197OApJS ... 19. .193H -11 The AstrophysicalJournalSupplementSeriesNo.173,Vol.19 © 1970.TheUniversityofChicago.Allrightsreserved.PrintedinU.S.A. are studiedbyusingmodel-atmospheretechniquesintheLTEapproach.Effectivetemperaturescan be safelydeterminedfromionizationequilibriaandBalmerjumps;surfacegravitiesdependlargelyon log g=4.1,£4.5kmsforrScoandT30900°K,—4.05,s“XLep; factorily predicted,probablybecausethemodelsfailinuppermostlayers.Thequestionofmicro- the choiceofhydrogen-broadeningtheories.ForrSco,Pfennig’stheoryandmass-luminosityrela- predicted withtheabundancededucedfromweaklines,ifrecentbroadeningtheoriesareapplied.The turbulence iscriticallyexamined.AnalysesofabundancearecarriedoutwithmodelsT=32000°K, tion bothpointtoavalueforloggofabout4.ThedeepcoresHiandstrongHelinesarenotsatis- and theuosmicironabundanceshouldberediscussed.ThewingsofdiffuseHeilinescansatisfactorily Mihalas’s unblanketedmodelsareused.Mostelementshavesolarabundances,neonisoverabundant, interpretation ofearly-typespectra,numerouscoarseanalyses,aswellfineanalyses to besmall. ratio ofheliumtohydrogenisabout0.10bynumber,anditsdependenceonthechoicemodelshown few years,nosatisfactoryagreementoneffectivetemperature,gravity,andotheratmo- summary, seeUnderhill1966).Nevertheless,althoughaccurateobservations,good models, andimprovedline-broadeningtheorieshavebecomeavailablewithinthelast and othermodel-atmosphereinvestigations,ofthesespectrawerecarriedout(fora satisfactory fortheveryhot(09-B1)main-sequence stars.Effectivetemperaturesand spheric parametersofthesestarshasyetbeenreached. Thesituationseemstobeleast gravities havebeenderivedfromdetailedanalyses for10Lac(09V)byTraving(1957; GÎÎ Hy profilethatT=27000°,logg4.0are more correctparametersforrSco.The Aller, Eiste,andJugaku(1957;35000°,4.3), and Scholz(1967;32800°,42).Onthe e{{ models usedintheseinvestigationsareunblanketed (wechangedHeintze’svalueac- other hand,Heintze(1969)concludesfromthe continuousenergydistributionandthe of thecontinuumandlinesistreatedby useofanLTEtheory;and,withtheex- cordingly foreasiercomparison;cf.§IVg)and inradiativeequilibrium;theformation influence oflineblanketing cannowbecorrectedforandwhiletheother assumptions ception ofScholz’srSco analysis,microturbulenceisnottakenintoaccount. Whilethe are usuallyconsidered good approximationsoftherealphysicalsituation, Underhill rff =37450°K,logg4.45)andforSco(B0 V)byTraving(1955;32800°,4.45), Brook. eîi ; e New observationsofthecontinuousandlinespectrarScoXLeparereported.These After Unsold’s(1941a,6,1942,1944a,b)fundamentalworkonthequantitative * Presentaddress:Department ofEarthandSpaceSciences,StateUniversityNew York,Stony t Presentaddress: LehrstuhlfürTheoretische Astrophysik,Heidelberg, Germany. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Mount WilsonandPalomarObservatories,CarnegieInstitutionofWashington, THE ATMOSPHERESOFTAUSCORPII(BOV)AND Institute ofTheoreticalAstronomy,Cambridge,England Hamburger Sternwarte,Hamburg,Germany,and Received 1969June20;revisedJuly22 LAMBDA LEPORIS(B0.5IV) California InstituteofTechnology Johannes Hardorp* I. THEPROBLEM M. SCHOLZt ABSTRACT AND 193 197OApJS ... 19. .193H -1 1 has aneffectivetemperatureofonly24500°.Forcomparisonwiththetemperatures posed, whereasthesolarvalue,accordingtoLambertandWarner,is0.06.Underhill et al.1967).However,accordingtoHeintze(1969)thisisabinarysystemandßCru derived fromthe1.0Âmmspectra,seeScholz 1967,especiallyFigs.1and2).Five The resultsforlinesintheultravioletandblue spectralregionsareingoodagreement profiles. Equivalentwidthsweremeasuredfrom intensitytracingsofthefirstnine set ofHeIandnlinesforwhichgoodobservationssuitablebroadeningtheories None ofthehithertopublishedinvestigationsincludesaninterpretationcomplete physically justifiedmakethereliabilityofchemicalabundancesresultingfromdetailed ing thesurfacegravityfromprofilesofBalmerlines;(iii)togiveamodeminterpretation are available.AlmosteveryabundanceVne/^nbetween0.05and0.20hasbeenpro- et al.1957)andoverabundances(nitrogen:Traving1955;magnesium:Aller1957; analyses quitequestionable.Indeed,theabundancesquotedbydifferentauthorsshow whether ornotthemethodsofconstructingmodelandcomputingspectrumare H5, Hy,HeiX4388, iX4471,HenX4686.Nosystematicdifferencebetween observa- with the100-inchcoudé spectrographattheMountWilsonObservatory (seeTable1). with theequivalentwidthsmeasuredbyAller etal.,butaresystematicallysmaller to accountforallrelevantobservationsatonetime;(ii)showtheproblemsinderiv- atmospheres ofveryearly-typestarsfromthosetheSim.Onlyanoverabundance aluminum: Traving1957;iron:Scholz1967)“found”intheseanalyses,comparedwith a largescatter,anditisnotclearifcertainremarkableunderabundances(carbon:Aller the unblanketedmodelsabove,bothvaluesshouldberaisedbyabout1500°(cf.§IVg). of treatingstellaratmospheresarenotsuitableforafullinterpretationtheobserved to obtainlineprofilesof highaccuracy.Wemeasuredhydrogenandhelium lineswhich than thosepublishedbyUnsold(foradiscussion oftheaccuracyequivalentwidths based onarevisedversionofScholz’slist,including numerousobservationsofline Aller etal.(1957;heliumlines:Jugaku1959), and Scholz(1965).Óurpresentworkis additional platescovering theblueregionatadispersionof4.3Âmm“ weretaken of plates,platequality,reliabilitytheintensity calibration,dispersion,andsoon. spectrograms listedinTable1.Eachlinewascarefully weightedaccordingtothenumber line spectra. damping constantsinananalysisofbotholdandnewobservationsthe“metallic” mentioned above;(iv)toinvestigatemorecloselytheproblemofoccurrencemicro- techniques nowinuse. Ne seems,sofar,tobecertain. the solarvalues(LambertandWarner1969),reallyindicatedifferentcompositionsin early-type staryieldsTn=26600°±1100°KforßCru(B0.5IV;HanburyBrown spectra ofveryearly-typestars. can beinvestigatedtheoretically byusingpresentbroadeningtheories: HeiX4026, of theheliumspectrumwhichresultsinareliableabundancedespiteuncertainties (1968¿>) concludesfromadetailedstudyofthe10Lacspectrumthatpresentmethods turbulence inearly-typestars;and(v)toapplythemostrecentdataon/-values (1966, 1968a)claimsthattheheliumspectrumcannotbeunderstoodbymeansof e 194 JOHANNESHARDORPANDM.SCHOLZ The uncertaintyinthecorrectchoiceofmodelatmosphereandopenquestion The onlyinterferometricdeterminationyetmadeofaneffectivetemperature The presentinvestigationintends:(i)todemonstratethatitisindeednotpossible The problemofafullunderstandingtheheliumspectrumisalsostillunsolved. Extensive listingsofequivalentwidthshave been publishedbyUnsold(1941a), Because ofthelargenumber ofplatescoveringthebluespectralregion, wewereable is) American Astronomical Society •Provided bytheNASA Astrophysics DataSystem a) LineSpectrumofrScorpii H. OBSERVATIONS 197OApJS ... 19. .193H -1 1-1 -1 -1 difference betweenthe two calibrations(col.4).Thisprocedureincreases theobserved calibration ofHayesas publishedbyWolff,Kuhi,andHayes(1968) byaddingthe frequency interval,in magnitudes. Thenumberswereobtainedby comparison with The thirdcolumnofTable2givestheaverage of twoobservationstheradiationper Balmer jumpbyabout0.10 magandsteepensthePaschencontinuum.Finally, weadded calibration isnolonger generally accepted,weconvertedKodaira’snumbers tothenew Oke’s (1964)standards, andarethereforebasedonhiscalibrationofa Lyr.Sincethat lines soshallowthatnoreliablewidthscanbe derived.Furthermore,numerouslines the photoelectricscannerof60-inchtelescope attheMountWilsonObservatory. which arewellseparatedintherScospectrum areblendedbyrotationandmustbe omitted fromtheoreticalinvestigationinmany cases. 19125.. 19150.. 19149.. lines weremeasuredandweighted,profilesforthesamestronghy- visual region)(seeTable1).Equivalentwidthsofmanyweakandmoderatelystrong 19143.. 19142.. 10067L drogen andheliumlinesintheblueasrSco. region from3218to6721Â.Theywerealltakenwiththe100-inchcoudéspectrograph 12763.. 12764.. 12766.. 12738 S/L 12732 S/L 12731 S/L 12736 S/L 12765 S/L at adispersionof4.3Âmm(inthephotographicregion)and6.5 satisfactorily withthoseofTraving(1955;HyandHô,measuredbyUnsold) tions at1.0Âmm”and4.3mmwasfound.TheBalmer-lineprofilesagree surements ofheliumlinesfromthe6.5and5.6Âmmspectra. taken fromthehigh-resolution1.0Âmmspectraaswellafewlessaccuratemea- Elste, Jugaku,andAller(1956,Hy).Weshallalsodiscussprofilesofseveralweaklines _1 The continuousspectrumofXLephasbeenmeasured byKodaira(1968),whoused Unfortunately, therotationalbroadening(29km s;see§Vd)makestheweakest Spectrum* We evaluatedintensitytracingsoffourteenspectrogramscoveringthewavelength * MountWilson100-inchcoudéspectrograph, î A=Aller(1955);BBonsack(1959);SScholz(1967,1968);TTravingTs t Evaluatedwavelengthregionontheplate. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem -1 Dispersion ( mm) 4.3 4.3 4.3 4.3 4.3 5.6 6.5 6.5 6.5 1.0 1.0 1.0 1.0 1.9 TAU SCORPIIANDLAMBDALEPORIS195 4339-4686 4026-4686 4026-4686 4026-4686 4026-4686 4922-5876 6560-6678 4922-5876 3995-4452 3991-4469 3355-3995 5696-6721 4447-4925 4409-4829 Sco (â) Xt c) ObservationsoftheContinua b) LineSpectrumofXLeporis The Spectrograms Observ- A Ts B s s S S B B T T T T B er Î TABLE 1 18983, 18997, 18989, 19062 19063 19066 19092 19064. 19065 4.3 18990. 18991. 19101. 18998. 18999. Spectrum* ... 4.3 ... 4.3 ... 4.3 ... 4.3 ... 4.3 ... 4.3 1 Dispersion ( mm-) 4.3 4.3 4.3 4.3 6.5 6.5 6.5 4820-5876 4169-4751 4068-4820 4026-4676 3954-4751 3954-4662 3954-4666 3954-3995 3286-3973 4820-5740 3614-3995 3218-3983 3218-3970 5680-6721 Tsuji (1968). X Lep (Â) Xt Observ- er Î 197OApJS ... 19. .193H 1 Norton (1966)weremadeinthesamemannerasthoseofKodaira,althoughwitha jump oíD—0.08forXLepcanbereadfromthisformofKodaira’sdata. with modelcomputationsin§Vc(Fig.6).AtthisstagewemerelynotethataBalmer another correction(col.5)inordertorelatethedatanewmeltingpointofgold and obtainedthevaluesincolumn7ofTable2.FromthesedataitappearsthatXLep different telescope;therefore,weappliedthesamecorrectionstotheirmeasurements and rScohaveidenticalcontinuousspectra. of 1337.58°K(cf.LabsandNeckel1968).Thefinaldatacolumn6willbecompared Wolff etal.1968;HeintzeHardorp,Bidelman, andPrölss1968).Thusitseems graphic means,avaluewhichagreesbetterwith thatoíD=0.08byAlleretal.than is concerned.Thereare cases,particularlyamongearly-typestars,where thesteeper jumps. Thesituationis not soclearasfarthesteepeningofPaschen continuum also trueforXLepandhaspreviouslybeenfound tobesoinseveralothercases(e.g., tween modelcomputationandobservationthan theoldonewouldhavedone.Thisis with D=0.04obtainedfromAlleretal.byusing Oke’scalibration.Aswillbeseenin continuum ismoredesirable; however,inthecaseofaLyritself(unreddened!) theold that mostinvestigatorswelcomethenewcalibration, atleastthenewsetofBalmer Palomar Observatoryandfound verygoodagreementwithAlleretal.(1966). 196 JOHANNESHARDORPANDM.SCHOLZ § IVc,theBalmerjumpbasedonnewcalibration leadstoabetteragreementbe- 1 For TSco,foursetsofobservationsareavailable.ThoseAller,Faulkner,and Chalonge andDivan(1952)foundaBalmerjump oíD=0.07forrScobyphoto- Veryrecently,Schild(1969) reobservedthecontinuumofrScowith4-inch telescope atthe © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 3390. 3297. 3846. 3704, 3636 3571. 3509 3448. 4673. 4566, 4464, 4367, 4255, 4032, 3906, 3862, 4785. 4167, 4082, 5000. 5868, 5840. 5556. 5263. 5127. (Â) (i) x Continuum MeasurementsofxLeporisandtScorpii 3.033 2.09 2.14 2.00 2.19 2.24 2.29 2.40 2.80 2.90 2.95 2.35 2.45 2.48 2.59 2.60 2.70 2.75 2.85 1.95 2.56 1.70 1.71 1.80 1.90 i/x (2) X Lep 0.92 0.78 0.85 0.98 0.78 0.59 0.52 0.47 0.44 0.41 0.39 0.68 0l¿4 o!¿ó 0.58 0.50 1.15 1.07 (3) mv Oke-Hayes -0.011 +0.026 +0.007 —0.026 -0.042 +0.033 +0.032 +0.040 —0.050 +0.032 +0.028 -0.072 —Ó. 061 —Ó! 069 —Ó. 070 TABLE 2 Amp 0.000 0.000 (4) Gold-Point Correction -0.025 -0.026 -0.027 -0.028 -0.025 -0.022 -0.024 -0.028 -0.029 -0.022 -0.022 -0.037 -0.038 -0.030 -0.031 -0.031 -0.033 -0.034 -0.035 -0.037 -0.030 -0.033 -0.035 -0.036 -0.032 (mag) (5) X Lep fflv cor 0.80 0.88 0.71 0.7Ô 0.96 0.44 0.40 0.38 0.55 0.50 0.56 0.47 0.58 0.48 0.52 0.49 1.17 1.05 (6) +0.07 +0.04 +0.Î8 +0.22 -0.01 +0.34 +0.27 -0.05 +0.47 -0.17 -0.20 -0.17 -0.26 -0.30 -0.10 -0.13 -0.28 -0.29 -0.27 -0.17 -0.23 -0.20 mp cor r Sco (7) 197OApJS ... 19. .193H 10-2-1 1968 factor whichmatchescalculated linestrengthstoobservedonesand that itsphysical meaning is not yetwellunderstood. Radiation-damping parametersofvirtually all into account;butwerealize thatmicroturbulenceisstillmoreorless amerefitting profile. Dopplerbroadening duetothermalaswellmicroturbulent motionistaken profile function,i.e.,a Gauss (Doppler)profileconvolutedwithaLorentz (damping) versions oftheprogramspublishedbyBaschek, Holweger,andTraving(1966,herein- excitation potentials,andmostrecentsourcesfor oscillatorstrengths. and Holweger(1966)forthecalculationofionization equilibria,thetablesbyMoore dance analysespresentedinthispaper,wascarried outbyusingmodifiedandextended system gaveresultsdifferingbyafactorof1.7,thevaluequotedisatleastthatuncertain. is 171X10~ergcmsÂ.Sincethetwoabsolutecalibrationsofdetecting further attentionbyexperimenters. after calledBHT)andPeytremanetal.(1967). We usedthetablesbyTraving,Baschek, by meansofasatellite,thebrightnessrScoat1376Â,whencorrectedforabsorption, places Willstrop’ssystemjusthalfwaybetweenthoseofOkeandHayes(comparewith (1945; 1965,Silines)andWarner(1965,Fem lines)forlaboratorywavelengthsand continuum by0.05magper2000ÂflatterthanHayesdoes.Clearlythispointdeserves col. 4ofTable2).WethereforeconcludethatLabsandNeckelmeasurethePaschen In thecaseoffOphbothsetsmeasurementsagree,whereasfor58Aql,eAqr,and directly, sincefourofOke’ssecondarystandardshavebeenobservedbyWillstrop,also. solar continuousradiationandofaLyrdisagree. Wills trop’sPaschencontinuumissteeperthanOke’sby0.05magper2000Â,which of thePaschencontinuum),wemustconcludethatmostrecentcalibrations Neckel andwithOke,butHayesdisagreesOke(withrespecttotheabsoluteslope flux unitsforoutsidetheEarth’satmosphere).Hence,ifWillstropagreeswithLabsand besides thecaseofaLyrmentionedabove,thereareotherreasonstobelievethem excellent agreement,evenintheabsolutefigures(Willstropgiveshisnumbers of theG2VstarHD20766,whichhassameB—FcolorindexasSun,andfound of thesolarcontinuousradiation,comparedtheirresultswithWillstrop’smeasurement reliable. LabsandNeckel(1968),whohavemadethemostcompletecarefulstudy does notmeanthatwewanttodiscardWillstrop’smeasurementsaltogether,for, better withtheobservationsofAlleretal.(1966)thanWillstrop^figures.This standards, hisfiguresarenotaffectedbyarecalibrationofLyr.ThevaluesAller et al.jifbasedonHayes^calibration,thereforedisagreefromthoseofWillstrop(see well withthoseofAlleretal.(1966)ifthelatterwerebasedonOke’scalibration.How- 109 VirWillstropderivesasteepercontinuum.Ontheaverageoverfourstars, Fig. 6). ever, sinceWillstropusedhisowncalibratedlampinsteadofrelyingonOke’ssecondary calibration ledtoabetteragreementwiththeionizationequilibria(HardorpandScholz tinuum ofrScophotoelectricallybetween4000and6500Â.Hisresultswouldagree ). The profilesofmostlines canberepresentedverysatisfactorilybyusing aVoigt- The computationoflineprofilesandequivalent widths,aswelltheiterativeabun- According toSmith(1967),whoobservedearly-typestarsintherocketultraviolet The agreementbetweenWillstrop’sandOke’sphotometricsystemscanbechecked As wepointoutin§Vc,giventheobservedcolorexcessofrSco,ourmodelsagree The thirdsetofmeasurementsisthatWillstrop(1965),whoobservedthecon- © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem TAU SCORPIIANDLAMBDALEPORIS197 m. COMPUTATIONOFLINES b) LineswithVoigtProfiles a) GeneralRemarks 197OApJS ... 19. .193H 2 2 stronger lineswerecalculatedquantum-mechanically;otherwise,weused10timesthe Waals constantsCewerecalculatedbymeansofUnsold’s(1955)approximation.When very coreoftheline,whereaswingsareformedbyquasi-staticionsandelectrons C andCeareknown,theimpact-dampingparameterscanbecomputedasafunction Bréchot andvanRegemorter(1964a,b).However,weshouldmentionthatGrienPs classical value.QuadraticStark-effectconstantsCcanbederivedfromformulaeand for whichthetransitionfromimpact(linecenter)toquasi-static(farwings)broadening dances. of lines,sothatsomethestrongestlinesarelessusefulfordeterminationabun- of theopticaldepth.Unfortunately,constantsCareavailableforonlyasmallnumber tables publishedbyGriemetal.(1962)and(1964;cf.Hardorp1966), theory tendstounderestimatebroadeningincaseofionlines(Griem1966).Thevander puted correctly,anyway, becauseoftheincorrectnessuppermost modellayers perimental resultsisachievedwhenonereplaces ybyabout2y.Wheneveritseemedto in theusualway,thoughPfennig(1966Ô)has shownthatbetteragreementwithex- Trefftz (1966)fortheESWtheory,low-frequency componentatachargedpoint for hydrogenlines,whichisassumedtobeafairlygoodapproximationtheHen function) thataretobe expected,atleastinthisregionoftheatmosphere. be necessary,weconvolutedthenon-LorentzH i,Hen,andiprofilefunctionswith computed theDebyeshieldingparameteryfrom theelectrondensityandtemperature broadening, analogoustoPfennig’shydrogen-linetheory.Experiencehasshownthat it seemsimpossibleatthemomenttoselectoneofthemdefinitely;sowewillpresent discussion. Unfortunately,thesetheoriesyieldsignificantlydifferentlinecontours,and must betakenintoaccount. of Pfennig(1966a)forPfennig’stheory,thelow-frequency componentofPfennigand yields anappreciablybetterrepresentationofthePickeringlineswithhighupper both theoriesarejustfairapproximationsforHenX4686,but,asexpected,thelatter X4686 wingaswell.ThisformulaoftenisalsoappliedtothemembersofPickering central profileforhighelectrondensitiesandproposesusinganasymptotic-wingformula and Griem(1968,hereinaftercalledKG);seeHardorpScholz(1968)forabrief results foreachofthem. T —0.1inMihalas’s (1965)(r=30000°, logg=4)-model. and thefailuresof pure-LTE theoryoflineformation(sourcefunction =Planck and Trefftz(1966)forthePTtheory.Incases ofPfennig’sandthePTtheorywe quasi-static broadeningisofminorimportance. WeusedtheEcker-Müllerdistribution of Hooper(1968a,b)fortheHencomputations, andthemixedcomponentofPfennig static theorybyPfennigandTrefftz(1966,hereinaftercalledPT;cf.Messerschmidt, quantum numbers. (1966a), Edmonds,Schlüter,andWells(1967,hereinaftercalledESW),Kepple 198 JOHANNESHARDORPANDM.SCHOLZ Gauss profiles.Butusually thisaffectsonlytheverycoreofline,which isnotcom- Scholz, andTraving1967). transitions andtheirforbiddencomponentscanalsobetreatedbymeansofthequasi- X4921 (Barnard,Cooper,andShamey1969,hereinaftercalledBCS)HeiX4471 4 4 (n =4)seriesofHen.Wealsousedapurelyquasi-statictheoryionaswellelectron 4 (Griem 1968andBCS).Thewingsoftheselinesaswellother{2P°-nD,n>3) eff 2 In HI,Hen,andthediffuseilines,impactbroadeningprevailsonlynear Calculationswerecarriedout for6—0.217andlogP=2.719,valuescorresponding tothedepth The choiceofthemicrofielddistributionfunction tobeappliedcomputationsof The HenX4686linehasbeenstudiedbyGriem(1964).givestabulationsofthe Recent theoriesforthetreatmentofhydrogenlineshavebeendevelopedbyPfennig e Complete broadeningtheorieshavebeenpublishedforthediffuseheliumlinesHei © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem c) LineswithQuasi-staticWings 197OApJS ... 19. .193H -1 2 -11 -2-11 because accordingtoourexperiencethemeasuredequivalentwidthsdependtoostrongly velocity mustbeknownifequivalentwidthsofmoderatelystronglinesareusedfor Mihalas’s valuesonlyinsignificantly.Inordertosavecomputingtimewehadmake some authorspreferusingequivalentwidths,butweshallnotfollowthismethod, is lostinthisapproach. additional informationaboutthecorrectnessoftemperaturestructuremodel determining theionizationequilibria.OnceTeaisfixed,gravitycanbefoundfrom continuous absorptionandscatteringcoefficientswereused;hisnumbersdifferfrom was carriedoutforeachcombinationofTfandlogg.Constantmicroturbulence on theadoptedpositionsofcontinuumandouterwings,alsobecauseany gravity independentandprovidegoodtemperaturecriteria.Themicroturbulence late-O/early-B main-sequencestarisfairlystandard.TheBalmerjumpandtheioniza- luminosity relation,sincethedistanceisknown. the Balmerlines,profilesofwhicharefairlysensitivetogravity.Insteadprofiles, some simplificationsandschematizations,which,however,donotaffectthebasic we canestimatethemassfrommass-luminosityrelation,andknowdis- tion andthecomputationofcontinuouslineintensities,Bode’s(1967)tables and theoreticalvaluesagreeweredeterminedbyinterpolation.Forthepressureintegra- and H7Hôprofileswerecomputed,thepoints(Tff,logg)forwhichobserved and 34000°K,withgravitiesrangingfromlogg=3.7to4.6.Thetempera- tion equilibriaofthoseions,thespectrawhichcanbeobserved,arebothnearly g from atmospheres. InthecaseofrSco,wecanderivesurfacegravityalsofrommass- ture stratificationsweretakenfromMihalas’s(1965)tables,andapressureintegration Table 3showstheresults fortheothervalue,too.ForM=—3.70 Allen(1963) following computationwillbebasedonthevalue —3.70fortheabsolutemagnitude,but from themeasured/3-indexof2.607.Thecolor excessisEb-v=0.04mag,andthein- model atmospheres,wecanderivetheradiusRof thestarandobtainsurfacegravity any chosenwavelengthwiththefluxttFperunit surfaceareaascomputedfromthe £(r) =5kmswasadoptedafterScholz(1967).Ionizationequilibria,Balmerjumps, tance r.Ifwefurthermorecomparetheobservedfluxf(correctedforabsorption)at trend ofourfindings. new goldpoint.Models with T=32000°K,ontheotherhand,givelog 7^4275=9.09. trinsic apparentvisualmagnitudeisFo=2.72, accordingtothelatterauthors.The the Scorpio-Centaurusstream.Gutierrez-Moreno andMoreno(1968)get—3.70mag Since/r =irFR,theradius comesouttobeR=6.6Ro,whichshould becompared tabulates amassoflog SJî/SDîo =1.2formain-sequencestars. e e v /4275 =74.5X10erg cms“,ifwecorrecthisvaluesforabsorption andthe eii We consideredeleventestatmosphereswitheffectivetemperaturesbetween28000° The opencirclesinFigures1and2indicatethevaluesofparametersourtest The methodofdeterminingeffectivetemperatureT^uandsurfacegravityga The radiusisderivedin thefollowingway:Willstropobservedat4275 Âafluxof Bertiau (1958)derivedMofrScoas—3.54mag, assumingthatthestarbelongsto For rScotherearetwodeterminationsoftheabsolutemagnitudeM.Accordingly, v v © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem IV. EFFECTIVETEMPERATURESANDSURFACEGRAVITIES b) Mass-LuminosityRelationandRadiusofrScorpii TAU SCORPIIANDLAMBDALEPORIS199 log g=4.44+50Î/39ÎO-2R/Ro. OF TAUSCORPIIANDLAMBDALEPORIS a) TheMethod 197OApJS ... 19. .193H as inFig.1.AstheobservedHôprofileisofinferiorquality, thedashedlineshavebeenignoredinfixing out withmodelTauP. at distancesof1.5,3,and6Âfromthelinecenterby applyingthebroadeningtheoriesof(a)ESW, by theBalmerjumpandionizationequilibria(lineslabeled C,N,andSiindicatethechoiceofparame- the modelparameters.Finalanalysiswascarriedoutwith modelLamP. of HickokandMortonhavebeenshiftedtothescale unblanketed models.Finalanalysiswascarried then givenbythemass-luminosityrelationorlineprofiles ofH7andHôwhichhavebeencomputed “best” modelsTauE,K,andP,aswell ofotherinvestigators.ThoseHeintzeand ters thatwouldsatisfytheobservedionizationequilibria oftheseelements,respectively).Thegravityis (b) Kepple-Griem,and(c)Pfennig.Opencircles,parameters oftestmodels;filledcircles,thoseour Fig. 2.—Determinationofeffectivetemperatureandgravity forXLep.Symbolsanddetails,same Fig. 1.—Determinationofeffectivetemperatureandgravity forrSco.Thetemperaturecanbefixed © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 197OApJS ... 19. .193H , 3 far moreseriousthanthe mereobservationalerrors.Atthispointweremind thereader lower effectivetemperatures.Anobservational errorofAD=0.01wouldmeanan parallel tothelinesgivenbyionizationequilibria, buttheypointtosystematically The secondandthirdspectraofcarbonnitrogenaswellthefourth is mainlyduetothefactthatheusedadifferentabsolutemagnitude.WithM=—3.7 4.0. InFigure1thelinederivedfrom9ÏÎ-Lrelationisgivenforbothvaluesof with azero-agemain-sequenceradiusof4.6Roforstar152)îo(Iben1966).Thusr sequences ofparametersyieldingtheobserved Balmer jumps.Theyrunapproximately connected torotationallybroadenedlines,sowe assumeblogT^u«0.03. lead tothesteeplinesinFigures1and2,representingionizationequilibriaCn/ Bertiau -3.54...6.2617815-9.139.096.14.04 described above.Uncertaintiesinmassenterlinearly,too,ofcourse;therefore,wedo instead of—3.1hewouldhavederivedlogg=4.1.Inviewtherathercloseagreement metric magnitude,whichisunnecessary),derivedlogg=4.3forrSco.Thediscrepancy use ofthemass-luminosityrelation.Thesurfacegravityloggisthenderivedtoabout acts mainlythroughitsweight, andthiscaneasilybecorrectedfor—thereallogg is0.05higherthan For XLepthisestimateisprobablytoooptimistic becauseoftheobservationalproblems concerning theOinlines(cf.§Vic),weomitionizationequilibriaofoxygen errors introducedbythecalibrationprocedure forthecontinuummeasurementsare uncertainty ofblog~0.015intheeffectivetemperature, butwemustrealizethatthe this study.Weselectedafew^representativelinesandcomputedabundanceswhich spectra ofsiliconareobservedinrScoandXLepcanbeusedtodeduceionization not expectthevaluesofloggTable3tobeoffbymorethan±0.1. distance enteralmostlinearly,ratherthanquadratically,inthevalueofgderivedas value shouldbebetterthanours. luminosity. Sco appearstobeamedium-agemain-sequencestar,conclusionwhichjustifiesthe abundance ratioofanypairionscanbedetermined accuratelyinsideafactor2(Alog C m,Nn/NandSim/Siivinthe(logrff,logg)-diagram.Ifweassumethat equilibria. OnealsofindsOnandmlines,but,sincetherearecertaindifficulties of thetwoindependentdeterminationsdistanceitseemshighlyunlikelythathis the modellogg.Inordertobring allentriesontothesamescale,9D7-Lrelationfines ofFigure1should therefore bepushedupby0.05. € <0.3),weobtainanerrorlimitÔlogFf« 0.015 forthechoiceoftemperature. § IVe.Theeffectofthisisdifficult toassessindetail,becauseheliumcontributes theopacity.Butit Gutierrez-Moreno v e e 3 and Moreno-3.702.726.4219216-9.139.096.64.00 Traving (1955),applyingessentiallythesameidea(exceptthatheusedbolo- We nowturntothedeterminationofeffectivetemperature,asoutlinedin§IVa. We shouldpointoutthat,owingtotheslopeofSDî-Lrelation,uncertaintiesin TherestoftheentriesinFigure 1correspondtomodelswithtoómuchhelium,as willbeshownin For alltestmodelswecomputedtheBaimerjump. InFigures1and2weplottedthe © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Surface GravityoftScofromWl-LRelation,for7^=32000°K lo M Vo(mag)(pc)ÇjJJos/logttFRqg v TAU SCORPIIANDLAMBDALEPORIS201 c) IonizationEquilibriaandBahnerJumps m—M rÍDI^ TABLE 3 X =4275 197OApJS ... 19. .193H u 4 been proposedbyPfennig(1966a),ESW,andKGyieldsignificantlydifferentresults, becoming smallerforincreasinglogg.Thatthedifferencesareinsignificantcanbeseen flux fromthePlanckfunctioninsteadofexactsourcefunction,lattereffect be somewhereabove3.9.TheresultsbyStrom and Peterson(1968),whoderivedmean we willseeinthefollowingdiscussionthat,foratmospheresareconsideringhere hand andfromthecontinuousradiationonotheroccurredwithaLyr(Hardorp lowered below28000°K.Weshalldiscussthis point later. because theresultshardlydiffer. for allthreechoicesofbroadeningtheoriesmentionedabove,exceptthatweusedthe fit theobservationsandplottedcorrespondinglinesinFigures12.Thiswasdone below theaccuracyofprofilemeasurements. gravities oflogg=4.05fromHyequivalent widthsofmain-sequenceBstarslater plied: simple methodemployedintheprogrampublishedbyBHTinsteadofKGtheory, He iiPickeringlinesbecausetheobservationsandtestcomputationsshowthatitis spectra ofearly-Amain-sequencestars(HardorpandScholz1968;Peterson1969),but from anexamplegiveninTable4. than B2(Griem's1967theory)andlogg=4.25 (ESW),cannotbeconfirmedforrSco center. Foreachofthesepointswedeterminedtherunmodelparametersthatwould Indeed, recentresearchhasshownthattheESWtheoryyieldsbestresultsincaseof absorption andscatteringcoefficientsaredifferentsincewecomputetheemergent procedure ofaLyr. cooler star.Therefore,wecannotsimplyblamethediscrepanciesoncalibration Scholz 1968).However,inthatcaseitwastheionizationequilibriademanded 202 JOHANNESHARDORPANDM.SCHOLZ selected hydrogen-broadening theory.Asthecentralprofilesaremost sensitivetothe along thisline,findbest models"whichproduceoptimalHyandHÔ profilesforany and XLep. to thetemperatureregionsindicatedbyionization equilibriaandtheBalmerjumps. Pfennig's theoryseemstobepreferable.Wehaveneglectedtheinfluenceofblending and weknowofnoconvincingargumentwhichrulesoutonethesetheoriesdefinitely. that asimilardiscrepancybetweentheresultsfromionizationequilibriaonone 4 ii) GoodBaimer-lineprofilescanbeobtained whentheeffectivetemperatureis The followingpropertiesareobviousfromFigures 1and2,whichevertheoryisap- We consideredthreeprofilepointswithdistancesAX=1.5,3,and6Âfromtheline As wehavementionedin§Illr,thetheoriesofBaimer-linebroadeningwhich Our computedBalmerjumpsareslightlydifferentfromMihalas’svaluessinceour iii) ThesurfacegravitiesdependontheHitheory adopted,butloggwillcertainly i) Noneofthemwillyieldcompletelysatisfactory Balmerprofilesaslongwestick If weassumethattheSi equilibriumlineisafaircompromiseforfixing rff,wecan, TheHôprofileofXLepis of inferiorobservationalqualityandwillnotbeconsidered here. e © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 0.085 Thisinvestigation,Bode’sopacities,S=B 0.088 MihalasandStone1968,non-LTE 0.080 MihalasandStone1968,LTE 0.079 Mihalas1965,Nue/Nn=^AS v D AuthorandMethod Balmer JumpsComputedbyDifferentMethods for aModelwithreff=30000°,logg=4.0 d) HyandH<5Profiles TABLE 4 197OApJS ... 19. .193H 30 3 a observational errors. ponent) andAX=—2.75 (bluewingoftheforbidden2P°-4Fcomponent). From of theallowedandforbidden componentsofHeiX4471butfoundit toosensitiveto puted profilesoftheHenX5412andiX4471 linesforwhichgoodtheoreticaldescrip- is agoodindicatorofheliumabundance.With the abundancesoderivedwethencom- models wethereforeanalyzedtheHeiX4438 line which,accordingtoScholz(1967), diffuse Heilinesaresensitivetothechoiceof the gravity.Foreachofeleventest Figure 3wecanderive temperatureandgravitywithestimatederror limitsofÔlog tions areavailable(cf.§IIIc).Theresults giveninFigure3,whereweconsidered Pfennig TauP4.505+0.0154.10±0.15Lam4.4900.034.050.15 Teff ~0.015andôlog g ~0.3,respectively.Wealsotriedtousethe intensityratio the profilepointAX=1ofHenX5412(quasi-static theory),whileforHeiX4471 temperature indicators.Ontheotherhand, shapesofthequasi-staticallybroadened (Griem’s theory)twopointswereselected:AX =1(redwingofthe2P°-4Dcom- KG TauK4.510±0.0154.30+0.15LamK4.4900.034.20±0.15 ESW TauE4.515+0.0154.600.15LamE4.4950.034.50 interpretation ofourobservationstoconcludefromthisthatPfennig’stheoryisthe satsifactory agreementwithourownmeasurements. most adequatetheoryofBalmer-linebroadeningforlate-O/early-Bstars. puted profileshaveapproximatelycorrectdepthsatAX=3and6Â.Themodelpa- rameters arelistedinTable5,whichtheciteduncertaintyloggcorrespondstoan that theHyprofileofXLepisgenerallyrepresentedbetterthanrSco,andfor accuracy of±2percentinthemeasureddepthaprofilepoint.Figures1andshow temperature structureofthemodels,wedeterminethesebestmodels”sothatcom- r Sco,Pfennig’stheoryyieldsthebestresults.However,itwouldcertainlybeanover- 1955) andElsteetal.(1956)inordertocheckforsystematicerrors.Table6shows H iTheoryNamelogTeffgrf e We realizethattheusefulness ofthismethoddependsuponwhether wederived Because oftheirextremelyhighexcitationpotentials theHenlinesprovideexcellent We finallycompareourrScoobservationswiththoseofUnsold(publishedbyTraving © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Elste etal31208.5 Hardorp andScholz29.519830.519.5 Unsold 29.519.5929198 Line DepthsintScorpii(percent):ComparisonofDifferentObservers Observer 1.5Â3Â6 Parameters ofModelAtmospheresWhichPredictthe Observed LineDepthatax=3and6ÂofHy TAU SCORPIIANDLAMBDALEPORIS203 e) HeliumLinesintheSpectrumofrScorpii r SeoXLep TABLE 6 TABLE 5 Hy m 197OApJS ... 19. .193H faith canbeputinanyanalysisofheliumabundance.Wedonotsharethisopinion,but behavior ofHenX5412stillfixesthetemperaturewithinôlogTu«0.03.Theimplica- from faintHeilinesisnotlargelyaffectedbytheuncertaintiesofmodelparameters. somewhat betterthanourmodelTauP(cf.§Vlb).Theabundanceofheliumasderived of hydrogen-linebroadening).Scholz’schoiceparametersfitstheheliumspectrum the heliumabundancecorrectlybeforehand.Underhill(1966,1968a)believesthatno 204 JOHANNESHARDORPANDM.SCHOLZ tions ofFigure3agreewiththoseFigureslband1c,butcontradictla(ESWtheory even ifweassumethattheadoptedheliumabundanceiswrongbyafactorof2, et al.(1957)(toohot)andHeintze’s(1969)proposalcool);themodelsofTraving e (1955) andScholz(1967),thoughnotoptimal,aresatisfactorilychosen. blanketed models,see§IVg)islogicalifoneconsiders onlytheBaimerlines,butnot broadening theory.However,thereisabsolutely nopossibilityofinterpretingthe low-temperature model,thegravitystilldepending onthechoiceofhydrogen- if oneconsiderstheremaininglinespectrumbecause oneisthenledautomaticallytoa formed mightbecooler than isexpectedforamodelatmospherewhose parametersare puted coresofH7andHÔarethensomuchshallower thanthemeasuredshapes.The is amoremeaningfulindicatoroftheeffective temperaturethantheBaimerlines,we be producedbysuchacoolatmosphere.Sincewe thinkthatthe“metallic”linespectrum of modelparameters. model TauP(cf.Fig.12).Notethathehumabundanceislittleaffectedbyuncertaintiesinthechoice beled withtheabundancederivedfromHeiX4438,whichinturnwasusedtocomputewingsofn which areformedindeeper layers.Weshalldiscussthispointinthe nextparagraph. most conventionalexplanationwouldbeanincorrect temperaturestructureofthemod- do notfollowHeintze’sproposal.This,ofcourse, raisesthequestionofwhycom- Because theproblemof theBaimer-linecoresisessentiallysame foranyofthe X5412 andHeiX4471.Scholz’schoiceofparametersfitstheheliumspectrumsomewhatbetterthanour derived fromthecontinuum, the“metallic”lines,andouterBaimer-line wings els: theupperlayersof theatmospherewherecentralprofilesof H7andHôare “metallic” linespectrumthatway,norcanthe observedHenXX4686and5412lines According towhatwehavefoundsofarmustruleouttherScomodelofAller Heintze’s choiceofaneffectivetemperatureaslow27000°K(inthescaleun- Fig. 3.—ModelparametersforrScoasindicatedbyheliumlines.Opencircles(testmodels)arela- © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem /) PreviouslyProposedrScorpiiModels 197OApJS ... 19. .193H portant totakethis“classical” effectintoconsiderationproperly.Unfortunately, our because non-LTEeffectsaremoreimportantfor thelatterlinesthanforH7andH6 her modelsmighthaveimprovedH7andH5 but notHaandH0.Thisisinteresting but thattheLTEapproachisinadequatefor the interpretationoflinecores.De- investigations indicatethatwemaytrustourcomputation ofH7andHôwingshapes Mihalas andStone(1968)haveshownthata simplifiedhydrogen-helium,non-LTE own HaandHßobservations arenotaccurateenoughforameaningful profilestudy. Mihalas (1968). partures fromtheLTEsourcefunctioninHe 11 lineshavebeenstudiedbyAuerand Auer andMihalas(1969),Peterson PetersonandStrom(1969).These first non-LTEcalculationsonBalmerlinesinearly-type starshavebeencarriedoutby point ofview,wecanrelyontheLTEapproachtocontinuumformation,since theories arelessreliable astheyareappliedtolowerseriesmembers, so that'itisim- has beensuccessfulinsofarasa“consistent”interpretationofvisiblespectracouldbe been takenintoaccountandwhichcouldlowerthetemperatureofupperatmosphere fore, sincetakingintoaccountlineblanketingonlymeans“relabeling”themodelbya problem whichiscausedbyseriouslyinadequatehandlingofhydrogenbroadening. hydrogen-broadening theoriesweapplied,itisveryunlikelythataredealingwitha ries) aswelltotheLTEtheoryofspectrumformationthatweapply.Fromob- duces thefullobservedspectrum.However,thiscouldbeduetoanerrorin“clas- in whichthecoresofBaimerlinesareformed. higher effectivetemperature.HickokandMorton(1968)computedaBOVmodelwith behavior ofH7andHô(cf.§Ve). Additional broadeningbyassumingstrongmicro-ormacroturbulenceintheupper atmosphere yieldsnearlythesamecontinuous spectrum astheLTEatmosphere.The servational facts,nodecisionbetweenthesepossibilitiescanbemade.Fromatheoretical sical” approach(unknownultraviolet-absorptionmechanism,wrongbroadeningtheo- achieved. This“consistency”nolongerexists.Wecannotfindanymodelwhichpro- different effectivetemperature,wekeptMihalas’sTuscaleforconvenienceandplaced that time.Thoughunsatisfactoryfromaphysicalpointofview,theLTEassumption any non-LTEdescriptionwascompletelyoutsidethecomputationalopportunitiesat energy inthisregionisstillsmallerthanpredictedbyblanketedmodels(cf.Davis observations oftheultravioletspectrumB0Vstarsindicatethatemergent same asthatofanunblanketedmodelwithTu=30360°andthegravity.There- ible spectrumisnearlyidenticalwiththevisibleofanunblanketedmodel the modelsbyHickokandMortonHeintzeintoFigure1accordingly.Some (Peterson andStrom1969). However,oneshouldalsorealizethat thebroadening that lineblanketingcoolsmoreorlessthewholeatmosphereinsuchawayvis- that coolstheupperlayersofearly-typeatmospheres.Recentworkhasshown,however, theory oflineformation,onecannot,unfortunately,drawanyconclusionsfromthe atmosphere wouldnotprovideasolution,either.If,finally,onefollowsUnderhill’s 1968). Thusitisnotimpossiblethatanabsorptionmechanismexistswhichhasyet (19686) suggestionthattheBaimerlinesmustnotbecomputedbymeansofanLTE Jeff =28640°Kandlogg4.0founditstemperaturestructureverymuchthe e e The LTEtheoryofcontinuumandlineformationwasoriginallyadoptedbecause In arecentstudyof10Lac,Underhill(19686) mentionsthatraisingthegravityof It haslongbeenbelievedthatblanketingbyultravioletlineswouldbeamechanism © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem TAU SCORPIIANDLAMBDALEPORIS205 h) OntheLTETheoryofLineFormation g) LineBlanketing 197OApJS ... 19. .193H a, -1 fact, abundanceanalyseswouldbemeaninglessifonecouldprovethatHeintze’slow- 206 JOHANNESHARDORPANDM.SCHOLZ ionization equilibria.However,byadoptingwhatwebelievearereliabletemperatures indicated byionizationequilibriaandBalmerjumps,weexpecttoobtainameaningful temperature andpressurestratificationsofthemodelatmospheresaresouncertain.In interpretation oftheweakandmoderatelystrongmetalliclines,alsowings temperature assumptionwerecorrect,becausethenwecouldnotevenmaintainthe different profilespredictedbybroadeningtheories.If,however,weconsider choice ofthegravitybyafactor2meansanerrorlessthanthisin too shallow,andtherewillbesimilardifficultieswiththestrongheliumlines. of thehydrogenandstrongheliumlines.ThecoresBalmerlineswill,course,be cannot fixthegravitybyusingshapesofBalmerlinesbecausesignificantly abundances oftheionsconsideredhere.Aswehaveseeninprecedingdiscussion, made forlowelectrondensities,temperatures,andhighupperquantumnumbers of about4forrSco,i.e.,thegravitypredictedbyPfennig’shydrogen-broadening the gravitydeducedfrommass-luminosityrelation,weareledtoavalueforlogg and roughestofthepresenttheories(cf.HardorpScholz1968);itwasactually theory (seen.3in§IV&).Thisraisesaseriousproblem:Pfennig’sisthesimplest close toorperhapsbeyondthelimitofitsapplicability.Onotherhand,wehave where theESWtheoryyieldsabetterHyprofilethanKGandPfennigtheories seen thattheprofilespredictedbythistheoryfitobservationsbetterthanKG which bothgivenearlyidenticalcontours(cf.HardorpandScholz1968).Forthis and certainlynotworsethanESWprofiles,theyconfirmthegravityresultingfrom reason wedonotsharetheopinionofsomeauthors(Heintze1968;StromandPeterson the mass-luminosityrelation.ThissituationisdifferentfromthatinanAOVspectrum, biguity isinvolvedinthischoice.WenotethattherScomodelwithinand studying observationsofstellarspectra. (cf. Pfennig19665);andacomputationofHyinBOVatmosphereisexpectedtobe less, toderivecorrectabundancesitisimportant toknowwhethermicroturbulent log grangededucedfromtheHehX5412andiX4471lines(cf.Fig.3). calling themTauPandLamP,respectively.Weareawareofthefactthatsomeam- higher thanthemicroturbulentvelocities.So far, onlyScholz(1967)hasintroduced motions exist.Forhydrogenandheliumlines, ontheotherhand,microturbulenceis because therearenostrong“metallic”linesand fewmoderatelystrongones.Neverthe- microturbulence inrSco,namely,5kms,independent ofdepth. unimportant sinceinalmostanycasethethermal velocitiesoftheseionsaremuch multiplets withalarge spread inintensitiesandreliableequivalentwidths. Multiplet1 systematic errorsof/-values canbiasthisprocedure,werestrictedourselves tosingle turbulent velocitymust beintroducedsothatabundancesderived from moderately 1968; Peterson1969)thattheproblemofhydrogen-linebroadeningcanbesolvedby strong lineswouldcoincide, ontheaverage,withthosederivedfromweak lines.Since as afunctionoftheequivalent widthsofthelinestheyarederivedfrom, for0,3,and of Oiibestsuitedthispurpose. InFigure4wehaveplottedthelogarithmic abundances One mayaskwhetheritisworthwhiletocarryoutabundanceanalysessincethe The gravityproblemislessseriousfortheabundancedetermination.Awrong The presenceofmicroturbulenceinearlyB-type atmospheresishardtoestablish, We finallydecidedtousethemodelsinlastlineofTable5foranalyses, Avoiding theconventionalcurveofgrowthfor rSco,weconsideredwhatmicro- © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem V. PROPERTIESOEMODELSCHOSENFORANALYSIS a) EffectiveTemperaturesandGravities b) Microturbulence 197OApJS ... 19. .193H portant totakethis“classical” effectintoconsiderationproperly.Unfortunately, our because non-LTEeffectsaremoreimportantfor thelatterlinesthanforHyandHô her modelsmighthaveimprovedHyandHÔ but notHaandHß.Thisisinteresting Mihalas andStone(1968)haveshownthata simplifiedhydrogen-helium,non-LTE Mihalas (1968). but thattheLTEapproachisinadequatefor the interpretationoflinecores.De- investigations indicatethatwemaytrustourcomputation ofHyandHôwingshapes point ofview,wecanrelyontheLTEapproachtocontinuumformation,since own HaandHßobservations arenotaccurateenoughforameaningful profilestudy. partures fromtheLTEsourcefunctioninHe n lineshavebeenstudiedbyAuerand Auer andMihalas(1969),Peterson PetersonandStrom(1969).These first non-LTEcalculationsonBalmerlinesinearly-type starshavebeencarriedoutby has beensuccessfulinsofarasa“consistent”interpretationofvisiblespectracouldbe fore, sincetakingintoaccountlineblanketingonlymeans“relabeling”themodelbya in whichthecoresofBaimerlinesareformed. been takenintoaccountandwhichcouldlowerthetemperatureofupperatmosphere higher effectivetemperature.HickokandMorton(1968)computedaBOVmodelwith behavior ofHyandHô(cf.§Ve). problem whichiscausedbyseriouslyinadequatehandlingofhydrogenbroadening. hydrogen-broadening theoriesweapplied,itisveryunlikelythataredealingwitha theories arelessreliable astheyareappliedtolowerseriesmembers, so that'itisim- servational facts,nodecisionbetweenthesepossibilitiescanbemade.Fromatheoretical ries) aswelltotheLTEtheoryofspectrumformationthatweapply.Fromob- duces thefullobservedspectrum.However,thiscouldbeduetoanerrorin“clas- different effectivetemperature,wekeptMihalas’sTfscaleforconvenienceandplaced Additional broadeningbyassumingstrongmicro-ormacroturbulenceintheupper atmosphere yieldsnearlythesamecontinuous spectrum astheLTEatmosphere.The sical” approach(unknownultraviolet-absorptionmechanism,wrongbroadeningtheo- achieved. This“consistency”nolongerexists.Wecannotfindanymodelwhichpro- that time.Thoughunsatisfactoryfromaphysicalpointofview,theLTEassumption any non-LTEdescriptionwascompletelyoutsidethecomputationalopportunitiesat energy inthisregionisstillsmallerthanpredictedbyblanketedmodels(cf.Davis observations oftheultravioletspectrumB0Vstarsindicatethatemergent same asthatofanunblanketedmodelwithT{=30360°andthegravity.There- ible spectrumisnearlyidenticalwiththevisibleofanunblanketedmodel (Peterson andStrom1969). However,oneshouldalsorealizethat thebroadening the modelsbyHickokandMortonHeintzeintoFigure1accordingly.Some that lineblanketingcoolsmoreorlessthewholeatmosphereinsuchawayvis- atmosphere wouldnotprovideasolution,either.If,finally,onefollowsUnderhill’s that coolstheupperlayersofearly-typeatmospheres.Recentworkhasshown,however, theory oflineformation,onecannot,unfortunately,drawanyconclusionsfromthe 1968). Thusitisnotimpossiblethatanabsorptionmechanismexistswhichhasyet (19686) suggestionthattheBaimerlinesmustnotbecomputedbymeansofanLTE Teff =28640°Kandlogg4.0founditstemperaturestructureverymuchthe e e The LTEtheoryofcontinuumandlineformationwasoriginallyadoptedbecause In arecentstudyof10Lac,Underhill(19686) mentionsthatraisingthegravityof It haslongbeenbelievedthatblanketingbyultravioletlineswouldbeamechanism © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem TAU SCORPIIANDLAMBDALEPORIS205 k) OntheLTETheoryofLineFormation g) LineBlanketing 197OApJS ... 19. .193H limit tothemicroturbulentvelocityfromobservedlineprofiles,keepinginmind central depth,half-width,andJwidth,inthesecondtofifthcolumns,respectively. is perfectlygoodenough.Ifwethuscomparemeasuredandcomputedhalf-widths, rower, accordingtoGriffin(1968),byasmuch20percent.However,sincetheeffect mental profile,takentobeidenticalwiththeprofileoffaintlinesironcomparison different microturbulentvelocitiesismadebyconvolutingthelatterwithinstru- the profilesofafew“metal”linesinformcentraldepth,(total)widthatf that thelinecanalsobebroadenedbymacroturbulenceandrotation.InTable7welist can derivefromeachprofilethemaximumvelocity,whichislistedincolumn7ofTable7. of instrumentalbroadeningonthehalf-widthsisverysmall,anyway,ouradoptedprofile arc, whichhaveahalf-widthof0.053Â.Theactualinstrumentalprofilemaybenar- 208 JOHANNESHARDORPANDM.SCHOLZ Column 6givesthenumberofspectraused.Comparisonwiththeoreticalprofilesfor from Figure4couldtherefore wellbepresent,butourwayoffindingit fromthatfigure Hô aswellstrongheliumlines,alllinedepths exceeding30percentarefoundlarger lence atall,whichthenalsomeansnorotation. However,thisisnottrueforthefaint would beinvalid:thesame effectthatmakesalineappearnarrowerby giving itadeeper core forastronglineandtherebymakingthe theoreticallineappearbroader.This row; butourmodelmaybetoohotintheoutermost layers,producingtooshallowa lines. Itisobviousfrommerelylookingatthescans thatfaintFemlinesarenonarrower central corealsoincreases theequivalentwidthofastrongline,thus mimickingthe exceeding 30percentthat yieldzerovelocityinTable7.Themicroturbulence derived than predictedbythemodel (cf.Figs.7-10),anditisjustthelineswith centraldepths explanation appearslessspeculativewhenonebears inmindthat,thecaseofH7and effect weattributetomicroturbulence. Thismightbetheexplanation forthepuzzling than faintlinesoflighterions.Someturbulence orrotationmustthereforebepresent. Since wehave.fourhigh-resolutionspectrogramsofrSco,canalsoderiveanupper The resultisrathersurprising:moststronglines arebestinterpretedwithnoturbu- Why dothestrongerlinesappearsonarrow?Possibly theyarenot,infact,toonar- © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Fe III4164.8. A1 III4512.5. O II4414.9.. Fe III4310.4. O II4417.0.. O II4189.8.. O II4396.0.. O II4366.9.. O II4185.5.. Si III4574.8. Si III4552.7. S III4285.0.. Si IV4116.1. Si IV4088.9. Si III4567.9. S in4354.6. 1 Profiles ofMetalLinesintScorpiifrom1Âmm"Spectrograms, Line (1) and UpperLimitsforMicroturbulenceVelocity Central Depth 37 45 30 34 24 21 57 28 50 25 26 14 (%) 9.4 9.0 (2) 5.6 7.2 } Width 0.16 0.19 0.16 0.14 0.15 0.15 0.16 0.16 0.18 0.16 0.12 0.16 0.10 0.12 0.12 0.16 (Â) (3) TABLE 7 i Width 0.25 0.26 0.26 0.26 0.23 0.24 0.24 0.26 0.28 0.22 0.20 0.24 0.23 0.13 0.20 0.20 (Â) (4) 1 Width 0.38 0.36 0.38 0.34 0.37 0.32 0.36 0^30 0.29 0.34 0.36 0.30 0.30 (Â) (S) Number Spectra (6) of -1 Maximum Velocity (km s) (7) 197OApJS ... 19. .193H -1 45 and95mÂforthe H- andK-lines,respectively,ofXLep.Inthe latterstarboth vapor, butinterstellarlines ofCanareobserved:28mÂfortheK-line ofrSco,and fitted togetherat4000Â.Thedifferenceinslope betweenthecomputedandob- reddening of0.04magfor rSco(Gutierrez-MorenoandMoreno1968) on theonehand, served continuumcanbeinterpretedasreddening ofE-v=0.01maginthecase corrected forabsorption;allothersetsarefittedwitharbitraryzeropoints.MeasurementsofAlleretal. and withthereddening weexpectfromthestrengthofinterstellar absorptionlines observations ofAlleret al. andWillstrop.Thisshouldbecomparedwith theobserved X Lep,whereasforrScowederiveE-v=0.05 and0.10mag,respectively,fromthe absolute measurementsofrSco;allotherfluxes havearbitraryzeropointsandwere in slopebetweenobservedandcomputedrScospectra correspondtoreddeningofEb-v=0.05mag weak lines.Aslongasthisworkssatisfactorilyforallions,theintroductionofmicro- velocity of4.5kms,independentdepth,forbothrScoandXLep.Forusthismeans on theother.TheNaD-lines arecompletelymergedwithlinesofatmospheric water the predictionsofmodelsTauPandLamP.The ordinatecorrespondstoWillstrop’s and LamP,respectively(curves).OrdinatecorrespondstoWillstrop’sabsolutemeasurements(smalldots), wrong microturbulentvelocity.Intheabundanceanalysesweshallusea ionization equilibria,sincetheaveragelinestrengthsareapproximatelyequalineach nothing butawayofcorrectingtheabundancesderivedfromstronglinestocase we haveshownsofaristhatcannot,fromobservations,ruleouttheexistenceof of rfandloggisexpectedtobefarmoreseriousfortheanalysisthanapossibly microturbulence inrSco.Fortunately,theissueofdoesnotaffect turbulence isjustified,independentofitsphysicalmeaning. of thethreepairsionsconsideredin§IVc.Moreover,ambiguityourchoice occurrence ofmicroturbulentmotionsinotherearly-typestarsaswell.Theonlything (circles) and0.10mag(smalldots),whereas0.04was derivedfromthecolors. (1966) (opencircles)aswellKodaira(largedots)arereducedtoHayes’scalibrationofVega.Differences B B e Figure 6showsthemeasurementsofcontinua discussedin§He,togetherwith Fig. 6.—PhotoelectriccontinuumobservationsofrScoandXLeppredictionsmodelsTauP © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem TAU SCORPIIANDLAMBDALEPORIS209 c) TheContinuousSpectra 197OApJS ... 19. .193H _1 -1 -1 -1 -1 -1 Mg iilinedouble.Thishasbeendonebyfirstconvolutingthetheoreticalunbroadened K-line intensityandreddeningfoundbyBinnendijk(1952)totheobservedline uniform distribution ofdirections of rotation,wethenexpect 0.05near-breakupstars on rotatingstarnearbreakup. Toobtainaconservativeestimate,let usassumethat would beincreased.(rfandloggaremeant as appropriateaveragesoverthevisible but theradiuswouldbelarger.Inbothcases thesurfacegravitywouldthereforebe fixed byobservation,butthemasswouldbesmallerbecausemass-luminosityrela- pole-on casesHardorpandStrittmatter(1968)haveshownthatrotationisnotlikely parallel tothelineofsightinorderthatvsinibeobservedvalues.Forthese profiles computedformodelLamPwiththeinstrumentalprofile(whichisatriangleof profiles ofsixOnlinesandMgX4481wederiveonly29+2kms,weightingthe broadened. BoyarchukandKopylov(1964)list85kmsforvsini.However,fromthe larger than,say,5kms.ThelineprofilesofXLep,ontheotherhand,arerotationally with newgalacticcoordinatesl=215°,b—26°.Ifweapplythecorrelationbetween weaker one.Thispointstocloudstructureoftheinterstellarmatterindirection all ofthetenstarswith 275^vsini<375kmsarenear-breakup stars.Assuming and 600kms.Since this isprobablyduetoamisinterpretationof thelineprofiles nitude. Inthecaseofß-indexdistance,however, themasswouldremainsame distance. Ifwebelievedthelatterdistance,radiusofrScowouldbesameas 4400 and4200Â,respectively(whichhavebeenderivedfrommodelLamP).Therota- In particular,cananysucheffectexplainsomeofthedifficultieswemetincase 0.1 Âhalf-width)andthenapplyingrotationalbroadeningbytheusualmethodsde- latter view. is notwhatFigure6suggests.Eithersomethingmustbeslightlywrongwiththecon- strengths, weexpectnoreddeningatallforrSco,andEb-v^0.06magXLep.This of B0stars,weshallusethedataonnonemission, nonshellB2-B5starsbrighterthan amount beingAlogg=0.1and0.2,respectively. Thusthediscrepancyfoundearlier smaller thanthatderivedin§115,ifrScowere arapidlyrotatingpole-onstar,the to introduceanyseriouserrorintoabundanceanalyses.However,thestarwouldbe scribed bySlettebak(1949)withlimb-darkeningcoefficientsoíu—0.33and0.35for lines appeardouble,withaseparationof0.14±0.02Â,theredcomponentbeing 210 JOHANNESHARDORPANDM.SCHOLZ that ourstarsarerotatingnearbreakup.Lacking anyreliablestatisticsontherotation stellar disk.) tion appliestoslowlyrotatingstars,whicharemoremassiveatagivenabsolutemag- ß-index distanceofrScowouldnolongercoincidewiththeassociation-membership that derivedin§lift,sincetheapparentmagnitudeandeffectivetemperatureare almost halfamagnitudebrighterthanweexpectfromtheH7orHßindices;thus tional velocitymustbewithin,say,15percentofthebreakup(see,e.g.,Collins tions intheratioofinterstellargastodust.Forrestthispaper,weshalltake tinuum observationsorthechoiceofmodel,thereareappreciablestatisticalfluctua- t ScoandXLep,weretheyreallyrotatingsofast,wouldthereforehavetobenearly the profiles. tional velocitywasthenobtainedbycomparingobservedandtheoreticalhalf-widthsof (Hardorp andStrittmatter 1968),smaller“observed”vsinicouldstillmean anequator- t Sco?Theanswerisnegative.Forgravitydarkeningtoaffectthespectrum,rota- (1954). Nostarsareobserved withvsiniatthebreakupvelocity,that is,between500 1966), whichisoftheorder600kmsforB0Vstars.Theaxesrotationboth F =5.5magandnorth of—20°declination,aspresentedbySlettebak andHoward e We haveseenthatrotationdoesnothelpus,and wenowindicatehowunlikelyitis It isobviousfrom§V¿>thattherenoprojectedrotationalvelocityvsinioítSco Can weexpectanyeffectofrotationonthespectrumbesidesbroadeninglines? © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem d) EffectsofRotation 197OApJS ... 19. .193H -1 from models TauPandLamP,respectively, byassuming depth-independentmicro- would stillbeobservable,too,ifitwerenotblended withHe1X3705;thisisespecially diffuse He1lines,§VIZ>). Notethatthepositionofcontinuum is inaccurateby of theobservedwingswithcontinuumat AX =25Â(AX12.5forHe11and about 1percent. not sufficientlyaccurateforacarefulprofilestudy. ThelinesbegintomergeatH9,and had beensochosen.Linedepthslargerthan0.3arenot correctlypredictedbecauseoffailurethe true forXLep,whereH15isaratherdeepfeature. NoHaemissionshavebeenfound. the lastvisiblememberofseriesisH15.It isquitepossiblethatthecoreofH16 model. Measurementsareaveragesoverbothwingson six plateseach. compared withobservations.Bestagreementisobtained forPfennig^theory,becausemodelparameters Hô isslightlyworsethanthatofH7inbothspectrabecausetheplatestendtobeunder- disturbed byrotationallybroadened“metallic”lineswhichcannotbeseparatedeasily. X Lepfromthepredictedprofileismainlyduetofactthatbothwingsarestrongly demonstrate theeffectofdifferentbroadeningtheories).Theobservationalquality cores aremuchtooshallow(Figs.7and8;weaddedKGESWprofilesinorderto none ofthesharp-linednonemission,nonshellB2-B5starsisnearrotationalbreakup. exposed inthiswavelengthregion.Thelargedeviationofthemeasuredshape to showasin¿^25kms,whereasnineteenareobserved.Inotherwordsprobably the H7andHôwingsbymeansofPfennig’stheory,but,asdiscussedabove,line The computedprofilesarerenormalized,withdue accountbeingtakenofthemerging In Table8we listtheobservedlines, togetherwiththeresultant abundancesderived Baimer linesotherthanH7andHôwerenotincluded becausetheobservationsare The gravitiesweadoptedformodelsTauPandLamallowtheinterpretationof Fig. 7.—Balmer-lineprofiles,computedformodelTauPwiththreedifferentbroadeningtheories, © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem TAU SCORPIIANDLAMBDALEPORIS211 a) AtomicandObservational Data VI. ABUNDANCEANALYSES e) BahnerLines 197OApJS ... 19. .193H -1 81 5 in milliangstroms,derivedabundancesloge(normalizedto€h=12),andaweighting factor forloge.ThelastthreecolumnsarerepeatedXLep.Anaveragedabundance turbulence of4.5kms.Thetablegives,inconsecutivecolumns,themultipletnumber constant, radiation-dampingparameterin10s”,measuredequivalentwidthforrSco is alsogivenforeachion.Table9showsthelineblendsusedabundanceanalyses. ion-broadening parameterspublishedbyGriem(1964).Electron-impactwidths (Moore 1945,1965),laboratorywavelength,oscillatorstrength,quadraticStark-effect 212 JOHANNESHARDORPANDM.SCHOLZ Peterson (1968,improvedcalculationsafterGriem’stheory)forHe1(2P°-nSand and Glennon(1966).OthersourcesarelistedinTable11. 2P°-nD transitions)andbyBréchot-Sahal(1968)forC11(4,6,33),Mg(4),Si11, for Hei(16,47,50)weretakenfromGriemetal. (1962).Thesignpreceding aradiation-dampingparameter ion-broadening parametersarenotknownand thatonlyelectron-impactbroadening included inTable9.Lineswhicharesituated inthewingofahydrogenlinewith cal calculations. measured wingdepthR> 3percentandlinesinthewavelengthregion betweenthe 7d meansthatimportanttransitionshavenot beenincludedinthequantum-mechani- Si in,andSmwereusedinsteadofGriem’s values. Theion-broadeningparameters weighting factorsofindividual abundancesincludetheobservationalweight ofW\,the Baimer jumpandH9have beencomputedasblends(markedbyanasterisk), andtheir Measurements ofHyareaveragesoverbothwingsonsix plates,whereasforH5onlythreeincomplete equivalent widthsarenormalized relativetothewinginsteadof continuum.The damping parameters. ra 6 Most oscillatorstrengthshavebeentakenfromtheextensivetablesbyWiese,Smith, Quadratic Stark-effectconstantsC4arederivedfromtheelectron-impactwidthsand A crossbehindtheequivalentwidthmeansthat thelineisblendedwithanother Fig. 8.—ComparisonofobservedandcomputedBalmer-lineprofilesforXLep(modelLamP). WeareindebtedtoMrs.V. PetersonforthedatacomputationofNnand Nmradiation- © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 197OApJS ... 19. .193H Mult 24 18 16 15 10 45 50 51 39 36 33 24 16 52 50 27 9 7 5 2 4 2 6 7 6 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 4187. 05 4056. 06 4067. 87 4068. 97 4070.30 4516. 93 4325.70 4663. 53 4650.16 4651.35 4647.40 3609. 61 4372.49 3883, 80 5696. 00 4618. 85 4374.28 4411.20 4074.53 4267. 02 4267.27 4437. 54 5145.16 4168.97 5114. 07 3876.40 3876. 18 5151. 08 6098. 62 3920. 67 6578. 03 3652.00 3447.59 3613. 64 this linehasbeencalculated as ablendwithhydrogen this lineisblendedwithanotherincludedinTable9 cm Hel cn lg gf •0. 07 -0. 56 -0. 60 •0. 12 •0. 21 -0. 21 -0. 24 ■2. 34 •2. 02 ■2. 24 -1. 89 -1. 64 1. 03 0. 98 0. 95 0.18 1. 11 0.40 0. 83 0. 24 0. 11 0. 09 0.10 0. 38 0. 69 0. 86 0. 66 0. 59 0. 27 0. 74 0. 16 0. 58 0.73 0.10 Table 8:ObservedLinesandDerivedAbundances -lg c < 13.3 < 13.3 < 13.3 <13.3 <10.3 13.3 14.2 10.7 10.1 9.6 lg e= lg £= > 102.7 ig e= >27.4 > 23.4 > 27.4 >23.4 >15.4 >23.4 >26.2 Jfrad 19.3 19.2 1.2 1.2 1.8 213 18 147 155 + + 48.5 46 35 55 37.5 * 44 44 15 16.5 55.5" 26 72 91 56.5 45.5 10 12.5 12 11 25 38 13 19 84 67 65 77* 68.5" W. ige 10.98 11. 60 11. 00 10.98 11. 00 ~C Sco 7.98 8.40 7.99 7. 62 8. 28 8.12 8.30 8. 63 8.30 8.19 8.82 7. 89 7.55 7.49 7.58 8. 60 8.94 8.54 8. 68 8.32 8.86 8.12 7.94 8.41 8.16 8. 08 8. 07 8.80 8.64 18 w 4 1 0 H + 359 164 131.5" 107 W. 54 53 28.5 41 40* 56 96 97 36.5 38 38.5' 90 66 64 85 + + lg 6 11.10 11. 06 11. 20 11. 00 10. 95 11. 04 % Lep 9.10 8.54 8.49 9. 67 7.58 7. 63 8. 00 8. 86 8.99 8.57 8.50 8. 09 8.44 8. 66 8.42 8. 85 12 rt* Ot 5 3 197OApJS ... 19. .193H Mult 48 42 59 55 50 30 24 19 15 13 12 39 38 33 21 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 4523.60 4510. 92 4514. 89 4634.16 4640.64 4041. 32 4073. 05 4994.35 4607.15 4530.40 4427.97 4431. 82 4433.48 4441.99 4237. 04 4432.73 4179.66 4176.16 4057. 00 4043. 53 4082. 28 4227.74 4507.55 4601.47 4643. 08 4613. 86 4447.03 3842. 20 5001.46 5005.14 5010. 62 5045. 09 5686. 21 5676. 02 5666. 64 3847.38 5007. 31 3437.16 3994.99 NHI NE -0. 34 -0. 07 lg gf ■0.17 ■0.17 ■0. 04 ■0.20 ■0.44 ■1.40 -1.40 ■0. 07 ■0. 82 ■0. 94 -0. 08 ■1.24 ■0. 37 ■0.49 ■0. 37 ■0. 35 ■0.73 -0. 52 ■0. 33 •0. 47 -0. 35 0.10 0. 24 0.19 0. 67 0. 31 0.58 0. 55 0. 60 0. 74 0. 85 0. 45 0.28 0. 01 0.16 0. 61 0. 29 -ig c. 12.8 12.8 12.6 12.8 12.8 12.8 13. 0 12.8 13.3 13.2 13.2 14.4 14.4 14.4 14.5 14.5 14.5 14.2 14.4 14.4 14.4 14.4 14.5 14.5 14.5 14.5 14.5 12. 8 12.8 12.9 13. 0 13. 0 12. 8 14.1 lg£ = Ig e Table 8(Continued) > 15.3 > 23.8 > 39.0 >24.2 117.8 117.8 ÿ'rad 17.7 17.7 17.7 42. 0 16.5 16.5 16.3 16.3 16. 0 16. 0 16. 0 24.3 24.3 24.3 24.3 24.3 24.5 24.5 17. 0 16.5 16.5 24.2 5.1 5.1 6.9 6.9 6.9 214 15 W, 47 48.5 44.5 31 72 49 65 10 46*5 26 30 35.5 19 99 56 29.5 32 33 21 37.5 14 12 12 53 26 5 35.5 55.5 H 15 11 25 17 36 80 + + 6 8 lg £ V Seo 7.84 8. 88 8. 83 8.74 8.43 8. 06 7.95 7.89 7.97 8.19 8.60 7. 80 7.77 9.55 9.62 8.14 8.12 8. 08 8.10 8.19 8.23 7.88 8.12 8. 07 8. 21 8.11 8. 06 8. 07 8.19 8. 29 8.26 8. 09 8.29 8.10 8.44 8.70 8.40 8. 52 8.78 10 16 12 12 12 w 4 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 2 8 8 8 8 8 0 0 0 0 22 W, 42 44 51 40 35 18 19 25 h 62 29 5 62 18 33 + lg £ “X Lep 7.72 7.68 8.19 8. 09 7.53 7. 62 7.58 7.57 7.59 7.63 7. 65 7.40 7.63 8. 06 8. 55 8.10 8. 06 w 197OApJS ... 19. .193H Mult 12 11 10 17 16 13 12 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 3864.68 3851. 04 3864.45 3874.10 4078. 86 3864.13 4085.12 4092.94 4069. 63 4069. 89 3907.45 4072.16 4075. 86 4452. 37 4416. 97 4319. 63 4366. 89 4349.42 3390. 25 3982. 71 4414. 90 4696. 36 4661. 63 4676. 23 4638. 85 3954.37 4650. 84 4649.13 4535.11 6721.35 4379. 09 4003. 64 4546.36 4544.80 4215. 69 4195.70 4518.18 6640.90 3938.52 3998. 69 3934.41 NIH (Cont’d) on lg gf -0. 67 -0. 35 -0. 74 -0. 89 -0. 59 -0. 32 -0. 23 -1.31 -0.28 -0.17 -0.30 -0. 26 -0. 74 -0. 68 -0. 35 -2.54 -1. 84 -1. 81 -0. 26 -0.14 -0. 25 -0. 07 >0.13 -0. 75 -0. 05 •0. 45 0.14 0. 35 0. 53 0. 69 0.11 0. 04 0. 31 1.26 0.10 0. 43 0.45 0. 61 0. 09 0.26 0.13 -lg c 14.4 14.4 14.4 14.4 14.4 14.5 14.4 14.5 14.5 14.5 14.5 14.5 14.5 14.4 14.5 14.5 14.5 14.5 14.7 14.5 14.7 14.6 14. 6 14.6 14.7 14.7 14.7 14.7 14.7 14.7 ig e= Table 8(Continued) > 26.9 >48.9 >48.9 >42.1 >26.9 >42.1 Jfrad 44.5 44.5 44.5 17.8 31.1 31.1 30.8 30. 8 30.8 29.9 29.9 12.1 12.1 12.1 12. 0 12. 0 12. 0 12. 0 12. 0 15.9 12. 0 68.3 68.3 17.7 6.2 6.2 6.2 6.2 6.2 6.2 6.2 215 130 20 + 24 16 42.5 12 49.5 23 38 91.5 45.5 46 75.5 51 W, 88.5 96 63 99 96 85 86 35 77 23.5 46 69 5 72 36.5 11 18 20 30 31 14 27 80 89 31.5 9 7 10.36 lg £ ~C Sco 7.94 9.52 8. 68 8.38 9. 81 8.59 8.55 8.37 8.48 8. 80 8. 57 8.59 8.95 8.95 8.80 8.60 8.47 8. 82 8. 61 8.92 8.68 8. 87 7. 84 9.79 8.55 8.80 8.89 8.94 8.80 8. 65 8. 64 8.12 8.57 8.44 8.43 8. 39 8.52 8. 35 8.72 8. 87 16 12 12 2 4 w 2 2 2 4 4 4 8 8 8 8 8 0 8 8 8 H + + 115 105 W 140 121 126 103 186 40 36 50.5 89 51 58 W, 66 50 55 97.5 84 21 35 18 24.5 10. 03 lg e > Lep 8.47 8. 65 9. 06 8. 67 9. 03 8.58 8. 67 9. 08 9.19 9.19 8. 84 8. 74 8.71 9.38 8. 88 8. 94 8. 86 8. 84 8. 85 8. 87 8. 79 8. 80 8. 79 14 12 12 12 10 2 2 2 8 8 8 197OApJS ... 19. .193H Mult 12 48 41 40 42 50 37 36 35 32 28 25 33 27 24 20 19 17 16 15 13 26 21 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 4087.16 4089. 29 4331.47 4327.48 4703.18 4048. 22 4196. 72 4192.50 4113. 82 4185.45 4189.78 4448. 21 4955.78 4443. 05 4941.12 4943. 06 4890. 93 4906. 88 4924. 60 4406. 02 4369.28 4751. 34 4395.95 4699.21 4705. 35 4710. 04 4112. 02 4084. 66 4119.22 4132. 80 4153. 30 4129. 34 4351. 26 4596.17 4590.97 5160. 02 5206. 73 4140. 74 5190.56 3470. 42 3470. 81 3911.96 3863. 50 3919.28 3857.18 OH (Cont'd) lg gf •0. 37 ■0. 59 ■0.34 -0. 94 ■0. 72 ■0.42 -0. 66 •0. 55 -0.20 -0. 31 •0. 01 -0. 35 -0. 09 -1.31 -0. 35 -0.16 ■0. 47 -0. 80 -0. 78 -0. 89 -0. 07 -0. 08 -1.12 -1. 61 -0.19 -1.22 -0. 83 0. 53 0.90 0. 22 0. 21 0.71 0. 82 0. 00 0.13 0. 08 0. 37 0.16 0.56 0.41 0.48 0. 07 0. 29 0.45 0. 22 -lg C / 14.4 14.4 14.4 14.4 14.4 14.4 14.4 13.4 14.4 14.4 14.4 14.4 14.4 13.4 14.4 14.4 14.4 14.4 14.4 14.4 14.5 14.5 14.4 14.4 14.4 14.4 14.4 Table 8(Continued) > 22.3 >22.1 >22.1 &rad 44.6 44.6 44.6 44. 6 45.3 45.3 45.3 25.9 25.9 25.6 22.7 22.7 25.9 19. 0 19. 0 19. 0 25.6 30.1 30.1 25.6 30.1 30.1 30. 0 6.7 7. 0 5.6 5.6 5.3 7. 0 5.3 216 + + 76.5 W. 48 49 40 46 59 90 23 29 10 20.5 43.5 51.5 73.5 17 68.5 30 37 50.5 33.5 79.5 10.5 22 52.5 26 30 53 20 25 23 92 15.5 81 69.5 77 66 9 1 9.5 6 6.5 8 lg & X Sco 9. 00 9. 07 9. 06 8. 37 9.18 8. 66 8.80 8. 77 8.80 8.70 8. 69 8. 74 8.21 9.29 8.55 8. 74 8. 54 8.68 8.97 8. 52 8. 62 8.48 8. 05 8. 31 8. 57 8. 80 8.35 8.56 8.75 8.45 8. 57 8. 80 8. 61 8. 83 8.50 8. 55 8.54 8. 69 8. 81 8. 74 8.74 8.80 12 12 w 4 2 2 2 2 8 2 2 2 2 2 2 2 8 8 8 8 8 8 8 8 8 8 8 2 6 8 8 8 0 8 8 8 8 8 8 8 8 8 0 101 115.5 115 105.5 119 H 113 W. 46.5 58 16 25 58 72 28 26 52.5 94.5 57.5 71 50 38 60 20 18 39 81 83 .+ lg £ "X Lep 9. 09 9.19 9. 00 9. 02 9.17 9. 03 9.17 8.93 8.99 8. 92 8. 66 8. 95 8. 99 8. 77 8. 97 8. 61 8. 67 8. 60 8. 66 8. 63 8. 84 8.77 8. 71 8.96 8. 69 8. 87 10 10 w 4 4 4 4 4 4 4 2 2 6 2 8 6 0 0 197OApJS ... 19. .193H 106 102 101 100 Mult 23 98 97 94 93 79 50 58 86 67 61 64 54 5 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 4073.90 5592. 37 3774. 00 4142. 08 4141.96 4253. 74 3757.21 3759. 87 4146. 09 4378. 41 4303. 06 4302. 81 4054. 55 4060.98 4060. 58 4465.40 4602.11 4613.11 4609.42 4489.48 4491. 25 4312.10 4271.90 4275.52 4315.35 4328. 62 4281.40 4308. 96 4701.23 4276. 71 4282. 82 4303. 82 4054.10 om OE (Cont'd) lg gf •0. 09 ■0.34 •0. 55 ■0.42 ■0. 96 ■0. 82 •0. 27 •0. 06 -0.64 -0. 24 -0.18 -0. 68 -0.98 -0.17 -0. 74 -0. 01 -1.12 0.20 0. 57 0. 95 0.04 0. 04 0. 62 0. 73 0.34 0. 51 0. 67 0. 26 0. 52 0. 76 0. 06 0. 07 0.64 -lg C, Table 8(Continued) ige >82.4 >16.1 >30. 0 >25.5 >25.5 >25.5 >16.1 Jfrad 41.3 41.3 41.3 44.7 44. 7 44.7 44. 7 7.6 7. 0 7. 0 5.6 5.6 6.7 217 4 11 H 15 42.5 26* 34* 21.5 87* 21. S' , 12 21.5 43.5 W, 32 16 14.5 16.5 86.5 30.5 39 26.5 51 16. 5 16 23 20 13.5 32 64.5 + 4 8 3 8.5 7 *C Sco ig e 9.31 9.00 9.60 9.40 9.14 8.99 9.54 9.27 9.54 9.11 9.17 8.53 8.78 8.40 9.42 8. 68 8.72 8.42 8.50 8. 83 8. 55 8.17 8.72 8.47 8. 25 8.76 8.42 8.53 8. 63 8. 23 8.13 8.41 8.77 8.22 12 4 2 4 w 0 8 8 8 8 8 2 8 8 8 8 8 8 8 8 8 8 6 8 8 8 8 8 8 57* 30* W 73 26 19 80 X Lep lg£ 9.20 9.10 9.10 8. 62 8.16 8.46 8.60 w 197OApJS ... 19. .193H Mult 49 41 74 70 51 31 22 21 13 11 10 57 56 53 52 34 28 20 19 64 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 3355. 05 3327.16 3297.74 3360. 63 4379.50 4397. 94 4150. 67 4231.60 4219.76 3557. 84 3481.96 3643. 89 3344.43 4432.26 4498.94 4409.30 4391. 94 4290.40 4369.77 4257. 82 4250. 68 3218.21 3232.38 3230.16 3319.75 3574.23 3574.64 3568. 53 3392.78 3378.28 3561.23 3371.87 3416. 87 3417.71 3388.46 4429. 60 4511.37 3571.26 3503. 61 3456. 68 3406. 88 3480. 75 3644.86 3594.18 3565. 84 3542.90 3459.38 3628. 06 NeE (Cont'd) lg gf -0.45 •0.15 -0.91 -0.17 -0. 35 •0.30 -0.48 •0. 91 -0.16 -0.14 -0. 89 -0.15 -0.16 -0. 92 •0. 63 ■0. 26 -0. 78 -0. 28 -0. 67 ■0. 28 -0. 26 -0. 28 -0. 01 -1. 21 -0. 33 •0.16 -0.98 -0.84 0. 22 0.15 0.15 0. 24 0. 06 0. 45 0. 31 0. 75 0. 09 0. 29 0. 35 0. 32 0. 55 0. 80 0. 92 0.15 0. 32 0. 68 0. 21 -lg c 14.7 14.7 14.7 14.8 14. 8 14.8 14.8 14. 7 14.8 14.8 Table 8(Continued) Ífrad 7.4 7.4 7.4 8.5 218 + W 42 46 40 22 12 37 12 31.5 22 54 29 38 28 70 12.5 35 13 31 15 11 14 11 11 12 11 22 23 19 25 13 61 16 38 12 35 9 8.5 6.5 8 lg e T Sco 9.16 9.17 7.71 9. 68 9.32 9.48 9.56 9.56 9.54 9. 04 9. 00 8.62 7.47 7. 85 9. 03 8.53 8.24 8.55 8.49 8.42 8.33 8.28 8. 68 8.93 8.48 8.62 8.53 8. 52 8.47 8.69 8.29 8.46 8.43 8.28 8.33 8.54 8.68 8.35 8.60 + W 41 47 42.5 45 5 23 55 37 36 36 22 20 30 38.5 17 27 36. 5‘ 22 54 39.5 16 60 17.5 35 31 34 33.5 29 18 lg £ ^ Lep 9. 03 9.46 9. 06 8. 68 8.77 8.44 8.49 8.45 9. 00 9.17 9. 00 9. 04 9.40 8. 86 8.37 8. 38 8.49 8.54 8.40 8. 37 8.90 8. 77 8.46 8.48 8. 96 8.59 8. 82 8.50 197OApJS ... 19. .193H Mult 13 10 8.14 8. 09 8. 06 4 9 4 7 5 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 4638. 27 4683. 79 4683. 02 4813. 33 4314.10 4819. 71 4828. 96 4328.17 4116. 09 4088. 85 4716. 65 3762. 43 3924. 46 3486. 91 4574. 75 4567. 82 3590. 46 4552. 61 3791. 41 5739. 73 4479.96 4150.13 4149. 89 4512. 53 4529.17 4390. 58 4481.32 3862. 59 3612.35 3601.62 SilV SiH! SiH ? Mgn Aim -0. 83 -0. 50 lg gf ■0.58 ■0. 58 -0. 17 -0. 43 •0.10 -0. 24 0. 00 0. 70 0. 82 0. 93 0. 93 0. 45 0. 22 0. 08 0. 31 0. 78 0. 43 0.20 0. 06 0. 04 0. 26 1. 02 0. 50 0. 65 0. 42 0. 67 0. 02 0. 78 -lg c. <14. 0 <14. 0 <13. 6 <14. 0 13.5 11.7 12.8 lg 6 ige lg e= ig e Table 8(Continued) >24. 3 >22.9 >24. 3 >24. 3 Yrad 49.1 49.1 11.2 219 + 127* 109 137 132. 5 14 14 27 10 18 32. 5 78 17. 5 56 28 15.5 15 70. 5 60 W- 41 15.5 21^5 15 90 9 5.5 lg e X Sco 7.90 7. 67 7.33 7. 70 7.53 7.55 7. 60 7. 83 8. 56 8. 57 7. 02 7. 14 7. 15 7. 77 7. 12 9.23 5. 86 6.11 7.51 7.49 7. 74 6.14 6. 35 6.40 6.15 6.21 7.63 7.51 6.90 7. 86 8. 00 + + 128 171 184 120 241 118 41.5 29 53 58 34 53 94 63 61 W. 23" 34 35' 17" 24 *+ lg£ Ts, Lep 7. 80 7. 70 7. 76 7. 80 7. 83 8. 12 7.48 7.46 7. 29 7.20 6.98 7.10 7. 82 8.28 5.96 7. 65 8.43 6.42 6.15 6.10 6.24 7. 65 8.40 6.11 10 4 2 4 2 2 6 5 3 197OApJS ... 19. .193H 118 127 Mult 90 32 25 7 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 4145. 64 4154.96 4189.11 4122.78 4140. 48 4166. 84 4164.73 4448. 88 4131.73 4430.18 4364.73 4284. 99 3932. 55 4354.56 4418. 84 4361.53 4212.40 4253. 59 3860. 80 3983.77 3928. 61 4631. 24 3662. 00 3234.17 3324.87 3632. 02 ein ? Fein ArH ? sni SiXV (Cont’d) lg gf -2. 89 -0. 32 ■0.12 ■0. 32 -0. 45 -0.18 -1. 63 -0. 73 -0. 42 -1. 59 -0. 61 ■0. 45 -0. 73 -1. 84 0. 75 0. 83 0.34 0. 08 0. 91 0. 02 0.12 0. 67 1.18 0. 09 0. 36 0. 81 -ig c <14.2 < 14.2 <14.2 <14.2 14.6 lg £= Ig e= Table 8(Continued) Jfrad 99.2 99.2 17.7 17.2 17.2 17. 2 17.2 32. 0 220 18 14 W. 14 47.5 14 33 27 16 12 22.5 73.5 29 32 63 5 3 5 4 8 4.5 7.5 6.5 8.5 11. 03 lg a T Sco 7.36 7.90 7.29 7.34 7.27 6.91 7.65 8.46 8.43 8. 06 7.77 7. 00 7. 21 7. 03 6.70 7. 88 6. 80 7.16 7.49 6.66 6. 81 6.98 8. 00 8. 62 w 21 28 26 5 W. 40 23.5 28 22 34 28 23 ig e 8. 00 7.56 7.10 7.49 7.25 7.42 7.99 6. 84 6. 68 7.14 6.90 8.33 Lep 197OApJS ... 19. .193H Hel Ion NH on cm cn NeH © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Blended Line Mult 101 106 48 52 16 27 12 11 24 19 10 39 36 33 33 50 25 17 70 54 54 51 97 54 22 13 19 64 4 2 7 6 8 9 1 4650.16 4120. 80 4276. 71 4282. 82 4054.10 4699.21 4085.12 4319. 63 4237. 04 4041. 32 4994. 35 4325.70 4074. 53 4267.27 4168. 97 4303. 82 5005.14 3447.59 4315.35 3470. 81 3911.96 3851. 04 3864.13 5001.46 5010. 62 3876.18 3354.55 4511.37 4253. 74 4060. 58 3876.40 4146. 09 3406. 88 3218. 21 3574. 64 3777.16 3371. 87 Table 9:LineBlendsusedforAbundanceAnalyses Ion Nil NH NH NH NH NeH on on on on on on cm on cn on on on NeH on on on on on on on cn cn cn on on on on on on on on on NeH on on on on on on on on Mult 100 100 107 106 101 40 48 13 33 19 20 20 27 44 98 36 33 33 33 19 27 17 12 12 12 12 21 19 70 79 61 50 64 64 97 67 67 67 64 52 31 2 6 9 4121.48 4325.77 4650. 84 4651. 35 4074. 89 4267. 02 4120. 55 4120. 27 4282. 96 4054.10 4699.21 4084. 66 4319.93 4236. 93 4041. 31 4994.35 4169. 23 4511.29 4315.35 4276. 71 4283.13 4303. 06 4302. 81 3875. 82 3876. 67 3876.40 3447. 98 4145.90 4253.98 4060. 98 3912. 08 3864. 68 5 005.14 5011. 24 3876. 67 3876. 05 3355. 05 3470. 42 3850. 81 3863.50 3864.45 5001.12 221 3407.38 3218.10 3371.85 3574.23 3777.60 Blended with lg gf -1. 89 -0. 46 ■1.2 ■0. 32 -1. 04 ■1. 06 ■0.28 ■0. 60 -0. 81 ■1. 67 ■0. 07 •0. 06 ■0. 35 ■0.90 •0. 74 •0. 83 ■0. 74 ■0. 35 ■0. 89 ■0. 47 ■0. 54 ■0.17 ■0. 92 •0.19 ■0.11 ■0. 95 •0. 92 ■0. 97 0. 62 0.20 0. 62 0. 49 0. 74 0.58 0.17 0.15 0. 38 0.28 0.17 0. 37 0. 60 0. 42 0. 04 0. 29 0.84 0. 62 0. 00 -lg c < 13.3 < 13.3 < 13.3 < 13.3 < 13.3 14.4 14.4 13.4 14.6 14.7 14.4 14.4 14.8 13.4 14.4 14.4 12. 8 14.5 14.4 14.4 14.4 14.5 13.4 > 27.4 >23.4 >39. 0 >30. 0 >22.1 &rad 44.6 44. 6 12. 0 12.1 30. 0 30.1 5.3 7. 0 7. 0 5.3 5.1 7.6 6.9 7. 0 5.6 X Sco^Lep spectrum of 197OApJS ... 19. .193H 2P4D 3 24S 1 1 2 P-5D 2V-53D 3o- 2P°-3D ^P°“q 2P°-4S 2S -3^P° C1II Ion Fem SilV snn Aim l Mgn Trans. 5S 0 5P -8 S -v -6 S -3 -3 D -5*S -S Vp -6 P° -1° -4V 6l © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Blended Line 118 118 Mult 25 13 4026. 2 4471.5 4387.92 4120. 8 4713. 2 4437. 54 5875.7 4168. 97 3652.0 3732.9 3867.5 5047. 73 6678.14 3354.55 3447. 59 3613. 64 3964. 72 5015. 67 4145. 64 4166. 84 4164.73 4088. 85 4683. 02 4529.17 4552.61 4479.96 4149. 89 4481.32 3860. 80 3762.43 3590.46 3791.41 3612. 35 Iggf -2. 02 -1. 60 -2.12 -1. 89 -1.64 -1.30 -0. 82 ■0. 37 ■0. 88 ■2. 24 •2. 03 -1.79 ■1.47 -1. 03 -2. 34 0. 05 0. 74 0. 33 <10.5 <10.3 NH on on Ion Fem Fem cm -igc on NeE on sim NH Aim cn cn om Aim Aim Aim NeH MgH 12.2 11. 0 11.6 10.7 12.2 11.4 10.1 10. 8 11. 8 9. 6 9.1 9.6 Table 9:(Continued) Table 10:ComputedHeILines 106 106 Mult 48 58 25 31 13 32 23 23 26 65 2 5 5 3 8 19.4 &rad 20.8 19.2 19.3 19.4 2.9 1.2 1.2 1.3 1.5 1.6 1. 0 1.2 1. 8 3.3 6.8 4683.79 4145. 90 4146. 09 4145.76 4166. 84 4164. 92 4089. 29 4552. 53 4479.89 4149.91 4150.13 4528. 91 4481.12 3762. 63 3590.47 3860.98 3590. 87 3589. 67 3791.26 3612.35 222 Blended with 138 225.5 603 210 725 175 123 114 275^ W, 65 67 77’ 68. 5" * lg gf -0. 03 • 0.64 •0.5 8 • 0.99 ■0.20 ■0. 07 ■0. 55 ■0. 65 ■0. 28 •0.76 ■0. 81 •0. 27 •0. 09 0.40 0.90 0. 33 0. 89 0.50 0. 60 0. 91 X; Sco 10. 99 11. 6 11. 07 11.29 11.10 11. 69 11. 0 10. 98 11.51 11.17 10. 9 11.30 lg e 11. 0 -ig c 12 18 12 13. 0 13.4 12. 8 4 3 2 3 3 1 2 3 3 0 + + 830 212* 299 258 201.5 117 149 282.5 85 870 }frad 40 46* 96 97 W. 90 + + 41.3 11.2 7. 0 "X Lep r Sco>Lep 11.25 11.2 11. 31 11.79 11. 06 10.9 11.17 11.1 11.57 10. 95 11.22 11. 0 11.0 lg 6 spectrum of 15 12 4 4 5 5 3 1 3 9 6 6 6 6 197OApJS ... 19. .193H 6 from theindividuallines havingremarkablysmallscatter(Table8). Twomoreweak 4388, theion-broadeningprofile isnolongerapureLorentzprofilesothatthenumbers —logC4andthe but fortheactualcalculations 7-splittingwasproperlytakenintoaccount.ForHe 1XX3448,3355,and by restrictingtheabundancedeterminationto weakHeifeaturesonelargelyreduces application ofaVoigt-profile functionaretobeconsideredapproximationsonly. of theStark-effectwings.Weanalyzedlineswith measuredequivalentwidthsW\< and deviationsfromthestandard,LTEtheory of lineformation,andtotheimportance the influenceofuppermostlayerswithregard bothtothetemperaturestratification Wiese etal.(1966)+L3'-coupling Trefftz andZare(1969)-hLS-coupling.. 100 mÂandfoundanaverage valueforlog€Heof11.0bothstars, theabundances Coulomb approximation-fLS'-coupling; Warner (1965) Schulz-Gulde (1969) Schnapauff (1968) Aller etal.(1957) Wiese etal.(1966) Froese (1965)-{-couplingafterWiese Griem (1964) Green, Johnson,andKolchin(1966)... Garstang (1954) Chapman, Clarke,andAller(1966) strengths. even smallerrorsinthetemperaturesresultdrasticmiscomputationsofline knowledge oftheelectrondensities,i.e.,logg. computation ofwhichrequiresgoodtheoriesStarkbroadeningaswellafairly After thefirstoptimisticapproachesledtoverydivergentresults,developmentof we adoptedthemeanionabundanceforothercomponent. derived fromlinesblendedwithalineofanotherionhavelowerweight;insuchcases terpretation: respondingly deepcomputedlinecores. atmospheres andnotheoryoflineformationhavebeenpresentedwhichyieldcor- the shapesofheliumlinesathighdispersionrevealedbasicdifficultiesinin- advanced model-atmospheretechniquesandbroadeningtheoriestheobservationsof estimated accuracyofloggf,and,ifnecessary,theknowledge—logC.Abundances termination oftheabundanceheliumhasbeenanunsolvedproblemformanyyears. 4 6 and Shomo(1968) Bates andDamgaard(1949),Oertel et al We followedherethesimpleandpromisingapproach suggestedbyScholz(1967): InTables8and10,X log gjofthelinesHeitripletcorrespondto whole multiplets, iii) TheexcitationpotentialsofthelowerstatesHenlinesaresohighthat Though thespectraof0andBstarsshowalargenumberheliumlines,de- ii) ThestrongHeiandthenlineshavestrong,Stark-broadenedwings i) ManyHeilinesarestrongfeatureswithmarkedlydeepcores.Sofarnomodel © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Paper TAU SCORPIIANDLAMBDALEPORIS223 Sources ofOscillatorStrengths He i(6,12,16,20,24,27,50) N ii(17),A1in(8),Si(8.14),Sm,Cl Ar ii(7) Nil (39,48),On(97,101) Fe in Ar il(32) Si ii Si in(2,4,5,7,8.06,8.09,13) C ii(23,24,51),N(38,50),m(2,12),On(41,42, All multipletsnotlistedbelow Mg ii,A1in(1,3,4,5),Siiv(1,3,4,5) C in(16,18),Si(9),iv(6) TABLE 11 O in(23),Neii(1,2,5,6,7,9,10,11) b) Helium Ar ii(90,127) 50,64,79,98,100,102), Nen(49,51,53,64,70,74), Multiplet 197OApJS ... 19. .193H 7 lines areobservedintheXLepspectrumbutnotincludedanalysis:Hei particular whentheobservationalaccuracyislowandtrueequivalentwidthofa features. H13. Adoptinglogene=11.04and€Ne8.76,wecomputedW\123mÂ(ob- 224 JOHANNESHARDORPANDM.SCHOLZ line isclosetothismaximumvalue.Inthatcase,thewillbeincludedinanalysis served: 117mÂ)andW\=11mÂ(observed:46mÂ),respectively,forthesetwo X3355 isblendedwithNenX3355,andHeiX3733only1.5Âfromthecenterof only whenitsmeasuredstrengthisaccidentallysmallerthanthemaximumvalue,i.e., 100 mÂissomewhatarbitrary,andonemightthinkofamorephysicaldefinition,in helium abundancenecessarilydependonthestronger linesoftheHeIspectrum.How- when theabundanceislikelytobeunderestimated. Table10showsthatthisproblemis classical radiationdamping,wereintroducedassolebroadening agents.AsinthecaseofBalmerlines, widths. ForUnderhill’smethod,1timeand2timesthe thermalbroadening,aswell100timesthe curves matchtheabundancederivedfromweaklines;dashedobservedequivalent not relevanttothepresentinvestigation. deep coresarenotcorrectlypredicted.Nodifferenceinthe behaviorofsingletandtripletlinesisnoticed. matches theobservedshape verysatisfactorilyinthecaseof“weak” lineHei Voigt-profile function,showsthatoneisvery likely tooverestimatetheheliumabun- When thecomputedequivalent widthsarefittedtothemeasuredvalues byincreasing dance inthiscase.Thereasonisobviousfrom Figure9:whilethecomputedprofile ever, Table10,whichincludesalllinesthatcan bereasonablywellrepresentedbya log e,thesaturatedlines gaintheadditionalareabyoverextendedwings whereasthe X4438, the“strong”lines tendtohavedeepercoresandwings thanpredicted. abundances forrScoandX Lep. 7 Of course,thedefinitionofa“weak”linebysomemaximumstrengthlikeW\= For manyfaintstars,high-dispersionspectra are notavailableandtheanalysesof Fig. 9.—ExamplesofHeilinescomputedformodelTauPwithaVoigt-profilefunction.Continuous Theaccuracyoftheindividual measurementsmaybeestimatedbycomparing theresulting © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 197OApJS ... 19. .193H 130 using theabundancederived fromweaksharplines.Observationsareaveragesover sixtosevenplates. cept whenUnderhill'smethod isapplied(with1Xand2thermalbroadening, respectively). Ifwe Again, deepcoresarenotwell represented,butcomputedwingsagreequitewellwith observationsex- force theStarkeffectofHei X4388toconformaVoigtprofile(whichisnotstrictly adequate),westill interpretation byrecentprogressinthetheoryofStark-effectbroadening(cf.§Hie). where ithasbeenaccountedforapproximatelybyconvolutingthecomputedprofiles broadening. AslightinfluenceispresentonlyinthecasesofHeiXX5016,5048,and6678, fit isobtained.Notethatmostheliumlinesaretoobroadtobeaffectedbyinstrumental represent the outer wingsofthisline. These lineshavestrong,quasi-staticallybroadenedwingswithforbiddencomponents, with theprofileoflinesatmosphericwatervaportotalhalf-widthwhichis unsaturated linesbecomedeeperbutremaintoonarrow.Inmostcasesnogoodprofile He iXX4388(2P°-5D),4471-4D)and4026aregiveninFigures10 dance. Sincetheshallownessoftheirouterwingsmakesitdifficulttomeasureaccurate 0.2 Â. and 11.ThecomputationswerecarriedoutbyusingthetheoriesofPTGriem equivalent widths,weshalldiscussprofilesonly.Measuredandcomputedshapesof and provideinformationaboutthesurfacegravityratherthanheliumabun- Fig. 10.—DiffuseHeilines computedformodelTauPbymeansofrecentbroadening theoriesby The diffuse(2P°-nD,n>3)linesofHeihavebecomeaccessibletoquantitative © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem TAU SCORPIIANDLAMBDALEPORIS225 197OApJS ... 19. .193H predicted bythetheoryofBCS(cf.ShipmanandStrom1969).AsimpleVoigt-profile hand, observedandcalculatedwingsagreeverywellforrSco.The function wasstillfoundtobeafairlygoodapproximationforHeiX4388.Apparently least partiallyduetotemperaturesintheuppermodelatmospherethataretoohigh, 226 JOHANNESHARDORPANDM.SCHOLZ sphere theeffectivetemperatureofwhichliesinrangerequiredbyionizationequilibria sical” onethatcanbeovercomebyusingrefinedbroadeningtheoriesandimproved the diffuselinespresentsamedeep-corephenomenonasstrongsharplines,i.e., atmospheric models.Asforthelinecores,onemustrememberthatanymodelatmo- that thepositionofcontinuumisinaccuratebyabout1percent. are toodeepforXLep,butthediscrepancyappearslessseriousifonetakesintoaccount X Lep,thelatteralsoappearingshallowbecauseofrotationalbroadening.Onother the computedlinecentersaretooshallow.ThisisequallytrueforlinesinrScoand and theBaimerdiscontinuityyieldshydrogen-linecoreswhicharetooshallow,that even theinterpretationofdeep“metallic”linesisratherdifficult(§V&).Ifthisat (1968) forHeiX4471.TheprofilesfromGriem’stheoryagreeverywellwiththose We feelthatthewingproblemofstronglinesneutralheliumisapurely“clas- © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 197OApJS ... 19. .193H l 1 l3 8 1 3 Z 3 not excludethepossibilityoffailureclassical,LTEtheorylineformationin line. Unfortunately,wehavenoreliableprofilemeasurementofthislineintheXLep We doubtthatanyimprovedmodelatmosphereordeviationsoftheoccupation numbers ofthe2P°and?>DstatesfromtheirLTEvalueswillproducesuchastrong saturated andhasanobservedcorethatisnearlytwiceasdeepthecomputedone. then onehastoexpectthesameeffectfordeepheliumlinesaswell.Ofcourse,wemust spectrum orofthecorrespondingtripletlineatX5876ineitherspectrum,butqualitative core. Probablynoncoherentscatteringplaysanimportantpartintheformationofthis He iatomdonotcorrespondtotheirLTEvalues,buttheatomstendaccumulatein first pointedoutthat,inthiscase,theoccupationnumbersofvariousstates comparison ofmeasuredandcomputedcentraldepthsindicatesthatbothlinesbehave that theLTEtheoryfailsatleastfor(2P°-3D)lineHeiX6678,whichishighly the uppermostlayersaslongthisquestionisstillunsolved.Infact,Figure9suggests however, doesnotnecessarilypointtonon-LTEleveloccupations,aspredicted,for from comparingobservedandcomputedequivalentwidths.Thedeep-corephenomenon, by non-LTE,possiblydilution,effects.WehavereproducedUnderhill’scalculationsfor are subjecttoadilutedradiationfield.StruveandWurm(1938;cf.Underhill1966) or early-Batmosphereformanextendedenvelope,forinsuchenvelopetheatoms with upperquantumnumbersn>3,thatindeednoreliableconclusioncanbedrawn B-type spectra,Underhill(1968a)concludesthatthesefeaturesarestronglyaffected strengths ofthelinewingsareunderestimatedsoenormously,especiallyfortransitions our rScomodel(cf.Figs.9and10)foundthatinhertheoreticalapproachthe the metastable2Sand,inparticular,levels.Fromthisconsiderationonemayexpect similarly inbothspectra. served ratiosofthestrengthsdiffuselinesHeiXX4922(2P°-45)and4471 to the2Slevel,willbestrengthened.Inarecentstudyoffive(2P°-nD)linesinO-and that absorptionsarisingfromthe2P°level,whichisconnectedbyastrongtransition example, bythedilutiontheory.ShipmanandStrom(1969)havecomparedob- sider onlyequivalentwidthsinsteadofprofiles,thereasonforthisbehaviorisnot served triplet/singletratioislargerthanpredicted,but,sinceShipmanandStromcon- satisfactorily bythestandard,LTEtheoryoflineformation.Inhotterstars,ob- from theLTEsourcefunction inamain-sequenceB-staratmosphere,whereasthewings areadequately shown inFigures10and11donotindicateadifferentbehaviorofsinglettriplet obvious. Unfortunately,wehavenoprofilemeasurementofHeiX4922inrSconor derived fromdifferentweaklineswith lowerandupperlevelsindicatesthat do notdeviateconsiderablyfromtheirLTEvalues. Thegoodagreementofabundances lines. the BCStheory.ForstarslaterthanB3,theyshowthattheselinescanbeinterpreted conclude, therefore,thattheheliumabundance innormalPopulationImain-sequence that theoccupationnumbersofstatesthose lineswhichareusedfortheanalysis X Lep.Ourobservationsandcomputationsofthewingsthreediffuse2P°~nDlines described bytheLTEapproximation. 9, 1151)haveshownthatthe coresofHeilinesarisingfromthe2P°statesaredeepened bydepartures reliable broadeningparameters areknownforHei.Ourresultisingood agreementwith stars aroundBOislogene=11.0±0.15,i.e.,Nne/Nu =0.10bynumberofatoms.The this conditioniswellfulfilledinthedeeperlayers wherethesefeaturesareformed.We (2P°-4Z)) inatmospheresofBstarswithratioscomputedaccordingtoGriem’sand two recentvaluesobtained fromdifferentmethods.Morton(1968)compares thetheo- the uncertaintyofchoice(cf.Fig.3)andstructure ofthemodels.Exact/-valuesand error wasestimatedfromtheobservationalinaccuracy ofequivalentwidthsandfrom 8 The HeispectrumcontainsinformationaboutwhethertheoutermostpartsofanO From thepointofviewclassicalabundance analysisitisimportanttobesure Noteaddedinproof:H.R. JohnsonandA.I.Poland(1969,J.Quant.Spectrosc. Rad.Transf., © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem TAU SCORPIIANDLAMBDALEPORIS227 197OApJS ... 19. .193H 9 value was,however,derivedfromobservationsofsolarcosmicrays.Wethinkthatthe value logene=10.80±0.1,afterLambertandWarner(1969),islower.Thelatter retical andobservedmass-luminosityrelationobtainslogene=10.90±0.1forA 228 JOHANNESHARDORPANDM.SCHOLZ between theSunandearly-typestars. difference shouldbeattributedtoinaccuraciesratherthandifferencesincomposition recombination linesofheliumobservedinHnregions.Ontheotherhand,solar and lateBstars.Palmeretal.(1969)findlogene=10.92±0.02fromradiofrequency and 13.Apparentlytheselinesarenotpredictedsatisfactorily,theobservedbeing of sixplates. it issomewhathotterthanmodelTauP(cf.Fig.3).Smalldots,singleobservations;largeaverages parameters Tu=32800°Kandlogg4.2proposed byScholz(1967;seeFig.1),the formation oftheselines (AuerandMihalas1968).Werecommendthat, wheneverpos- choice ofthemodels,forifwereplaceourrSco modelbyaslightlyhotteronewiththe deeper thanthecomputedcontours.Thisresult possiblyreferstotheuncertaintyin neutral-helium lines,wouldbeabitlargerforthis modelwhichmakestheHenprofiles observed andcomputedprofilesmatchmuchbetter. Infact,logene,asderivedfrom still deeper.Thesituation isfurthercomplicatedbythefactthat twobroadening broadened theoreticalprofilesformodelLamP. One mustalsokeepinmind thatthepositionofcontinuumisinaccuratebyabout 1percent. sible, Heilfinesbeavoided forabundancedeterminations. theories givedifferentresults andthatnoncoherentscatteringplayssome partinthe e 9 Observed shapesofHenlinesarecomparedwithcomputedprofilesinFigures12 Fig. 12.—TheHenlinesinrSco.LinesareratherbetterrepresentedwithScholz’smodel,because Fig. 13.—Observedprofile(averageofthreeplates)He nX4686inXLepcomparedwithrotationally ThePickeringlineHenX5412 isveryshallow,soanygoodprofilemeasurement isverydifficult. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem -2-1 012Ä A* 197OApJS ... 19. .193H 20 10 be reversedaccordingtoRisberg (1955)(4481.32:3D3/2-4F6/;4481.12:A/2-4F°7/2). We alsosearchedcarefully forthepossiblepresenceofSi11linesand foundoneweak multiplet 1ofSirvareless usefulforabundancedeterminationsbecause theyarenotice- The samebehaviorhasbeenobservedinthe spectrum oflHer(B3V;Kodairaand requires thereversesituationinLTE,provided thatLS-couplingprevails(seeFig.14). ably affectedbydamping, butnoquadraticStark-effectconstantC4is sofaravailable. formed indeeplayersoftheatmosphere,andwehavenoreasontodoubtrelatively tiplets, allyieldingsimilarabundances. Scholz 1969)andinProcyon(F5IV,Griffin1969). WefoundlinesoffourAlmmul- high abundancesresultingfromouranalyses(cf.§Vie). ionization potentialofNeiandthehighexcitationnlines,theyare a fewlines.TheMgnanalysesarebasedon nX4481,andweshouldmentionthat ultraviolet ontheshort-wavelengthsideofBalmerdiscontinuity.Becausehigh lines; thederivedabundancesarethereforesomewhatuncertain.However,thesevalues r Scoshowsthebluecomponentstrongerthan thered,althoughcomputation strong linesoftheOmmultiplet3lieinwavelengthregionmergingBalmer mÂ), wewouldobtainanaverageequivalentwidthW\=76Âandloge7.9forthis agree wellwiththosededucedfromOmXX5592and4074intherScospectrum. equivalent widthsandoscillatorstrengthsareconsiderablyreduced.Themoderately number ofOnlinesissolargethatonecanhopenonsystematicerrorsmeasured between 31and80mÂ.Ifwetookintoaccountonlythethreelargestvalues(73-80 most importantNnlineatX3995waspoorlyobservedintheXLepspectrum;aver- line. we areunabletoexplainthestrangeionizationequilibrium,cannotconcludethat line spectra.ThenitrogenequilibriumforXLep(butnotthatofrSco)indicatesa lines inthespectrumofrSco.Itisnotclearwhetherthisduetoaslightenhancement for TSco.Whenwerestrictourattentiontothoselinesthatarecommonbothstars, 2 sphere, thenumberofnitrogenatomsissmallerbyroughlyafactor2.Since,however, nitrogen linesintheXLepspectrumareappreciablyweakerthansameonesob- much highereffectivetemperaturethantheotherequilibriaofC,O,andSi,thatis,about age valueW\=62mÂwasderivedfromfiveplatesyieldingindividualmeasurements served inrSco,andwhereverthe(logTu,logg)-diagramweplaceXLepatmo- X LepseemstohaveabouttwiceasmuchcarbonrSco,inbothstagesofionization. both stars.TheaveragedabundanceswerefoundtobesomewhathigherforXLepthan there isarealabundancedifferencebetweenthetwoatmospheres.Unfortunately, element presentstheonlyreallyseriousproblemininterpretationof“metallic” causes smallsystematicerrorsoftheW\measurements. dispersion ofmostXLepplatesandtherotationalbroadeninglineswhich of theheavierelementsinXLepatmospherecomparedwithrSco,ortolower In fact,mostXLeplinestendtoyieldhigher“metal”abundancesthanthecorresponding the temperatureregionindicatedbyionizationequilibriafortSco.Moreover,most e 10 Dr.D.Lamberthascalled toourattentionthatthelevelassignmentgivenbyMoore (1945)should There areseverallinesofSimandivpresent. Unfortunately,thestronglinesof The spectraofelementswithatomicnumbershigher than10arerepresentedbyonly Neon ispresentinitssecondspectrum,andthemajorityoftheselineslie Most linesinthespectraofrScoandXLepcanbeattributedtoOn.Indeed, Like carbon,nitrogenispresentintwostagesofionization(NnandNm).This Numerous linesofsinglyanddoublyionizedcarbonarepresentinthespectra © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem d) Magnesium,Aluminum,Silicon,Sulfur,andOther Elements TAU SCORPIIANDLAMBDALEPORIS229 c) Carbon,Nitrogen,Oxygen,andNeon 197OApJS ... 19. .193H from Siinandiv.Since,however,theoscillatorstrengthforthislineisstillvery width isveryinaccurateandgivesloge=9.2,i.e.,50timestheabundancederived feature intherScospectrumatpositionofSinX3863.Themeasuredequivalent uncertain (cf.Schulz-Gulde1969),andsinceSinlineswouldbeformedintheupper- most atmosphere,thepresenceofSincannotbeexcludeddefinitely. lator strengthsbyWarner(1965)wereavailable. Itwouldbeveryhelpfulforthein- formally toCln(rScoandXLep)Aru (r Sco),buttheseidentificationsarejust instrumental profile. the rScospectrumcoincidewithpositionsofSnlines,buttheseidentificationsare agree well,withtheexceptionofSmX3632.Thewavelengthsafewweakfeaturesin extremely questionable.Similarly,thereareacouple oflineswhichcouldbeattributed 230 JOHANNESHARDORPANDM.SCHÖLZ terpretation ofO-andB-type spectratoprovidealargernumberofgood Femtransi- as questionable;weincludesomeoftheminTable 8. tion probabilities. (B3 V;KodairaandScholz 1969;PetersandAller1969),theSun (Lambertand The sulfurabundanceisderivedfromseveralSmlines.individualabundances The spectraofbothstarsshowseveralFemlines whichweanalyzedwheneveroscil- Fig. 14.—TheMgnX4481doubletathighresolution. Theoretical profilewasconvolutedwiththe Chemical abundancesof tenelementsaregiveninTable12forrSeo, XLep,lHer © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Fe 7.37.56.7/7.46.1/7.66.51 A1 6.26.16.2/6.16.56.40 Mg 7.57.77.37.48 Ne 8.68.88.77.88 0 8.78.88.49.08.77 N 8.38.07.77.93 He 11.010.8...10.80 H 12.00 C 8.18.58.88.55 S 7.27.47.1/7.07.1/7.27.21 Si 7.67.87.1/7.37.1/7.67.55 Element tScoXLepKSPASun (1) (2)(3)(4)(5)(6) The LogarithmicAbundancesofElements e) Discussion TABLE 12 t Her 197OApJS ... 19. .193H 11 Y. Richter,Astr.andAp.,4, 446).ThisagreeswithwhatwasfoundfortheBstars fromFemlines. Metal abundancesare therefore determinedwithanaccuracyofafactor 2only,but to alogarithmicironabundance of7.6inthesolarphotosphereff.Garz,H.Holweger, M.Kock,and normal starsaroundB0 V cannotbeachievedbymeansofpresenttheoretical techniques. model ismuchtoocoolandshouldthereforenot becalledaB0Vmodel. parameters failcompletely. yield reasonableresultsunlessthestandard methodsofdeterminingatmospheric and Morton(1968)whichwasmentionedin§IV/ andFigure1.Itisobviousthatthis terpreting therScoobservationsbymeansof line-blanketedB0VmodelofHickok models arestillslightlysmallerthanourvalues, butthisdifferenceisnearlycanceledby non-LTE effects(seeTable4).Ourmodelsare compromisemodelswhichweexpectto lower temperatures.Infact,theBalmerjumpsthatMihalas(1965)computedfromhis fore, ourmodelsaretoocoolwithrespecttoionizationequilibrium,and,fromthispoint we haveseenthatthemeasuredBalmerjumpsandH7H3lineprofilespointto by Scholz(1967)woulddefinitelybepreferabletothoseweadopted.Ontheotherhand, of viewaswellfortheinterpretationHenlines,rScoparametersproposed equilibria weusedforcomputingthe(logTen,logg)-diagramsin§IVc.Asknewbe- The observationalquality;thenumberofobservablelines;knowledgeof/-values factor of4mightbeabetterguess. cases occurbecauseoffailurethestandard,LTEtheorylineformation.Wefeel analysis, modelsTauPandLamP.Theydifferonlyslightlyfromthepreliminary that mostabundancesshouldbeaccuratebyafactorof2,butinunfavorablecases which canbededucedfromsolar[Fen]lines(GrevesseandSwings1969). of themodel;andotherfactorsplayanimportantpart.Additionalerrorsmayinsome and broadeningparameters;thechoiceofrf,logg,microturbulence;structure dant byaboutafactorof5-10intheBstars.Astoiron,situationisunclearbecause compositions oftheseatmospheresexist,withtheexceptionneonwhichisoverabun- Warner 1969).Thedoublevaluesinthefourthandfifthcolumnsrefertosingly of aserious/-valueproblem:ironabundancesderivedfromFemlines(rSeo,XLep, doubly ionizedstates,respectively.Apparentlynosignificantdifferencesinthechemical the otherhand,FemresultforBstarsisidenticalwithvaluelog€=7.5 i Her)aresubstantiallyhigherthanthosefromFen{iHer,Sun)andI(Sun).On e 11 We haveseenthatareally satisfactoryinterpretationoftheobserved spectraof Noteaddedinproof.—Recent recalibrationofthesystem/-valuesforFe1and Fenlinesleads In Table13wealsolist,inthelastcolumn, ionizationequilibriaobtainedbyin- Table 13showstheionizationequilibriaoffourpairsionsforourrScoandXLep It isverydifficulttoestimatetheaccuracyofresultsanabundanceanalysis. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem O m-0II0.490.26 Nm-Nll 0.410.831.18 Si iV-SiIII0.050.070.66 Cm-Cll 0.380.131.13 Note.—The higherstateofionizationyieldsthelargerabundance. A logtTauPLamHickok-Morton TAU SCORPIIANDLAMBDALEPORIS231 VII. SUMMARYANDCONCLUSION The IonizationEquilibria t Seo,XLep,rSco, TABLE 13 197OApJS ... 19. .193H -1 } f within thisaccuracywefoundthesolarvalues,exceptforanoverabundanceofneon. features intheheliumspectrumcanwellbeinterpretedbymeansofpresenttheoretical 232 JOHANNESHARDORPANDM.SCHOLZ ing especiallytoplayanimportantpartintheformationofdeeplinecores.Further- improved line-blanketedmodelatmospheres.Amethodshouldbefoundwhichenables including therocketultraviolet,areurgentlyneeded.Theyshouldbecomparedwith be wellsuitedforspectralanalysis. methods. StarswithmoderaterotationalvelocitylikethatofXLep(29kms)seemto A higheraccuracycanbeachievedfortheheliumabundance,providedthatonlyfaint profiles shouldtakeintoaccountnon-LTEeffects;wewouldexpectnoncoherentscatter- He ilinesareused.Heliumcomprisesabout30percentofthemassinbothstars.Many published dataatourdisposal.PartofthisworkwassponsoredbytheU.S.AirForce more, thisinvestigationdemonstratesthatonemustbeverycarefulindrawingcon- us toselectdefinitelyoneofthecurrenttheorieshydrogen-linebroadening,butob- clusions abouteffectivetemperaturesandsurfacegravitiesonthebasisofBaimerjump servations ofstellarspectradonotprovidesuchamethod.Futurecomputationsline meinschaft. under grantAFOSR68-1401,monitoredbytheAirForceOfficeofScientificResearch and hydrogen-lineobservationsalone. Aller, L.H.,Faulkner,D.J.,andNorton,R.H.1966,Ap.144,1073. 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