usedfor8Deland Set.Theplateswerecalibrated photometrically by the radialvelocity,coudé spectrasimultaneouswiththescansweretaken coveringthe distributions werereadfrommonochromaticlight curvesderivedfromtheobservations 2.35. 3.03. of pPup,whileforôDeland8Setthelisteddistributions arediscretescans,thephase 0.96. 2.80. 2.85. 0.98. 2.00. 2.40. 2.48. 2.75. 2.90. 2.95. 2.09. 2.19. 2.24. 10 Âmmintheultraviolet, visual,andred.KodakbakedIlaO, unbakedIlaO, 103aD, and103aFplates wereusedforpPup,77Lep,andaCMi, KodakTaOand 1.72. 1.80. 1.01. 1.19. 1.24. 1.27. 1.41. 1.47. 1.57. 1.65. 1.85. 1.90. 1.95. 1.03. 1.14. 1.33. 168 M.S.BESSELL In ordertocorrectforline blanketingandtomeasurethehydrogen-line profileand © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1A Absolute EnergyDistributions(-2.5logF+const.)forVariousPhases y 4.574 4.566 4.641 4.759 2.748 2.719 2.703 4.386 4.456 2.726 2.530 2.668 2.713 2.703 2.713 2.696 2.694 2.689 2.701 3.071 3.106 3.196 3.256 2.708 2.781 2.801 2.868 2.869 2.923 2.873 2.994 0.0 4.529 4.613 4.718 2.729 2.713 2.693 2.521 2.653 2.705 2.699 2.699 2.684 3.084 3.164 3.234 4.354 4.432 4.541 2.714 2.681 2.696 2.684 2.689 2.761 2.776 3.049 2.845 2.848 2.902 2.853 2.965 0.1 4.496 4.489 4.571 4.675 2.506 3.002 3.125 4.318 4.397 2.712 2.697 2.676 2.706 2.636 2.688 2.686 2.681 2.661 2.668 2.676 2.736 2.741 3.039 3.193 2.668 2.674 2.813 2.818 2.874 2.816 2.926 0.2 JDq2435560.756,Period0.14088143 4.457 4.448 4.528 4.636 2.701 2.674 2.660 3.001 3.083 3.144 4.280 4.349 2.694 2.494 2.669 2.666 2.646 2.642 2.655 2.644 2.651 2.703 2.615 2.661 2.716 2.787 2.791 2.842 2.784 2.886 2.966 0.3 TABLE 1 4.449 4.441 4.526 4.626 2.693 2.661 3.063 3.116 4.262 4.344 2.651 2.683 2.480 2.606 2.651 2.664 2.662 2.639 2.631 2.644 2.636 2.640 2.691 2.713 2.776 2.774 2.980 2.826 2.766 2.873 2.948 0.4 p Pup 4.479 4.467 4.551 4.659 2.689 2.651 3.072 3.136 4.286 4.366 2.672 2.477 2.610 2.658 2.668 2.642 2.651 2.640 2.646 2.711 2.806 2.681 2.671 2.636 2.785 2.777 2.832 2.971 2.994 2.781 2.891 0.5 2.652 3.102 3.167 4.388 4.513 4.501 4.586 4.694 2.661 2.736 2.731 3.021 4.316 2.695 2.671 2.686 2.689 2.486 2.624 2.669 2.686 2.668 2.651 2.663 2.805 2.798 2.853 2.916 2.996 2.683 2.802 0.6 4.541 3.138 3.206 4.344 4.415 4.533 4.621 4.729 3.027 3.056 2.698 2.688 2.696 2.700 2.500 2.699 2.668 2.756 2.828 2.941 2.638 2.683 2.692 2.678 2.681 2.664 2.681 2.758 2.830 2.827 2.879 0.7 4.569 4.569 4.371 4.446 4.639 4.760 2.684 3.056 3.091 3.176 3.242 2.706 2.701 2.704 2.699 2.698 2.711 2.692 2.711 2.514 2.655 2.858 2.909 2.861 2.975 2.855 0.8 691 673 696 769 784 4.586 4.651 4.391 4.466 4.583 4.774 2.708 3.079 3.111 3.198 3.258 2.716 2.716 2.696 2.682 2.706 2.778 2.803 2.878 2.706 2.526 2.671 2.711 2.704 2.716 2.694 2.701 2.875 2.930 2.881 2.998 0.9 r"m

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© American Astronomical Society • Provided by the NASA Astrophysics Data System 19 6 9ApJS. . .18. .167B 0.98. 2.35. 2.80 1.03. 1.14. 1.19. 1.24. 2.00 2.09 2.19, 2.40 2.75. 1.00. 1.27. 2.24. 2.48 2.85. 2.90 2.95. 1.33. 1.41. 1.47. 1.57. 1.65. 1.72, 1.80, 1.85. 1.90 1.95, © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 1/X 2.09. 2.00. 2.19. 2.24. 2.35. 2.40. 2.48. 2.75. 2.80. 2.85. 2.90. 2.95. 1.90. l/A N=0.127 4.57 4.58 4.62 4.41 4.45 4.57 4.58 4.55 4.57 4.53 4.58 4.59 4.61 4.64 4.62 4.56 4.62 4.64 4.65 4.69 4.72 4.59 4.76 4.76 5.94 6.04 5.84 5.95 6.09 N=0.143 4.54 4.54 4.58 4.39 4.45 4.54 4.54 4.50 4.51 4.50 4.53 4.53 4.53 4.56 4.59 4.59 4.58 4.59 4.59 4.63 4.67 4.70 4.74 4.75 5.92 5.84 5.96 5.99 6.03 3.74 4.96 3.76 3.81 3.86 3.78 3.90 3.94 3.96 4.91 5.03 v Lep 5.02 5.09 Mi¡\ N=0.160 4.72 4.65 4.65 4.66 4.52 4.57 4.62 4.58 4.58 4.57 4.55 4.57 4.55 4.57 4.61 4.63 4.62 4.61 4.58 4.62 4.65 4.69 4.74 4.74 5.85 5.92 5.95 6.00 6.03 TABLE 2—Continued a CMi 0.46 0.43 0.46 0.54 0.61 0.66 0.71 0.75 1.62 1.77 1.69 1.81 1.85 Delta Delphini,JDq2439313.0+N N=0.175 4.61 4.63 4.74 4.52 4.58 4.65 4.61 4.59 4.58 4.58 4.57 4.54 4.62 4.59 4.55 4.55 4.62 4.59 4.61 4.64 4.66 4.70 4.73 4.74 5.83 5.91 5.98 6.00 6.03 1.00. 1.03. 1.19. 1.24. 1.27. 1.33. 1.47. 1.41. 1.57. 1.65 1.72 1.80 N=0.190 4.59 4.61 4.50 4.68 4.57 4.52 5.35 4.58 4.63 4.57 4.57 4.56 4.60 4.58 4.54 4.63 4.57 4.63 4.63 0.00 4.69 4.72 4.76 4.74 5.85 5.93 5.96 6.03 6.06 i/x N=0.205 4.58 4.57 4.53 4.61 4.47 4.56 4.67 4.61 4.56 4.54 4.58 4.60 5.34 4.56 4.56 4.58 4.62 4.62 4.60 4.68 4.73 4.65 4.77 4.76 5.88 5.97 6.03 6.08 6.12 3.69 3.67 3.67 3.65 3.64 3.65 3.64 3.63 3.64 3.65 3.67 3.69 i) Lep N=0.220 4.62 4.65 4.64 4.73 4.49 4.58 4.60 4.57 4.55 4.60 4.60 4.57 4.60 4.66 4.66 4.66 4.65 4.68 4.56 4.64 4.70 4.74 4.78 4.77 5.92 5.98 6.04 6.06 6.10 a CMi 0.27 U.35 Mi¡\ N=0.237 .26 .25 .23 .24 .24 .25 .24 .27 .27 .32 4.65 4.67 4.70 4.49 4.57 4.63 4.59 4.57 4.58 4.60 4.60 4.59 4.66 4.66 4.73 4.55 4.57 4.65 4.67 4.66 4.72 4.74 4.78 4.77 5.91 5.98 6.02 6.06 6.07 N=0.252 4.61 4.69 4.71 4.51 4.66 4.66 4.50 4.64 4.61 4.62 4.61 4.55 4.57 4.57 4.63 4.64 4.65 4.65 4.64 0.00 4.69 4.73 4.78 4.81 5.92 5.95 6.01 6.07 6.12 19 6 9ApJS. . .18. .167B gether withanadditional correctionduetothemetallines(StromandKurucz 1966),was near B=0.70theBalmer-line-blanketed modelsgavedapproximately 0.02coolerthan profiles andenergydistributions formodelsinthetemperatureoverlap indicatethat applied toall thetemperaturesderived usingtheunblanketed models. grams fortherange0.700.70,itwasnecessarytouseHyprofilescomputedbySearle profile andtheblanketing-correctedcontinuatotheoreticaldataasdescribedabove Lungershausen continuashouldbeincloseagreement.Independentobservationsby This comparisonindicatedthatthesameeffectivetemperaturewithin0.01in0would made betweentheenergydistributionsofflux-constantmodelscomputedbySwihartand and Oke(1964)forgraymodels.Thesewereusedonly0>0.75,because<0.75 Mihalas for0<0.70.However,astherewerenoHyprofilescomputedtheflux- the fluxesat2,4,8,10,and15Âfromlinecenter.Then,byusingthesegraphs, were drawnoffluxversus0andloggforfixed,respectively, e these theobservedprofilescouldbefittedtoanaccuracyof0.01in0and0.2logg. theoretical profileswerereconstructedataspacingof0.01in0and0.5logg,with the graymodelsaresuspectowingtoopacityformulabreakingdownfor0<0.40 results in6=0.80andlogg4.0beingderivedfrombothobservations. Baschek etal.(1967)ofßVirconfirmedthisproposal,becausefittingthepublishedHy be derivedbyusingeithergridofmodelsbetween0=0.65and0.85.Thusitis Fischel (1961)andthoseforgraymodelscomputedbyCanavaggiaPecker(1952). (Searle andOke1967,privatecommunication).Usingtheprofilesfrombothgrids,graphs systematic photometric errorsnortoasystematicabsolutecalibration error.Theob- in thecontinuumfitting.Nomodelwithlogg= 4.05(theactualvalueforaCMi)could model continuawhichwereselectedasfitting the observationsbest.Figure2showsa 8 served energydistribution ofaCMiatthesewavelengthsisconfirmedby Bahner(1963), similar comparisonfortheHyprofiles.Itisseen thatforbothrjLepandaCMi,the e and theexcellent agreementbetween observedandmodel continua hasbeenshown by observed continuumbelowtheBalmerjump to befitted,thecontinuumabove be fittedtotheobservedcontinua,and,although decreasingthegravityenabled of themodelcontinuaforrjLep.ForaCMi,however, therearesignificantdiscrepancies to beexpectedthatthetemperaturesderivedbyusinggrayHyprofilesand Balmer jumpbetweenX =4000and4300Âwasstilldepressedbyabout 0.03magfrom e the modelcontinuum. temperatures derivedfromrespectiveHyprofiles areidenticalwiththosederivedfrom the respectivecontinua.Furtheragreementisshown bythegoodfit,atallwavelengths, e e e e e e e e e The modelenergy-distributiongrid-spacingof0.05in6and0.5loggwastoocoarse The observedHyprofileswerefittedbyusingthetheoreticalcomputed To checkontheeffective-temperaturescaleofdifferentmodels,acomparisonwas e These discrepanciesinthe fittingoftheobservedcontinua,aCMi are notdueto In Figure1theobservedcontinuaofrjLepand aCMiareshown,togetherwiththe © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem SHORT-PERIOD VARIABLESTARS173 a) TheContinuum-FittingProcedure b) TheHyProfileFittingProcedure c) TheFittingofr¡LepandaCMi 19 6 9ApJS. . .18. .167B model combinedwitheitherunderestimatedlineblanketingoranactualloweredcon- Hyland (1968)formanyAandBstars,aboverjLep.Itwillnowbeshownthat the discrepanciesresultprobablyindirectlyfromanincorrectheliumabundancein 0.29, andZ=0.02isabetteragreementforPopulationIobjects.Aneffectoflowering determined fromananalysisofBstarsinseveralgalacticclustersthatX=0.69,Y Mihalas forthemodelsisA=0.612,F0.363,Z0.020.Hyland(1969),however,has tinuum betweenthelinesinultravioletspectralregion. different gravity,themodeloflowergravityalsohasaelectronpressurethrough the heliumabundanceinamodelatmosphereistolowerelectronpressurethrough using aMihalasmodeloflowergravity.Quantitatively,anincreaseabout0.1in the atmosphere,effectofsuggestedcompositionchangecanbeapproximatedby the atmosphere.Since,inmodelatmospheresofsameeffectivetemperaturesbut 174 M.S.BESSELL of aCMi.Continuouslinerepresents theoreticalfluxofunblanketedmodeld=0.74 andlogg=3.9. of 7]Lep.Continuous linerepresentstheoretical fluxofunblanketedmodel of9=0.71andlogg 3.8. e e The compositionbymassofhydrogen,helium,andmetalsinthemixtureused Fig. la.—Closedandopencircles representrespectivelytheobservedandblanketing-corrected flux Fig. lb.—Closedandopencircles representrespectivelytheobservedandblanketing-corrected flux © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 19 6 9ApJS. . .18. .167B profiles ofwhichfitthe observations. ThisistheeffectfoundforaCMi also,butin8Set continua ofthevariable stars,itwasapparentthattheblanketing-corrected continuum and pPupinparticular the depressionisgreater.Theobservedcontinuum shortwardof shortward ofX=4300 Â fellbelowthatofthemodels,redcontinua andtheHy the Balmerjumpwasaccordingly raisedtoamoreprobableposition (as outlinedfora CMi) before fittingthemodelcontinua totheobservations. perature. and ofSearleOke(1964)arealsosatisfactory fordeterminingtheeffectivetem- Mihalas modelsaresatisfactoryfordetermining loggff,aswell0(OkeandConti servational errorsof±0.01indand in logg.Itappears,therefore,thatthe that for0<0.70and>0.75,respectively, the H7profilecomputationsofMihalas Balmer jumpisgreaterthanelsewhere,theobservedcontinuumbelow ing thegravityofmodelsforlowerchoice ofheliumabundance,amodel discrepancy, andso,bytakingintoaccounttheviolet-continuumcorrectionadjust- atmosphere. Ineithercase,itistobeexpectedthatthestrongerlineblanketing, and ultravioletspectralregioninaCMidoesnotresemblethatofhotterline-free been underestimatedorthecontinuousenergydistributionbetweenlinesinviolet suggests thattheobserveddepressionmustbeduetostrongerlineblanketingat discrepancy foraCMi;however,thefactthatcontinuumbetween1/X=2.48and low heliumcontentwillbelargerby0.03magthanthatofthemodelMihalas,which 1966), fromthecontinuumfluxes.Furthermore, intheprecedingsectionsitwasshown 6 =0.74andlogg4.05willthenfittheobserved continuaofaCMiwithintheob- greater thecontinuumdepressionwillbe.Hence,aslineblanketingbelow has ahigherheliumcontent. these wavelengthsinaCMi.Thisimpliesthateitherthemeasuredlineblanketinghas 2.35 alsofallsbelowthemodelcontinuumforaCMi,butnotr¡LeporAstars, composition change.ThustheBalmerjumpinamodelof6=0.74andlogg4.0with addition ^blanketing00^6^0^issufficienttoremovetheremainingBalmer-jump in aCMiwillbedepressedbyatleast0.03magfromthetruecontinuum.Thispostulated log ginthenominalgravityofMihalasmodelsnear0=0.70willaccountfor e e e e e ogg =3.8. og g=3.9.Opentriangle,rjLep;continuouslinerepresentsprofileofunblanketedmodeld0.71, e When anattemptwasmadetofitthemodel-atmosphere energydistributiontothe This increaseinthemodelBalmerjumpremovespart,butnotall,ofBalmer-jump Fig. 2.—Opencircle,aCMi;continuouslinerepresentsprofileofunblanketedmodel0«=0.74, © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem d) TheEffectiveTemperaturesandGravitiesofpPup, 8Set,andDel SHORT-PERIOD VARIABLESTARS175 19 6 9ApJS. . .18. .167B fluxes areidenticalwiththosederivedfromtheH7profilesatsamephaseshownin corrected violet-bluecontinuum,aswasdonebyDanzigerandKuhi(1966) the fittedtheoreticalenergydistributionareshowninFigure3forpPup,5Set,and of pPup.Continuouslinerepresents theoreticalfluxofunblanketedmodel0=0.71 andlogg=3.25. Figure 4. ô Delatmaximumlight.Theeffectivetemperaturesderivedfromthesecontinuum of 8Del.Continuouslinerepresents theoreticalfluxofunblanketedmodel6=0.67 andlogg=3.6. 176 M.S.BESSELL e e These observationsshowthatifthemodelcontinuawerefittedtoblanketing- The observedenergydistributionover50Â,theblanketing-correctedcontinua,and Fig. 3b.—Closedandopencircles representrespectivelytheobservedandblanketing-corrected model Fig. 3a.—Closedandopencircles representrespectivelytheobservedandblanketing-corrected flux © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 19 6 9ApJS. . .18. .167B several otherDeltaScutistars,incorrect,loweffectivetemperatureswouldbederived. and Danziger(1967)forpPup,8Set,Del,byDickens Furthermore, astheblanketingcorrectionsusedbyDanzigerandKuhiforpPupwere This resultsfromthefactthatinFstarssizeofBahnerjumpdecreaseswithde- authors followasadirectconsequenceoftheunderestimatedeffectivetemperatures. mined. also smallerthanthoseusedhere,anevenlowereffectivetemperaturewouldbedeter- creasing temperatureandincreaseswithdecreasinggravity;thus,underestimatingthe effective temperaturerequiresthechoiceofalower-gravitymodeltofitgivenBahner jump. of ôSet.Continuouslinerepresentstheoreticalfluxunblanketedmodel0«=0.69andlogg3.45. log g=3.6. log g=3.4.Closedcircle,b Del; continuouslinerepresentsprofileofunblanketed model of0«=0.67, log g=3.2.Opentriangle,b Set;continuouslinerepresentsprofileofunblanketed model of0«=0.69, The unexpectedlylowgravitiesdeterminedformanyDeltaScutistarsbytheabove Fig. 3c.—Closedandopencirclesrepresentrespectivelytheobservedblanketing-correctedmodel Fig. 4.—Opencircle,pPup; continuouslinerepresentsprofileofunblanketedmodel ofd=0.72, e © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem SHORT-PERIOD VARIABLESTARS177 178 M. S. BESSELL

THE VARIABILITY Figure 5 shows the observed variations in light at 1/X = 2.35, , ac- celeration, radius, and Qe (from Hy) for p Pup. The phases refer to the epoch JDo 2435560.756 and period 0.14088143 days. Table 5 lists the amplitudes of the variations in these parameters. This small range of 0.015 ± 0.005 in Qe or of 130° + 40° K in the temperature is consistent with the measured light amplitude and the adopted bolo- metric magnitude of Mb = 0.7. In Figure 6 are shown the observed variations in light (1/X = 2.35) and in the Hy derived temperature for ô Set and 5 Del. The phases are expressed in fractions of a day from JDo 2439310.000 for 5 Set and from JDo 2439313.000 for 8 Del. By using the radial- velocity curves of Paddock and Struve (1954) and adopting Mh =1.0 and 6e = 0.72 as the median values for 8 Set, the observed variation of 0.03 in 6e can be shown to be con- sistent with the observed light variations of 0.22 mag at 1/X = 2.35 or 0.15 mag at 1/X = 1.80 (closer to the bolometric amplitude).

0.2 0.4 0 6 0.8 1.0 PHASE Fig. 5 Fig. 6 Fig. 5.—Observed variations in p Pup. Fig. 6.—Observed variations in ô Set and 8 Del.

TABLE 5 Observed Variations of p Puppis

M2.i R (km s-1) R (cm s~2) R (km) Range 0.015 0.130 9.5 440 6 X 104 Mean error... 0.005 0.005 0.5 30 2 X 104

© American Astronomical Society • Provided by the NASA Astrophysics Data System 19 6 9ApJS. . .18. .167B 2 2 measured. Afourth-orderpolynomialwasfitted tothefiftyvaluesofcentraldepthand lines wereselectedfromlineidentificationsofDunham(1929),Greenstein(1948),and from thetemperatureamplitude-lightamplituderelationfordSetandpPup,tem- measures fromothermultiplets werethenshiftedtothiscurve.Theexcitation tempera- values, centraldepths,andderivedequivalentwidths foreachstararegiveninTable7. line profilesforblendedlines.Aboutfiftyunblended linesfromeachtracingcoveringthe from listsofWarner(1966,1967),Corlissand(1964,1966),(1965), perature variationovertheobservedcyclewasprobablylessthan0.008ind. line, aphenomenon foundbyWright (1951)forotherstars. Theexcitationtemperature plots oflogW/\versusg/Xmadeforalllines ofthesameelementandionization oftheseDeltaScutistarsandothersarediscussedbyDanzigerDickens agreement betweentheobservedgravityvariationandthatpredictedfromac- until thepointsfromdifferent multipletsliealongacommoncurve.Inthis investigation all otherlinesfromthecentraldepth-equivalent widthrelation.Thelistsoflines,g/- equivalent width,andthefittedpolynomialwas usedtoderivetheequivalentwidthsfor range ofintensitiesthelinestobeusedwere selected,andtheirequivalentwidths accurate methodbecauseitdidnotnecessitate thesubjectivedrawinginofindividual Only thespectralregionX=4000-4800Âwasconsidered,andrelativelyunblended these parametersandfromtheadoptedluminositiesarealsogiven.Thesourceof observed light,temperature,andgravityamplitudeforpPup,ôSet,Del,de- celeration changessupportsthevalueoflogg=3.6formeangravityôSet. ured. Differentiatingtheradial-velocitycurvesshowsthatrangeinaccelerationover cm s~,whichwouldcauseavariationof0.2inloggforstarmedian=3.6.The a cyclewithluminosityamplitudethesameasobservedisfrom—430cms~to+210 wide rangeofstrengths, wereusedinitiallytodefinethecurveof growth, andthe the linesfrommultiplets 38-43ofFe1(excitationpotentialabout1.5 eV),coveringa Conti (1964).Absoluteg/-valueswereused,andthesetaken(inorderofpreference) to derivemicroturbulentvelocitiesandrelativeabundancesforsomeoftheelements. termined fromthisstudyarelistedinTable6.Themassesofthesestarscalculated proximately forôSetbyadoptingthesameblanketingcorrectionatallphases.Varia- ture thusdeterminedwas notunique,butdependedontheexcitation potentialofthe Corliss andBozman(1962). 8 Del. pPup. Ô Set.. (1967). e tions of0.2±0.1indagreementwiththeH7variationsandloggweremeas- e The excitationtemperaturesareinpracticedetermined byshiftinghorizontallythe The medianvaluesoftheeffectivetemperatureandgravity,aswell Line strengthsweredeterminedfromcentraldepths, asthiswasfoundtobethemost No temperaturevariationcouldbedeterminedforôDelwithintheerrors;however, The variationsin6andloggfromthecontinuumobservationsweredeterminedap- Curves ofgrowthwereconstructedfor77Lep,aCMi,pPup,ôSet,andDelinorder e © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Sp. Type F2 III F6 III A7 III Data andDerivedMassesforObservedVariables SHORT-PERIOD VARIABLESTARS179 M 0.7 v 1.3 1.1 CURVE-OF-GROWTH ANALYSIS 0.70 0.72 0.745 TABLE 6 log g 3.6 3.75 3.4 0.008 0.030 0.015 Ade A logg 0.0 0.2 0.1 0.05 0.125 0.22 AB (Mo) Mass 2.0 2.1 1.9 19 6 9ApJS. . .18. .167B Fe I Lambda 4427.31 417^.92 4489.74 4199.97 4398.24 4375-93 4216.29 4147.68 4139.93 4172.75 4383.56 4271.76 4250.79 4143.87 4063.60 4733.60 4602.94 4132.06 4291.47 4415.12 4325.77 4404.75 4528.62 4602.00 4494.57 4442.34 4282.41 4632.92 4630.11 4047.32 4430.62 4187.04 4447.73 4222.22 4235.94 4187.80 4260.48 4191.45 4271.16 4233.61 4210.36 4250.12 4181.76 4049.33 4132.90 4062.44 4466.55 4184.89 4044.61 4647-44 4422.57 4213.65 4203.99 4175.64 4476.02 4376.78 4691.42 4245.26 4079*84 4490.08 4199.IO 4017.15 4772.82 4248.23 4143.42 4480.14 4067.98 4267.83 4387.90 4517.53 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 0.00 1 .48 1.48 2.18 1 .48 1 .48 2.20 2.20 2.18 1.48 2.42 2.28 2.28 2.22 2.20 1 .56 1 .56 1.56 1.56 1.56 2.54 2.42 2.40 1 .61 1.61 2.48 2.45 2.54 1 .61 1.61 1.61 2.48 2.47 2.47 2.83 2.69 2.59 2.83 2.83 2.83 2.84 2.84 2.84 2.84 2.84 2.84 2.86 2.84 2.99 2.86 3.02 3.02 3.05 3.05 3.02 3.05 3.05 3.21 3.11 3.07 3.07 3.07 CHI MULTLoggf .05 .05 .00 • 99 .12 .09 .96 .91 359 409 218 152 115 355 354 117 359 350 152 152 152 152 152 152 354 357 152 152 350 355 471 409 359 355 152 469 350 352 527 467 482 522 472 515 482 523 559 42 42 29 43 38 39 41 42 43 41 41 71 4l 42 43 T9 39 18 68 68 39 68 68 68 38 2 2 2 3 2 3 -1 .47 -2.86 -2.33 -2.34 -3.40 -4.21 -3.90 -2.51 -2.59 -2.98 -0.28 -1 .46 -1 .99 -0.07 -2.38 -O.13 -O.16 -0.20 -2.50 -0.50 -O.16 -2.31 -1 .83 -1.84 -0.58 -1 .02 -0.35 -0.35 -0.47 -1 *35 -O.19 -0.05 -O.I7 -0.02 -0.22 -0.55 -0.21 -0.74 -0.44 -0.52 -1 .27 -0.54 -1 .01 -1 .05 -1.11 -0.53 -O.I7 -0.62 -0.34 O.5I 0.20 0.43 O.25 O.36 O.63 0.17 O.13 0.25 0.31 O.25 O.06 O.09 0.46 0.18 0.05 0.14 0.10 0.81 O.6I O.29 -log W/LRC 4.771 4.570 4.655 *24 4.696 .21 4.768 4.463 4.231 .56 4.665 4.354 .41 4.287 .46 4.205 .55 4.771 .20 4.240 .53 5.096 4.277 .50 4.238 4.559 .27 4.409 4.595 4.673 4.420 4.511 4.278 4.630 4.718 5.095 5.418 4.588 .26 4.367 4.497 4.421 .36 4.350 4.788 4.602 4.329 4.600 4.559 4.591 4.669 5.086 4.729 4.521 4.786 4.732 4.646 4.787 4.653 4.891 4.528 .28 1) Lep .552 ,726 ,189 ,966 ,382 933 .28 .18 .33 .18 .22 .09 • 54 .38 .27 .23 • 38 .31 .10 .05 .21 .40 .48 .25 .09 .31 .29 .19 .27 .22 .43 .25 .20 .25 .18 .23 .27 .18 .23 .17 .31 .21 .38 .20 .13 .27 .08 .13 -log W/LRC 4.489 4.816 4.603 4.484 4.510 4.559 4.508 4.439 5.077 4.285 4.907 4.657 4.202 4.221 4.919 4.319 4.199 4.226 4.266 4.268 4.744 4.350 4.506 4.426 4.522 4.436 4.829 Line List 4.285 4.528 4.566 5.011 4.336 4.401 4.489 4.405 5.013 5.146 4.424 4.375 4.356 4.939 4.414 4.464 4.742 4.489 4.508 4.546 4.393 5.351 4.541 4.563 4.634 4.505 4.456 4.684 4.465 4.633 4.861 4.746 4.926 5.180 TABLE 7 4.669 4.397 4.936 4.897 4.451 4.479 4.835 4.570 4.951 a CMi 180 -.32 • 33 .45 .13 .42 .43 .36 .23 .17 .47 .72 .40 .61 .64 .72 .75 .60 .25 .20 .72 .66 .69 .52 .38 .43 .48 .23 .16 .16 . 11 .42 .43 .51 .65 .41 .51 .59 .55 .07 .57 .27 .^9 • 50 . 16 .52 .43 .37 .41 .43 .37 .27 .47 .38 . 11 .31 .41 .21 .46 .27 .31 .19 .51 .18 .18 .44 .42 .36 .21 .29 .17 • logW/LRC 4.259 4.501 4.359 4.843 4.283 4.256 4.038 4.237 .50 4.680 .21 4.172 .57 4.109 4.712 4.389 4.042 4.525 4.090 4.013 4.017 4.102 3.980 4.125 4.823 4.317 4.242 4.292 4.187 4.202 4.632 4.077 4.753 4.31 1 4.091 5.015 4.162 4.228 4.163 4.092 4.186 4.178 4.773 4.450 4.596 4.214 4.277 4.251 4.323 4.269 4.266 4.078 4.235 4.298 4.389 4.221 4.230 4.936 4.272 4.377 4.581 4.484 4.113 4.553 4.652 4.274 4.829 4.495 4.424 4.256 4.718 4.427 P Pup .48 .39 .51 .17 .^9 .31 .7^ .22 .40 .71 .71 .29 .64 .65 .71 .66 .64 .73 .45 .48 .59 .55 .25 .18 .67 .20 .12 .46 .53 .59 .52 .58 .65 .65 .57 . 18 .24 .45 .36 .56 .53 .50 .66 .41 .48 .51 .49 .37 .37 .27 .14 .34 .48 .54 .47 .52 .18 .28 .22 .45 .63 .47 .21 .31 .35 .35 -log W/LRC 4.648 4.729 4.507 4.373 4.563 4.330 4.534 4.913 5.066 4.125 .45 4.658 .21 4.095 .52 4.108 .48 4.255 .37 4.102 .61 4.196 4.O67 .53 4.I3O .47 4.099 4.927 4.998 4.296 4.489 4.589 4.317 4.312 4.143 4.093 4.984 .09 4.168 4.293 .35 4.7^5 4.134 .45 4.288 .35 4.377 4.369 4.230 4.364 4.357 4.255 4.277 4.544 .24 4.350 4.647 4.120 4.266 4.675 5.018 4.678 4.249 .36 4.533 4.301 4.357 4.653 4.990 • 239 ,182 ,081 6 Set 373 .17 .26 .31 .23 .21 .34 .08 . 1 .24 .52 .41 .50 .27 .23 .35 .35 .47 .35 .12 .10 .38 .31 .52 .42 .41 . 18 .38 .30 .31 .40 .31 .33 .20 .31 .37 .46 .36 .20 • 09 .34 . 10 .25 .19 .31 .20 ■log W/LRC 4.522 .29 4.915 .14 4.952 4.531 .31 4.627 .25 4.554 4.736 .22 4.221 .53 4.231 .51 4.625 .25 4.342 .42 4.139 .58 4.289 4.244 4.253 .48 4.345 4.204 4.634 4.452 4.253 4.697 4.550 4.476 4.282 4.634 4.330 4.533 4.387 4.287 4.453 .35 4.417 .37 4.447 .35 4.646 4.413 4.504 4.629 4.442 4.667 4.478 .33 4.529 .30 4.611 .27 4.826 .17 4.667 .24 4.677 .22 4.253 .4£ 4.957 .IT 4.595 «2< 4.924 .11 6 Del .13 .30 .54 .43 .45 .51 .25 .26 .35 .35 .49 .26 .23 .43 .30 .46 .46 .39 .35 .24 .23 .36 .25 .33 19 6 9ApJS. . .18. .167B Lambda 4438.35 4611.29 4678.86 4303.17 Fe II 4735.85 4264.74 4392.58 4276.68 4690.17 4479.61 4485.68 4745.81 4673.17 4643.47 4495.97 4433.22 4246.09 4596.06 4432.57 4382.78 4705.46 4547.85 4065.39 4629.33 4583.83 4520.24 4416.82 4385.38 4296.59 4273.31 4233.17 4178.86 4265.16 4484.23 4388.41 4587.13 4219.36 4240.37 4059.73 4072.52 4238.03 4157.80 4137.00 4208.61 4264.21 4228.72 4136.51 4227.43 4607.67 4140.44 4200.93 4247.43 4133.87 4268.74 4o4o.65 4022.74 4668.15 4504.84 4707.28 4070.77 4736.78 4531.63 4625.05 4285.44 American Astronomical Society* Providedby theNASA Astrophysics DataSystem 4.08 3.88 3.68 3.96 3.93 3.88 3.69 3.69 3.65 3.65 3.64 2.81 2.81 2.70 2.70 2.58 2.81 2.78 2.78 2.70 2.58 3.69 3.65 3.65 3.65 3.65 3.60 3.60 3.60 3.60 3.57 3-57 3.57 3.57 3.55 3.55 3.43 3.43 3.42 3.37 3.37 3.55 3.54 3.42 3.42 3.41 3.40 3.40 3.37 3.37 3.37 3.33 3.30 3.30 3.28 3.26 3.24 3.24 3.21 3.26 3.26 3.24 3.24 3.21 CHI MULTLoggf 1042 828 993 976 828 830 821 826 797 993 973 820 820 820 825 830 906 821 820 828 830 795 799 800 755 764 767 726 752 698 698 689 695 695 689 690 594 689 692 693 698 693 649 655 556 554 554 555 554 554 597 558 554 555 37 27 28 38 37 27 27 28 27 27 -2.O9 -2.02 -2.00 -1.78 -1 .25 -1 .87 -2.36 -1 .43 -2.27 -2.00 -0.37 -O.94 -O.71 -O.96 -0.75 -0.79 -O.7O -0.99 -0.40 -0.55 -0.53 -0.59 -O.I3 -0.99 -0.14 -0.42 -0.87 -O.9I -0.82 -0.16 -I.27 -0.10 -0.59 -0.52 -0.43 -O.7O -O.I9 -1.11 -O.O7 -0.22 -0.78 -1.65 -0.82 -0.48 -0.63 -0.30 -1.17 -0.30 -0.66 -I.5I -0.23 -O.63 -0.42 -0.02 -1 .20 O.O5 0.08 0.02 0.79 O.I7 0.45 0.90 0.01 0.12 ■ logW/LRC 4.595 4.765 4.922 4.904 .15 4.798 .19 4.729 4.534 4.627 4.530 4.521 4.292 4.451 4.837 .17 4.933 4.794 4.667 4.531 .29 4.879 4.971 4.878 4.786 4.757 4.964 4.612 4.800 .17 4.502 .31 5.105 .10 5.165 .08 5.249 .07 4.688 4.737 .19 4.340 .42 4.900 .14 4.654 .22 4.900 4.744 4.935 4.837 4.646 5.OO6 5.150 5.059 .10 4.533 .29 4.790 4.701 5.492 5.I35 567 399 T1 Lep TABLE 7—Continued .29 • 30 .19 .40 .25 .30 .26 .47 .34 .15 .23 .31 .19 .04 .14 • 23 .09 .21 .16 .15 .25 .08 .21 .13 .22 .12 .18 .23 .16 .12 .14 .17 .18 14 ■log W/LRC 181 4.568 4.438 4.588 4, 4, 4.580 4.974 4.963 4.936 4.633 4, 4. 4.449 5.030 5.441 4.873 4.936 4.695 4.711 4.704 4.850 4.748 4.816 4.751 4.702 4.806 4.818 4.598 4.522 4.943 4.459 4.890 4.413 5.294 5.155 5.315 4.844 4.883 4.764 4.657 4.443 4.791 4.556 4.838 4.644 4.340 4.787 4.596 4.906 4.849 4.722 4.851 4.639 4.524 4.655 5.187 5.152 5.160 5.199 5.037 5.649 4.702 5.376 5.061 .531 .513 .472 ,502 a CMi .39 .51 .35 .46 .08 .20 .30 .36 .19 .51 .37 .41 .42 .45 .42 .08 .15 . 11 .06 .16 . 11 .18 .19 .20 . 11 .21 .10 .22 .22 .34 .39 .16 .31 .45 .04 .20 .30 .59 • 23 .32 .17 .22 .31 .16 .22 .28 .24 .29 .26 .31 . 1 .47 .15 .26 .27 .21 .21 .30 .07 .29 .22 .38 .33 .14 • logW/LRC 4, 4.269 4.159 4.234 4.200 4.213 4.291 4.057 4.774 4.830 4.782 4, 4, 4, 4, 4, 4.891 4.942 4.863 4.510 4.253 4.266 4.363 4.226 4.208 4.629 4.526 4.246 4.588 4.248 4.21 1 4.119 5.188 4, 4, 4, 4.467 4.419 4.476 4.665 4.383 4.406 4.547 4.497 4.533 4.605 4.374 4.667 4.635 4.287 4.117 4.755 4.498 4.302 4.398 4.952 5.038 4.215 4.515 5.567 4.385 4.526 4.435 5.187 713 437 P Pup 966 903 948 597 618 591 633 .52 .55 .15 .47 .29 .62 .54 .54 .46 .62 .20 .12 . 17 .09 .18 .14 .25 .22 .27 .25 .36 • 35 .40 . 16 .14 .28 .17 .31 .28 .24 .38 .49 .22 .39 .52 .23 .54 .04 .23 .45 .63 .48 .18 .27 .09 .41 .34 .43 .14 .52 .55 .69 .25 .14 .33 .34 .23 .37 .53 .30 .27 .33 .31 .40 ■log W/LRC 4.544 4.787 .16 4.460 4.482 .26 4.371 .31 4.765 .16 4.292 .35 4.457 4.573 4.377 4.682 .18 4.713 4.852 .14 4.169 4.290 4.225 4. i4o 4.335 4.686 4.987 4.488 4.594 4.533 4.857 4.677 .19 4.733 .15 4.218 4.743 4.654 4.526 4.350 4.300 4.202 4.104 4.140 5.O67 ,.08 4.745 4.597 .22 4.419 .29 5.IIO .07 5.197 6 Set .36 .36 .39 .45 .44 .27 .23 .30 .19 .34 .45 .41 • 33 .48 .18 .20 .10 .23 . 14 .24 .27 .39 .06 .18 .20 .24 .27 .25 ■ logW/LRC 4.408 4.334 4.413 4.362 .41 4.557 .29 4.281 .47 4.605 .26 4.460 .34 4.424 .37 4.804 .18 4.326 .43 4.552 .28 4.617 .25 4.466 4.347 .42 4.883 .16 4.976 .13 4.913 .15 4.690 .22 4.590 .27 4.993 .13 4.994 .13 4.806 .18 4.335 .42 4.739 .21 4.413 .37 4.952 .14 4.976 .12 5.186 .08 4.994 .12 5.OI7 .11 6 Del .40 .45 .39 .35 19 6 9ApJS. . .18. .167B Lambda 4472.92 4491.40 4582.84 4576.33 4620.51 4489.18 4425.43 4635.35 4731 4541 .52 4508.28 4522.63 4515.34 4585.87 4578.56 4283.01 4226.73 4294.77 4415.56 4455.89 4318.65 4302.53 4435.69 Ca I 4651.28 4616.14 4591.39 4274.80 4254.35 437^.^6 4314.08 4431.37 4400.36 4320.75 4325.01 4305.70 4261.92 4252.62 4269.30 4718.45 4646.17 4626.07 4371.28 4652.16 Cr I 4246.83 4555.02 4588.22 4275.58 4284.21 4209.35 Sc II 4618.82 4592.OI 4558.66 Cr II 4634.11 © American Astronomical Society *Provided bytheNASA Astrophysics DataSystem 0.00 0.00 0.62 O.60 0.59 0.59 0.59 O.31 5.95 2.85 2.84 0.98 0.98 0.96 0.00 0.62 O.60 O.60 O.60 2.52 2.51 2.89 2.85 2.85 2.84 2.84 2.84 2.83 2.83 2.82 3.18 1 .87 4.07 4.07 3.86 3.85 3.83 1.89 1.89 1 .89 1 .88 1 .88 4.07 4.07 3-86 3.86 3.85 1.03 1.00 1.00 1.03 1 .07 CHI MULTLoggf 186 186 43 37 38 37 38 38 37 38 38 37 37 23 23 21 21 21 22 21 21 21 44 44 44 31 44 44 31 31 26 31 31 15 14 15 15 15 14 15 14 14 4 7 4 5 5 2 5 1 1 1 -0.49 -1 .00 -O.9O -0.79 -0.97 -0.95 -1.18 -0.39 -O.27 -O.60 -O.25 -2.02 -0.80 -0.39 -1.37 -0.9^ -O.50 -1 .33 -O.31 -0.82 -0.54 -0.15 -0.55 -0.37 -0.33 •0.55 ■ 1.43 .2.26 -2.29 ■1.76 ■2.09 •2.44 • 2.22 • 1.51 • 1.91 ■2.63 •2.23 •2.60 -1.19 -0.98 -1 .37 -0.45 -1.44 -1.33 -1.21 -1 .85 -1.64 -2.O6 -1.75 O.30 O.16 0.82 -log W/LRC 4.605 4.686 4.400 4.509 4.870 4.576 4.771 .20 4.660 4.492 4.782 4.722 4.897 4.597 4.555 4.667 4.192 5.2OO .08 4.565 .28 4.337 .43 4.626 .25 4.558 .28 4.308 .45 4.609 4.423 4.650 ^.387 .39 4.338 .43 4.560 .28 4.815 4.877 4.973 4.453 .34 5.062 .10 4.994 4.780 4.836 4.751 4.902 5.OO8 5.422 5.l4o .09 4.657 .25 4.770 4.481 4.6o4 5.220 4.787 .19 5.013 Î1 Lep .16 • 33 .27 .19 .23 .40 .32 .28 .21 .15 .26 .26 .28 .23 .61 .24 .36 .24 .07 .18 .13 .16 .14 .12 .12 .15 .05 .20 .19 I27 .19 . 1 .34 TABLE 7—Continued •log W/LRC 4.563 4.643 4.698 4.441 4.569 4.796 4.625 4.751 4.552 4.466 4.524 4.156 4.729 .28 4.694 4.745 4.858 4.552 4.466 4.39^ 5.089 .13 4.349 4.347 4.862 4.694 4.936 4.836 4.925 4.801 4.644 4.624 4.612 4.939 4.770 4.852 4.704 4.79^ 4.550 5.022 3.789 4.732 4.673 5.028 .465 .359 .045 .502 .416 .720 .572 .425 .537 .336 a CMi 182 .34 .78 .39 .27 .29 .51 .38 .24 .26 .39 .46 .39 .45 .41 .29 .32 .21 .53 .14 .26 .50 .39 .46 .43 .51 .38 .59 .20 .25 .18 .22 .18 .58 • 58 • 57 .28 .17 .24 .14 .15 .29 .21 .28 .24 .40 .24 .33 .32 .33 .31 •log W/LRC 4.388 4.156 4.467 4.272 4.342 4.312 4.228 4.262 4.341 4.244 4.372 4.666 4.417 4.233 3.975 4.479 4.724 4.384 4.311 4.361 4.435 4.491 4.857 4.458 4.649 4.565 4.573 4.799 4.674 4.132 .62 4.125 .63 4.423 4.239 4.450 4.299 4.330 4.449 4.674 4.392 .40 4.34s .44 .313 .306 ,260 , 106 P Pup 347 263 303 253 606 127 126 147 .62 .53 .34 .40 .44 .50 .43 • 39 .40 .75 .24 • 39 .47 .55 .51 .33 .21 .45 .52 .45 .45 .49 .46 .25 .42 .50 .62 .50 .63 . 11 .61 .34 .17 .35 .24 .27 .28 .19 .23 .35 .40 .42 .33 .31 .22 .37 .54 .48 ■ logW/LRC 4.357 4.492 4.474 4.318 4.378 4.431 4.408 4.231 4.263 4.581 4.358 4.439 4.081 4.340 4.194 4.630 4.683 4.375 4.440 4.142 .45 4.188 .41 4.092 .53 4.219 4.411 .30 4.799 .16 4.240 4.189 4.573 4.545 4.737 4.636 .22 4.926 .12 4.459 .29 4.343 4.575 4.432 4.471 5.009 6 Set 228 415 655 155 .30 .38 .33 .27 .28 .32 .31 .40 .24 .20 .29 .57 .35 .22 .32 .41 .29 .32 .30 .33 .20 .38 .41 .40 .44 .39 .17 .24 .09 .34 .30 .23 .27 .24 ■ logW/LRC 4.383 4.443 4.838 4.579 4.748 4.529 4.411 4.560 4.689 4.568 3.621 4.719 4.119 4.840 .18 4.771 4.454 4.654 4.660 4.863 4.990 4.407 .38 4.672 .24 4.602 .27 4.524 .31 4.251 .49 4.568 .29 4.393 .39 4.999 .12 4.753 4.703 4.814 .19 4.871 .16 4.4o4 .38 4.343 .42 4.516 4.958 4.729 4.809 -19 4.496 .34 6 Del .37 .18 .29 .21 .39 • 30 .24 .30 .41 .13 .32 .20 .26 .35 .25 .24 .22 .63 .17 .20 .22 .13 .21 .33 19 6 9ApJS. . .18. .167B Lambda Ti I 4294.10 Ti II 4512.73 4287.40 4312.86 4300.05 4301.93 4545.14 4468.49 4443.80 4395.03 4012.37 4759.27 4617*27 4534.78 4548.76 4286.01 4290.93 4399.76 4568.31 4394.06 4464.46 4417.72 4501.27 4493.53 4457-43 4289.07 4386.86 4163.63 4316.81 4571-97 4529.46 4589.96 4395.85 4390.98 4563.76 4411.94 4055.54 4035 73 4o4l.36 4034.49 Mn I 4488.32 4367.66 4421.95 4028.33 4418.34 4502.22 4783.42 4754.04 4082.94 4033.07 4265.95 © American Astronomical Society *Provided bytheNASA Astrophysics DataSystem 0.83 0.83 0.83 0.82 0.82 0.81 0.57 0.82 0.00 2.25 0.00 2.60 2.13 3.12 2.69 2.58 2.06 2.05 2.93 2.27 2.13 2. 1 2.9I 2.29 2.17 1.16 I.I6 1.13 1.13 1.12 1.08 1 .08 1.08 1.08 1.23 1.22 1.22 1.22 1.18 1 .18 1.17 1 .74 1.54 1.89 1.57 1.57 1.24 1 .24 1.22 1.24 1.24 CHI MULTLoggf 233 145 113 104 1 o4 105 115 42 42 44 44 4o 4i 44 4i 41 40 20 42 44 82 82 30 31 31 93 94 87 51 50 51 61 61 60 50 61 51 18 19 23 22 19 11 16 16 2 5 2 5 5 5 -0.46 -0.39 -1.14 -1 .07 -O.65 -O.34 -1 .52 -1.61 -1.67 -1 .06 -1.53 -2.03 -1.93 -0.86 -2.11 -1 .47 -1 .06 -Ö.52 -1 .66 -1.18 -1 .08 -1.61 -O.65 -0.79 -1 .92 -O.74 -O.50 -O.90 -1 .58 -O.25 -0.14 -0.18 -0.10 -0.12 -O.16 -0.88 -0.64 0.41 O.72 O.7I 0.53 0.45 0.37 0.93 0.01 0.37 0.18 0.11 O.13 O.25 0.47 -log W/LRC 4 4.328 4.311 4.359 4 4 4.370 4.4o4 4.317 4.936 .14 4.94o 4.638 4.624 4.836 5.249 5.000 .12 4.308 4.701 4.519 4.442 4.851 4.688 4.351 4.679 4.332 4.436 4.370 4.773 .19 4.814 4.914 5.954 ■ 777 ,605 1] Lep 441 833 431 098 472 507 415 284 552 531 668 TABLE 7—Continued .32 .17 .42 .39 .07 .45 .46 .42 .48 .35 .41 .45 .19 .05 .23 .33 .29 .22 .13 .44 .25 .17 .26 .38 .10 .21 .41 .38 .31 • 34 .16 .21 .26 .19 .15 .34 .43 .02 ■log W/LRC 183 4.471 4.788 4.582 4.432 4.846 4.395 4.399 4.333 4.292 4.321 4.781 4.754 4.827 4.609 4.407 5.089 5.157 5.400 4.421 4.316 4.602 5-087 5.475 5.167 4.726 4.452 4.777 4.788 4.414 4.595 4.639 4.681 4.486 4.667 4.534 4.435 4.529 4.364 4.743 .26 4.468 4.464 5.076 5.009 4.674 4.664 4.668 4.317 4.346 4.266 5.104 5.127 <* CMi .06 . 1 .07 .35 .46 .49 .21 .55 .54 .61 .65 .58 . 11 .24 .24 .13 .25 .21 .54 .13 .34 .62 .35 .27 .54 .36 .33 .45 .30 .40 .14 .52 .50 .46 .46 .24 .29 .15 .38 .59 .54 .56 .65 .23 .43 .12 .12 .32 .33 .28 -log W/LRC 4.629 4.970 4.953 4.599 .25 4.062 4.584 4.792 .18 4.238 4.165 4.510 4.161 4.726 4.179 4.098 4.094 5.011 5.125 4.205 4.073 4.170 5.308 4.382 4.327 4.257 4.404 4.250 4.145 4.300 4.322 4.388 4.224 4.291 4.826 4.201 4.645 4.378 .40 4.156 4.451 4.522 4.217 4.145 4.177 4.147 4.035 4.925 4.949 4.475 4.453 4.600 .4311 P Pup .25 . 10 .13 .14 .53 • 59 .31 .59 .66 .13 .08 .27 .61 .61 .21 .66 .66 .68 .54 .39 .47 .18 .58 .24 .44 .55 .51 .37 .51 .64 .48 .46 .39 .58 .55 .58 .59 .34 .29 .51 .14 • 35 .36 .24 .42 .69 .14 -log W/LRC 4.884 .13 4.797 .15 4.094 4. l4o 4.814 .15 4.221 4.194 4.600 4.259 4.161 4.208 4.ni 4.347 .33 5.077 4.558 4.249 4.284 4.404 4.346 4.536 4.163 .44 4.391 .31 4.536 4.630 4.310 4.179 4.543 .25 .191 .809 .369 .299 . 103 .258 6 Set .23 .41 .53 .45 .45 .40 .41 .45 .08 .38 .43 .32 .35 .38 .24 .38 • 25 .21 .44 .31 .34 .25 .49 .35 .33 .15 -log W/LRC 4.581 .29 4.391 .39 4.376 .41 4.278 .48 4.293 .46 4.108 .61 4.350 4.396 4.360 4.765 .20 4.764 .20 4.402 .40 4.455 4.257 4.678 4.647 .25 4.424 .36 4.837 4.495 4.858 4.648 4.819 4.515 .32 5.009 4.703 .23 6 Del .35 .43 .40 .17 .12 .49 .24 .43 .17 .26 .'18 .31 19 6 9ApJS. . .18. .167B -1 -1 5.8, and4.2kms,determined forpPup,ôSet,and8Del,respectively. Fargreater curve-of-growth analysis.Theabundancesare listed onlyforthoseelementswhich relative torjLep,themicroturbulentvelocities, andtherelevantdetailsusedin was 0.3smallerthanthatobtainedfromtheionization equilibria.Asimilardifference with theionizationequilibriaofFeandTi,which isadditionalevidencethatthederived than the2.8kmsfound forr¡Lep,thesevelocitiesarecomparablewith thosedeter- accurate assessmentsoftheabundancescould be made. and thepartitionfunctionfromAllen(1962). Table8liststhederivedabundances was alsofoundfortheSun(Unsold1955).In viewofthisanomaly,theionization- relations foreachstar.For77Lep,pPup,8Set,andôDelitwasfoundthatthetempera- both theionizationlevelsandcontinuumopacityhencederiveabundances. is thechoiceofionizationtemperatureandpressurewhichareneededtodetermine damping constantsforFeiweredetermined,andthesevaluesthenadoptedall adopted foreachstarwasthatobtainedfromthoselineswithexcitationpotentialgreater X^exc) areshownforeachstar.Fromthesecurvesthemicroturbulentvelocitiesand equilibrium parametersofB=0.80andlogp = 1.5wereadoptedforaCMi. tures andpressuresatr=0.5estimatedfrom theMihalasmodelswereinagreement of modelatmospheres,itwasdecidedtousetheatmosphereT(t)andlogg{r) In Figure7theFeiandncurvesofgrowth(X=logW/\versusYgfk— relative ^/-valuesinthiswork,therelationship6—0=0.03wasfoundforallstars. than 2eV.Itwassignificantthatthederivedexcitationtemperaturesdifferedfromstar 6 andloggforthesestarsarecorrect.ForaCMi, however,thevalueoflogpe&tr=0.5 the sameexcitationtemperatureswerederivedforFstars.Byusingexperimental to star,because,whenthesolarlinestrengthswereusedincurve-of-growthanalyses, the otherelementsinordertoderiveabundances. e exce e 184 M.S.BESSELL The firstresultsofinterest weretheunusuallylargemicroturbulentvelocities of6.6, The abundanceswerethenderivedbyusingthe continuum opacitykfromBode(1965) Having derivedloggand6byfittingtheobservedcontinuaH?profilestothose The mostcriticalpartoftheabundancedeterminationinacurve-of-growthanalysis e © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Fig. la.—CurvesofgrowthforFeiandn;solidline,theoreticalcurve RESULTS 19 6 9ApJS. . .18. .167B 1 _1 mined formanymetallic-linestars,andthevalueof6.6kms“"derivedpPupis microturbulence, theoverabundanceofiron-groupelements,andlowerapparent velocities areaccompaniedbyanapparentoverabundanceintheFe-groupelements ratios arelowerinallthreestarscomparisonwithrjLep;particular,theCa/Hand among thelargestfoundforanyA-Fstars.InpPupandôSetthesehighturbulent of themetallic-linestars. relative torjLep,butin8Deltheseabundancesappearnormal.TheCa/FeandSc/Fe 3.5 kmsisidenticalwiththatdeterminedbySchroeder(1958). Sc/H ratiosin5Delarelowerbyatleastafactorof2comparedwithrjLep.Thehigh Ca andScabundancefoundfortheseDeltaScutistarsarereminiscentoftheproperties The abundancesforaCMirelativetorjLeparenormal,andthemicroturbulenceof © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Fig. 7b.—Curvesofgrowth for Feiandn;solidline,theoreticalcurve. Fig. 7c.—Curvesofgrowth for Feiandn;solidline,theoreticalcurve. SHORT-PERIOD VARIABLESTARS185 19 6 9ApJS. . .18. .167B about twiceasstronginpPupaCMi. growth forpPupandaCMi.Thelinesonthemedium-strengthportionofcurveare were foundinthisinvestigationforpPupand<5SetissupportedbytheStrömgren(b—y) the energydistributionfromyellowtovioletpositionofspectrum.InFigure 8 thoseDeltaScutistarswithStrömgrencolors(Cameron1966)areshownrelativeto and nt!colors.Theindexnh=(v—b)(by)measuresthechangeinslopeof 186 M.S.BESSELL The unusuallinestrengtheninginpPupisseenvividlybycomparingthecurvesof The unusuallystronglineblanketingandcontinuumdepressioninthevioletwhich © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Fig. Id.—Curvesofgrowth for FeiandFeii;solidline,theoreticalcurve. Fig. le.—Curvesofgrowth for Feiandn;solidline,theoreticalcurve. THE [mi/(b—y)]-DIAGRAM 19 6 9ApJS. . .18. .167B [Sc II]. [Ca I]. [Fe II], [Fei]. [Ti II]. [Mm] [Cm], [Cri]. Fig. 8.—DiagramofWiversus (b—y)forDeltaScutistarsandstandard © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem log p. V ariable Curve-of-Growth Details + 0.21 + 0.36 + 0.50 + 0.28 + 0.36 - 0.08 - 0.18 - 3.2 + 0.45 24.17 Pup 0.80 0.77 0.77 0.74 3.2 5.82 1.5 1.50 TABLE 8 b-y + 0.39 + 0.14 + + 0.29 + 0.39 + 0.34 5 Set 24.00 0.72 0.75 0.72 0.70 0.08 0.18 3.6 5.76 2.0 1.8 1.76 + 0.35 - 0.43 - 2.0 - 0.18 - 0.53 - 0.11 - 0.11 Ô Del 24.00 0.72 0.72 0.72 0.70 3.6 0.00 5.62 1.8 1.76 + 0.18 + 0.10 + 0.05 - 0.19 - 2.2 4 0.06 - 0.04 - 0.04 - 0.03 24.12 CMi 0.77 0.80 0.80 0.80 3.8 5.54 1.5 1.20 19 6 9ApJS. . .18. .167B diagram theseDeltaScutistars,likethelatemetallic-linelieinregionnormally reddest metallic-linestars.TheeffectofthestronglineblanketingonJohnson in aregionwherenootherstarsfall,while20CVn,DQCep,and4CVnfallamongthe an abnormaldepressioninthespectrumofvariablestars.Inthisdiagram,pPuplies metallic-line starsandsomeDeltaScutithusservesasanexcellentintrinsic the locusofHyadesstars.Itisapparentthat20CVn,DQCep,4pPup,and occupied bythegiantsequence. color indicatorforallA-Fstars.Figure9showsa[(F—iQversus0]-diagram Ô Setallexhibitlargermiindicesatagiven(b—y)thandotheHyadesstars,signifying versus 0]-relationshiptohighervaluesof,owing toaloweringofloggby1.0.These (Z7 —2?)-indexmimicstheeffectoflowgravity,andthusin[{UB)/(BF)]- Danziger andDickens(1967) differsignificantlyfromtheeffectivetemperatures deduced shifts wereestimatedfromthetheoretical-model energydistributions. derived byusingmodelatmospheresthereferred authors,andtheunbroken several brightDeltaScutistarsandnon-variable starsforwhich(F—Æ)-colorsare Hyades starsandbyBaschek etal.(1967)forßVir. plained bythelowgravities. Thevaluesof0derivedforaCMi,rjLep,p Pup,8Set,and from their(F—i?)-colors, andthatthedisagreementismuchlarger thancanbeex- pirical relationshipandwith thetemperaturesderivedbyOkeandConti (1966)forsome derived byJohnson(1964)and(1966), respectively.Theshorthorizontallines broken linesrefertotheempiricalrelationship between (V—R)and6fordwarfstars available andwhichareidentifiedinthelegend (Iriarte etal.1965).Thevaluesof0were at particularvaluesof(F—i?)indicatetheprobable shiftoftheempirical[(F—R) 8 Delinthiswork,onthe otherhand,areseentobeinexcellentagreement withtheem- 188 M.S.BESSELL e e e e e The Johnson(V—I?)-indexislittleaffectedbythestronglineblanketingin It isseenthattheeffectivetemperaturesofpPup, ôSet,Del,and20CVngivenby © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Fig. 9.—Diagramof0versus(V—R)forDeltaScutistarsandstandard e the [d/(V—Æ)]-diagram e 19 6 9ApJS. . .18. .167B derived bytheaboveauthorsforDeltaScutistarsareincorrectandhence gravities andmassesaretoolow. Table 9thepropermotions,radialvelocities,adoptedluminosities,andcomputed space motionsaregivenforallknownDeltaScutistars.Thevelocityvectorofthese The lowspacevelocitiesoftheDeltaScutistarsarestrongestevidencethatthey stars, ÔSet,20CVn,and4appeartobemembersoftheHyadesmovinggroup. stars fallswithintherangefoundforPopulationIAbyEggen(1963),andthree supports thisproposition. the sameageaslocalAstars.ThepositionofDeltaScutistarsinH-Rdiagram the theoreticallogg^6instabilitystrip.ClosedtrianglerepresentscomponentsofADS2849. left-to-right evolutionawayfromthezero-agemain sequence.Thesameconclusionwas Dashed linesjoinpointsofequalloggontheevolutionarytracks. view oftheprecedingcriticismtheirtemperature andgravitydeterminations.All gated. Thelowmasseswhichtheyderivedforthe coolerstarscannowbediscountedin drawn byDanzigerandDickens(1967)forthehotter DeltaScutistarsthattheyinvesti- using the(F—Æ)-colors,orbymeansofa[dversus (B—F)]-relationcalibratedfrom New temperaturesweredeterminedeitherby refittingthepublishedinfraredscans, provided bytherecently discoveredvariableHD24550,thebrightest member ofADS Delta Scutistar.Dickens (1967)investigatedandfoundvariationsofabout 0.03magin these starsinvestigatedbyDanzigerandDickens (1967)arealsoshowninFigure10. (± 0.2Mo),respectively.Thesemassesandthepositions ofthestarsinH-Rdiagram 2849. Onthebasisofits colorandluminosity,Eggenhadsuggestedthat itcouldbea (Fig. 10)areseentobecompatiblewiththeir beingoldAstarsundergoingnormal those DeltaScutistars with well-knowntemperatures. a periodof0.0758 day.Thepositions ofthesestarsinthe H-R diagramrelativeto the e e The (F—Æ)-colorsthenofferconclusiveevidencethattheeffectivetemperatures One ofthemostfundamentalindicatorsageastarisitsspacevelocity.In The derivedmassesofpPup,ôSet,andDellisted inTable6are2.1,2.0,and1.9Mo Fig. 10.—H-RdiagramshowingDeltaScutistarsrelativetothetheoreticalevolutionarytracksand Possibly themostconclusive evidenceontheevolutionofDelta Scuti starsis © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem THE EVOLUTIONARYASPECTSOEDELTASCUTISTARS SHORT-PERIOD VARIABLESTARS189 b) The(Mb/6)-Diagram e a) SpaceMotions r"

Delta Scuti Stars and Standard Stars American Astronomical Society •Provided bytheNASA Astrophysics DataSystem lrv l Tl,,:| , I0000^-H00i>.l0í^í>-N0 i>»mOOOc3*^PO'--i''^i-HOCNio t^cOi-H^iOOOiOiOOCMCMlO í^oOLoc^T-ioOOooOsOrMC^^ CO t-OCMi—ii—l 00 CMi^i—lO CO i—iooloro ^POt^'OTtHVOt^OO'rHiOr^rOiO P-iQcoOhí^CJS^^O c^çj ^5 i—ll-H 00íMi-Hi-HO\O\00cO OTfCNOOt^J>-'OCN'^i—ií^-On-’-'O tHCSC0í>*t-itH00^-i^h^hCSO ++I +++I!I a^oooQO. ^cmt^i—i^i—iCJÖ« I I++1+1 I +1++ • .r*nddl • ..oâ^J^OiHôa) CO 1—I i-H CO ++ I+ T-I ^-Hro ’-h ro'i—ii—ivhcs lO i-iOn00CM O' 00i-HiOO to oo do i-H O wT O I + CM lO I ++1 On r+. NOi-H U ^>c/2O CM LONO On O»Oco CO LOQ00 CO CMLO»—1 ^ o•—tuD-i LO NOCMCO 1-H CO 00 CMr>.CO O ^rhoCO 00 CMLOO TtNOO^COt". CM COO CM COO o NO1-1^ On co^ Ö p-QO.p* I +++ I ++ I + I ++Ï ! I+ O L''»co CO w 1 w 3 8 tí g if PQ-S SI II 1^ ¿4 S •si COT3 li N ^ d lO, "doJ Sä Ov IO S) on 2 2) o" dTD _ d gs S3 o2 ”! S O d bn p «TÎ5 s?| 3 « 2w 3 M) > SS u 2 u d O *-M «.vo :co NO 19 6 9ApJS. . .18. .167B 8 8 -1 masses of1.5and2.25Mocorrespondtothesametimeabout5.2X10years,in fainter starwasderivedfromthe[Sversus(B—F)]-relationforHyadesstars(Oke star toshowlowerCa/H andSc/Hratiosthannormalstars,hasbeenfound recentlyby models applicabletotheDeltaScutistarshaveyetbeenmade,butonbasisofex- . probable spectroscopic binaries, itmaybesignificantthatbDel,the only DeltaScuti is notinconsistentwiththissuggestion. nection betweenthemetallic-linestarsand DeltaScutistars.Theprobableageof The meanrotationalvelocitiesoftheDeltaScutistars,however,areconsistentwithwhat instability striponthe(logg,log7%)-plane.Theboundariesofthishavebeen past thestageinwhichheliumisburnedcoreandhavereturnedto zero-age mainsequencewithmassesbetween1.5and3.0Mo. instability stripinthe(logg,logr)-diagram.Nospecificinvestigationsofpulsation vicinity ofthemainsequence. stars evolvedfurthestawayfromthemainsequenceratherthanbeingwhichare for bSetand5Delweretoolow,alowtemperaturegravityhencemass gravity ofHD24550inthiswayalso,butbecausethevaluesparametershetook colors andtemperaturesofbSetDel(Dickens1967derivedthetemperature and Conti1966),thetemperatureofvariablestarfromacomparison whereas manyofthemetallic-linestarshavefields, nogeneralizationshouldbemadeon only theslowrotators.Althoughnomagneticfield wasfoundforpPup(Babcock1958), shown bythecurve-of-growthanalysisdosuggest thattherecouldbeagenericcon- would beexpectedfortheformermain-sequencepositionsofvariables. high rotationwaspreviouslyunknownforanypulsatingstar.Inthisproperty,theDelta center ofthistheoreticalstripsuggeststhattheyareindeedevolvingawayfromthe cal evolutionarytracksofIben(1966).Thefactthattheknownvariablesliealong diagram ofbSet,20CVn,and4CVnisconsistentwiththeDeltaScutistars’being relation tothesearrowsitisseenthatthepositionsoftwocomponentsADS2849 evolutionary tracksofIben(1966)areshowninFigure10.Thetemperaturethe Preston (privatecommunication) tobeaspectroscopicbinarywith highlyelliptical as thesestarsareallapparentlyslowrotatorslike themetallic-linestars,itisnotpossible Scuti starsalsodifferfromtheAIVelorumstars,allofwhichappeartobeslowrotators. to decidewhetherthespectralpeculiaritiesare afeatureofalltheDeltaScutistarsor 5 X10yearsforthemetallic-linestars(Eggen 1965) andthebrightestDeltaScutistars transferred tothe(M&/0)-diagram(Figure10)bytakinggravitiesfromtheoreti- tensive calculationsonRRLyraeandCepheidmodels,Christy(1966)hasderivedan are inperfectagreementwithevolutionawayfromthemainsequence. therefore derivedforHD24550.)Thearrowsontheevolutionarytracksofstarswith the basisofonestar.However,inview factthatallthemetallic-linestarsare Scuti stars,thevaluesofwhichrangefromlessthan10kmstoover100.Such e e e The spectralsimilaritiesofbSet,Del,and^pPup tothemetallic-linestarswhichwere More supportingevidenceforthisproposalcomesfromconsiderationofthetheoretical The relativepositionsofthesetwostars,andthepositioninHyades-groupH-R The evidenceavailable at thepresenttimedoesnotsuggestthatall DeltaScuti Danziger andDickens(1967)drewattentiontotherotationalvelocitiesofDelta Unfortunately, onlypPup,bDel,andSethave beenexaminedinanydetail,and, © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem SHORT-PERIOD VARIABLESTARS191 e) CharacteristicsofMetallic-LineStars c) TheInstabilityStrip d) RotationalVelocity 19 6 9ApJS. . .18. .167B oscillation. Untilmodels ofDeltaScutistarsareinvestigatedforinstability, thealterna- interacting overtonesthe observedperioddoesnotcorrespondto the fundamental Q foundbyEpstein(1950)andSchwarzschild (1941),butapartfromHD24550the magnitude ofthestar.MostthesevaluesQ aresmallerthanthetheoreticalvaluesof plain theabundanceanomaliesinmetallic-linestarsbyintroducingarbitrarytempera- ever, appears tobeconsistentwith valuesofQbetween0.026 and0.040. tives cannotbedistinguished. ThepulsationofthemajorityDelta Scuti stars,how- Delta Scutimodelsdeviate slightlyfromthoseinvestigated.Theotherpossibility isthat discrepancies arenotlarge andmaybeduetothefactthatenvelopes ofthepossible evaluated forthetwovaluesofabsolutemagnitude whicharelikelytobrackettheactual now thattheperiodsofmanyDeltaScutistarscorrespondtoevenlowervalues respectively, indicatedthelowerlimitofpossiblevaluesQforrealstars.Itappears reasonable procedurebecauseithasbeenshown thatthemodel-atmospheretempera- relative totheIbenevolutionarytracksofcomposition X=0.708,Z0.02.Thisisa Q, althoughnotaslowDanzigerandDickens(1967)hadsuggestedonthebasisof interest toinvestigatealltheshellhydrogen-burningstarsonevolvedmainsequence hydrogen burningintheshellends.Inthesecircumstances,large-scaleatmosphere inbothgroupsofstarsarerelated. calculated byadoptingmassesfromtheposition ofthestarsin(M&/0)-diagram established luminositiesandperiodsarelisted. The valuesofQ(=P\/p/po)havebeen of effectivepolytropicindexn=4.0andratiospecificheats7Itwassupposed must holdfortheDeltaScutistars,also.However,inthisconnectionitwouldbeof nosity andtemperatureoftheDeltaScutistarsincomparisonwithmodelsrequire stàrs areevolvedmetallic-linestars;rather,itraisesthepossibilitythatcausesof the starsarepulsating in modeshigherthanthefundamentaloneor thatbecauseof tures andgravitiesareconsistentwiththese theoretical models.ThequantityQis that thesevaluesof0.030and0.028forthefundamentalfirst-overtonepulsation, of awell-populatedclusterforevidencemetallicityandduality. ture andgravitystratificationintomodel-atmospherecomputations,thisconclusion that theybeundergoingrapidcorecollapseandenvelopeexpansionasthephaseof then referencetotheevolutionarymodelsofIbenmayprovidesomeinsight.Thelumi- the lowderivedgravitiesofseveralDelta Scutistars. turbulence wouldnotbeunexpected.Conti(1964),however,founditimpossibletoex- (1950) foundthatthelowestvaluesofQ,pulsationconstant,werederivedforamodel 192 M.S.BESSELL e In Table10thetemperaturesandperiodsofthose DeltaScutistarswiththebest If theDeltaScutistarsareevolvingnormallyawayfromzero-agemainsequence, From aninvestigationofthelinearadiabaticpulsationseveralmodels,Epstein © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 4 CVn.... HD 24550. 20 CVn... p Pup ß Cas.. Ô Del ô Set Star Possible ValuesofQforKnownDeltaScutiStars /) ThePeriodsoftheDeltaScutiStars 0.71 0.69 .70 .74 .72 .70 .72 0.104 0.14 (days) .076 .135 .142 .194 .17 TABLE 10 P (if 5=0.5) 0.025 0.019 .027 .012 .033 Q (if 6=1.0) 0.021 0.028 .021 .015 .027 .036 .031 Q (if 5=1.5) 0.028 0.039 Q SHORT-PERIOD VARIABLE STARS 193

CONCLUSIONS As a result of this investigation it was shown that the Mihalas models are satisfactory for determining log geff as well as de from the continuum flux when the helium abundance of the models is altered to F = 0.27. It was also shown that for 6e < 0.70 and 6e > 0.75, respectively, the Hy profile computations of Mihalas (1965) and Searle and Oke (1964) can be used with confidence to derive de. Conclusive evidence was presented showing that the Delta Scuti stars are Population I stars of age about 5 X 108 which are evolving away from the zero-age main sequence. The anomalous low masses derived by other investigators for the cooler Delta Scuti stars were shown to result indirectly from a great strengthening of the Fraunhofer lines in the violet spectral region. From a comparative curve-of-growth analysis, the line strengthening could be explained as resulting from unusually high micro turbulence and an apparent overabundance in the Fe-group elements. In addition, low Ca/Fe and Sc/Fe ratios were found for these stars. The similarity in the spectrum peculiarities of the metallic-line stars and p Pup, d Set, and 5 Del is an important discovery and suggests several interesting lines of investigation.

I would like to thank Dr. A. W. Rodgers and Dr. L. T. Searle for suggesting this project and for valuable encouragement and criticism during the course of the investiga- tion. The many helpful discussions with Dr. O. J. Eggen are gratefully acknowledged. I would also like to record my gratitude to Dr. A. W. Rodgers for obtaining most of the spectra of p Pup; to Dr. A. R. Hyland for obtaining the spectra of 5 Set and 8 Del and for providing the helium abundance of the cluster B stars; and to Dr. J. B. Oke, who made the Lungershausen model-atmosphere energy distribution available prior to publication. I am further indebted to Dr. A. R. Hyland, who initiated and collaborated on the investigation and consequences of the revised absolute calibration of a Lyr. This investigation was part of a Ph.D. dissertation submitted to the Australian National University. This paper was prepared for publication at Yerkes Observatory.

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