1962ApJ. . .135 . .408K hm G GemitselfaresimilartothoseofSSCyg,andthishasledthedesignation velocity variationbutwithanasyetundetermined period.Thereisatpresentnoevi- paper describesaspectroscopictestforbinarymotioninseveralUGemvariables;re- variables havebeenshowntovaryirregularlyinlightatminimum(Walker1957);this for ms,inpart,aring,ordisk,surroundingthebluestar.SeverallinesofargumentsuggestthatUGem ponents ofUGemvariablesareseriouslyunderluminousfortheirmasses.Evidenceispresentedwhich observations mayradicallyaltersomeoftheconclusions drawn. a somewhatpreliminaryreportatthistime.Thepossibility remains,ofcourse,thatnew dence indirectcontradictiontothehypothesisthat allstarsofthisgroupare,indeed, definitely binarieswithP<9hours;oneiscomposite, andoneothershowsevidenceof maining papersoftheserieswilldealwithotherstarsgroupandcertain with componentsofspectraltypesdG5andsdBe.Thisresult,coupledWalker’s old novaeandnova-likepbjects(Walker1957). whole group,bysomeauthors,asSSCygstars;thiswillnotbedonehere.Afewofthese some magnitudeintermediatebetweenminimumandmaximum.Thepropertiesof roughly 100knownstarsofthistype,twosubgroupsarerecognized:SSCygniandZ a smallrange(2-6mag.)andbytheexistenceofan^inductiontime”betweenoutbursts. The datareportedherewereobtainedovera30-month interval.Certainfairlydefinite spectroscopic binariesofshortperiod. conciusions canbereachedfromthislimitedmaterial, anditwasthoughtbesttomake thus observationalmaterialisgatheredratherslowly evenwiththe200-inchtelescope. the oldnovae.TheresultsforUGemstarscan besummarizedasfollows:fiveare to atenthofmagnitudeormore.Thevariationsaresimilarthosefoundinvarious the latterdonotalwaysdescendtominimumaftereachoutburstbutrathermaintain The latterhasatimescaleoftheorderdaysorweeks,whichcanbedescribedas mined period.Thereisnoevidencecontradictingthehypothesisthatallmembersofthisgrouparespec- shown tobebinarieswithP<9hours(SSCyg,UGem,RXAnd,RUPeg,SSAur),onespectrumis to thespeculationthatallcataclysmicvariablesmightbebinarysystems.Thepresent “flickering” hasatimescaleoftheorder1-10minutesandrangefewhundredths indicates thattheredstarsoverflowtheirlobesofinnerLagrangiansurface;ejectedmaterial and theirspectra(whenphotographed)seemconsistentwithastarofmass^4SD?©;Thustheredcom- composite (EYCyg),andoneother(ZCam)showsevidenceofbinarymotionwithanasyetundeter- “periodic” whenaveragedforanyonevariableoveralongenoughtimeinterval.Ofthe troscopic binariesofshortperiod. Camelopardalis .Theformerhaveamoreorlesswell-definedminimumbrightness; (1954, 1956)discoverythatNova(DQ)Herisaneclipsingbinaryofperiod439,led -f-9.5 ±1;thebluestarsinthesesystemsareprobablywhitedwarfs.Themassesofredcomponents variables aredescendantsoftheWUMastars. hm © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The cataclysmicvariablesoftypeUGeminorum(dwarfnovae)arecharacterizedby In 1956JoyannouncedthatSSCygwasaspectroscopicbinarywithP=638and The peculiarradialvelocitiesaresmall,andthecorrespondingstatisticalparallaxleadsto{M)= Itlshould bestatedattheoutsetthatUGemstars areveryfaintatminimumlight; A spectroscopictestforbinarymotionamongseveralUGemvariablesispresented.Fivestarsare v BINARY STARSAMONGCATACLYSMICVARIABLES Carnegie InstitutionofWashington,CaliforniaInstituteTechnology I. UGEMINORUMSTARS(DWARFNOVAE) Mount WilsonandPalomarObservatories Received October9,1961 Robert P.Kraet I. INTRODUCTION ABSTRACT 408 1962ApJ. . .135 . .408K T Leo(100-inch)andZ Cam (60-inch).Itisnotcertain,therefore,towhat extentthe in Table1.Allspectrograms wereobtainedwiththe200-inch,exceptfor EX Hyaand roughly inorderofdecreasing emission-linewidth;observationaldetailsare summarized light areshowninFigure1.Notallstarsobserved are included.Thespectraarranged wasabinaryofshortperiod,asalreadymentioned.Sincethepresentsurveyhas Z Cam RU Peg,whichwereobtainedatadispersionof90 A/mm. trograph atPalomar;thesehavedispersionof 180 A/mm,exceptfortheplatesof in general,satisfythelastcriterionmentionedabove; theymustberegardedasexplora- three importantrespects:(1)almosttheentireeffortwasputonobtainingspectrograms Mount Wilson,usingboththe60-inchand100-inch telescopes;thedispersionwas was, toaconsiderableextent,plannedpermitsufficient timeresolution. its purposethedetectionofbinarymotion,itdiffersfromthatElveyandBabcockin Joy (1956)showedthatthespectrumofSSCygatminimumwascompositeand tory incharacter.Thelargerbulkofspectrograms wasobtainedwiththenebularspec- EY Cyg posure required2-3hours(Babcock,privatecommunication)—rathertoolongtoprovide at minimumlight;(2)nodispersionlessthan180A/mm wasemployed;(3)theprogram T Leo. broad, brightBalmerlines,feebleremissionofthetripletHeiandlines during themomentsofoutburst.Inmostcasesminimalspectracontainedrather spectra werefoundtohaveacontinuousdistributioncorrespondingtypeBorA, sufficient timeresolution,asweshallsee. tained faint,narrowemissionfeatures.Atthisdispersion,however,asatisfactoryex- SS Aur EX Hya had theabsorptionlinesofastartypedG3aswellusualemissionfeatures.Later occasionally crossedbybroad,veryshallow,absorptionlinesofH;thesesometimescon- and Babcock(1943)attheMcDonaldObservatory.Sincebrightestofthesestarsis tensity distributionsimilartospectraltypeGorK.At,near,maximumlightthe twelfth magnitudeatminimum,lowdispersionwasemployed(^340A/mm)except 180 A/mm.Becauseofthefaintnessstarsin question,thesespectrogramsdonot, RU Peg Ca il(HandK)superimposedonanapparentlycontinuousbackgroundhavingin- U Gem RX And same, operatingatthe60-inch © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Some representativespectraofUGemandsuspected UGemvariablesatminimum * N=200-inchprime-focusspectrograph;B=MountWilsonNewtonianfocusspectrographoperatingatthe100-inch; Several spectrogramshavebeenobtainedwiththe gratingnebularspectrographat A surveyofspectraUGemvariablesandrelatedobjectswascarriedoutbyElvey Somewhat earlier,Joy(1940)hadindicatedthatthespectrumofRUPegatminimum Star b I c Plate No* ÍN1149a ß 1758b N1162a B 925a N1156b B1607a N1324a N1164 Summary ofObservationalDataforFigure1 II. ASURVEYOFSPECTRAATMINIMUMLIGHT 1960 Aug. 1960 Aug 1960 Aug. 1960 Feb 1960 Aug. 1956 Mar. 1960 Dec. 1961 Feb. Date (U.T) (Mid-exp ) Aug Aug. BINARY STARS 30.494 30.312 26 352 28.320 23.443 26 375 26 329 10.162 19 444 5 371 TABLE 1 Length of Exposure (min ) 150 122 101 40 30 31 30 29 31 16 Dispersion Approx. (A/mm) 180 180 180 180J 1801 1801 180 90 90 90 Sharp emissionlines city lights por inLosAngeles arise fromHgva- Remarks 409 410 ROBERT P. KRAFT wide lines of these three stars may result from integration over significant velocity changes. The spectra reproduced in Figure 1 confirm the results obtained by Elvey and Bab- cock and also give some new information. He n (X 4686) is present in a few spectrograms of U Gem (see Fig. 6) ; there may also be lines of Fe n (see appendix). A faint trace of the Balmer jump in emission is present in SS Aur and T Leo; however, in all the stars, the Balmer lines converge long before the series limit is reached, and thus they effectively merge with the Balmer continuum. The emission lines of U Gem, EX Hya, and possibly Z Cam are doubled—in the case of U Gem, very conspicuously so. We are not yet certain whether the emitting region is optically thick or thin, so it is not clear whether self- absorption plays a role. The absorption lines of a late-type dwarf star are present in the spectra of RU Peg and EY Cyg; some indication of these lines is found in the spectrum of SS Aur, but completely satisfactory agreement with the features of a G- or K-type dwarf star has not been found. TABLE 2 Orbital Elements for U Geminorum Variables

RX And SS Aur U Gem EY Cygt SS Cyg RU Peg P 5 05 3 30(?) 4 10 5 6 38 8 54 (hr., min.) P. . 0 21173 0 15(?) 0 1739825 0 276244 0 3708 (days) Kx* 77 5 ~85 265 (?) 122 137 (km/sec) K2 115 112 (km/sec) 7 -18 '■'-'+45 +42 ^—10 -9 -7 (km/sec) Sp. (1) sdBe sdBe sdBe sdBe sdBe sdBe Sp. (2) .. . KO V dG5 G8 IVnî ai sin ¿X10 10 (cm) 2 09 'M) 88 6 31 4 63 7 02 02 sin ¿X10-10 (cm) 4 37 5 73 0.40 (?) Ó 05 '■^'0 ^0 220° (?) 160° SDÍi sin3 i (O) 0 18 0 27 m2 sin3 i (O) 0 20 0 32 mi/m2 0 90 0 85

* Subscript 1 refers to the blue star, regardless of whether or not it is the more massive, f Probably viewed nearly pole-on X The luminosity class varies during the cycle, but averages MK class ^ IV

In spite of the considerable variation in width from star to star, the emission-line spectrum of these variables is very characteristic. We have not been able so far to confirm the finding by Elvey and Babcock that AY Lyr has no emission lines at minimum; the star is very faint and is in a crowded field—misidentification is a possibility. However, even if this result should be confirmed, it is reasonable to state that a sufficient condition for class membership is the presence of an emission spectrum similar to those of Figure 1. On this basis we include EX Hya and T Leo in the group (cf. Brun and Petit 1952,1959; Kukarkin, Parenago, Efremov, and Kholopov 1958; Petit 1959). III. RADIAL VELOCITIES AND ORBITAL ELEMENTS The journal of observations and velocity-curves for RX And, U Gem, and RU Peg are given in the appendix. In Table 2 we summarize the orbital elements for these stars, in- cluding also the results from Joy’s (1956) study of SS Cyg. In addition, preliminary re-

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1962ApJ. . .135 . .408K © American Astronomical Society Provided bytheNASA Astrophysics DataSystem 1962ApJ. . .135 . .408K 10 1 10 10 former. EYCygmayhaveasmallvelocityvariation,butitisclosetothelimitofde- spectrum. also givenintheappendix. Z Camshowsevidenceofvelocityvariation,buttheperiodcannotbedeterminedfrom tection; thestarmaybeasystemviewednearly“pole-on.”Ourassuranceofbinary suits forSSAurandEYCygaregiven;weexpecttoobtainmorespectrogramsofthe most easilydetectedinstarshavingthenarrowestemissionlines. 9.00 X10cmand12.75cm;hencetheminimumvaluesofrforSSCyg or dK;themassratioisnearunity,withredstarslightlymoremassivethanblue. characteristics isbasedonthefactthatspectrumcomposite.Theof fill thatsurface.FollowingKuiperandJohnson(1956),if/z=äfe/C®?!+Sfe),theef- as soonÿJli/3Jl2andasiniareknown)indicatesthatthestar,evenifdwarf,may eccentricity isalsotheonlystarbelongingtoZCamsubgroup. characteristics eitherfromvelocityvariationsorthepresenceofacomposite the availabledata.Ashortdescriptionofsomespectraldetailsthesestarsis P, wecanestimatetheinclinationoforbit.Thusi=35°and59°,respectively,for type starandthesizeofcorrespondinglobeinnerLagrangiansurface(given scarcely beregardedasmorethanroughestimates.However,Grant(1955)foundthat it isawhitedwarf)intermsofthedimensionssystem,thiswouldmeanthat and dG8,wewouldhavePs=6.2X10cm5.9cm.Ifsetr fective radiusrofthelargerinnerlobeisgivenby late-type componentactsasifitfilledonelobeof theinnerLagrangiansurface.Classi- not known,however.Thevaluesofifoundabovecertainlysatisfythislimit. i <76°;thelimitingvaluewouldbesameifRUPeg,aswell,didnoteclipse;thisis SS CygandRUPeg.Consideringthecrudityofargument,theseinclinationscan fication ontheMKsystemispossible,sincedispersion ishighenoughtoresolvethe RU Pegare3.6X10cmand5.1cm,respectively.ButforstarsoftypesdG5 of Srii.Thehighestluminositycorrespondstophases whenthestarsareinconjunction, hydrogen linesobviouslycannotbeused.Onthis basis,spectraltypesarelistedinthe of X4226;itisfilledintosomeextentbytheblue continuum ofthehotcomponent.The ratio X4254/A4260.Lesssatisfactoryasabasisfor classificationistheabsoluteintensity SS Cygdoesnoteclipse.Sincethebluestarisquitesmall(theresultsofSec.Vshowthat spectral typeisroughlyconstantatG8.However, theluminosityclassrunsfromVto appendix. Thelinesarealwayssomewhatdiffuse (broadenedbyrotation?),andthe component. where aistheseparationofcentersmass.Thuswehavelogr/a=—0.396and HI, apparentlydependingonaspect,asjudgedfrom thestrengthsofX4077and4215 inner Lagrangiansurfacemightbeexpectedto imitate astarofhigherluminosity, red starbehind.Aofdwarfdimensionswhich, atthesametime,fillsalobeof 2 2 —0.400 forSSCygandRUPeg,respectively.Theminimumvaluesofaeachstarare SRU2 2 2 1 © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem 4. Fromthematerialathand,itappearsthatlate-typeabsorptionspectrumis The mainconclusionssummarizingTable2arethefollowing: In thecasesofSSCygandRUPeg,acomparisonprobableradiuslate- 3. Inthosecasesinwhichalate-typespectrumisdetected,thespectraltypedG 5. Itispossibly,thoughnotnecessarily,significantthattheonlysystemofhigh 2. Themeanperiodofthefourbest-studiedstarsis(P)=0.25day. However, thereismorecompellingevidencethat,atleastinthecaseofRUPeg, 1. NoUGemvariablesofarstudiedindetailhasfailedtoshowevidenceofbinary Throughoutthispaper,thesubsciipt 1referstothebluestar,whetherornotitismore massive log —=0.335¿U0.511,(1) CL BINARY STARS411 1962ApJ. . .135 . .408K 11 4 11 17 17 17 on whethertheemitting region isopticallythickorthin—thelatterleads tozjsinf= where 0,2=6.31X10cm andP—1.50X10sec.Thevalueofv,however, depends v =670km/sec.Equation (3)canthenbebalancedreasonablywellfor üDíi/Sfe lying i —500km/sec,asderivedfrommicrophotometer tracings.ForSSCyg,theleft-and masses oftheblueandredstars,respectively, X isafactorofproportionalitydescrib- where vsiniistheprojectedhalf-half-widthofemissionline,andSDÎ2are of components(Kraft1959);viz., from theinnerLagrangianpointtoringaroundbluestar,approximatelycon- for UGem,unfortunatelythespectrumofredstarhasnotyetbeenphotographed. a radiusof1.5X10cm,theorbitalinclinationwouldthereforebeabout18°,and Thus thevaluesofXareverysimilar,and= 1.31. ing thefractionalchangeofangularmomentum. For bothSSCygandRUPeg,vsin serves itsangularmomentumwithrespecttothebluestar.Inthatcase,wecanderivea gravity causedbythecentrifugalacceleration. 412 ROBERTP.KRAFT see inSectionV,theluminosityisprobablynearMv—+9.5.Thusitseemslikelythat mass oftheredstarwouldbe120!Thisiscompletelyunreasonable,since,asweshall especially atsuperiorconjunction,becauseofthereductionineffectivesurfacegravity. right-hand sidesofequation(2)are5.3X10and 4.2X10X,respectively;thus= listed inTable2arerathersmallerthantheactualmasses.Thoughiisprobablynear90° binary. inner Lagrangiansurface.Materialspillsoutfromthepointandforms relation betweenthewidthofemissionlines,periodinorbit,andmasses character oftheemissionlinesSSCygandRUPeg,suggeststhatminimummasses plane oftheorbit,andasingleemissionifideviatesfrom90°toanyappreciableextent. gardless ofitsopticalthickness,thediskwillproduceadoubledemissionifseenin not spherical,theshapeofemissionlinewilldependonorbitalinclination.Re- a ringordiskaroundthebluecompanion.Ifemittingregionistrulyflattenedand plicable totheUGemstars.Wesupposethatlate-typecomponentfillsitslobeof and Kraft1956),TCrB(Kraft1958),DQHer1959)isprobablyalsoap- the spuriouslyhighspectroscopicluminosityresultsfromreductioninsurface expected forUGemvariables.TheargumentofSectionIII,coupledwiththe“single” the hotcomponentofDQHer(GreensteinandKraft1959),awell-knowneclipsing this proposalisfoundinthepresenceofconspicuouslydoubledemissionlinesarisingnear are viewedneartheplaneoforbit—theymayevenbeeclipsingbinaries.Supportfor We maytentativelysuppose,therefore,thatUGemandpossiblyEXHyaZCam Consider, then,thefollowingindirectargumentfordeterminationofmasses. the caseinRUPeg.)Ifstarwere,fact,anormaloftypeG8IV,itwouldhave (The effectwouldbemorepronounced,ofcourse,ifiwerenearerto90°thanisprobably 1.26. CorrespondingvaluesforRUPegare8.0 X10,5.9X,and=1.36. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem If thesamevalueofXappliestoUGem,wehave The precedingdiscussionsuggeststhatthemodeladvancedforAEAqr(Crawford Kuiper (1941)hasshown,onthebasisofJacobi’sintegral,thataparticle,infalling If theprecedingmodeliscorrect,wecanmakearoughestimateofmassestobe 3 G SDÎisini v sini G3)îi_i , =1.31a 1/T v IV. MASSESFORTHECOMPONENTS 1 K- 39 0.39 ) 2 27T ~Y (3) (2) BINARY STARS 413 between 0.8 and 1.9, implying 1.9 < SDîi < 5.5 ®îo. Since, as already mentioned, Mv~ +9.5 for these stars, a mass greater than 1.2 9Jio is unlikely because the blue star must be essentially a (Schwarzschild 1958). On the other hand, equation (3) cannot be balanced within the error of measuring the width of the emission line if SDîi < 1.0. Moreover, if the emitting region is optically thick, v < 670 km/sec, and the value of SDîi required to balance the equation is driven up still further. It seems most likely that SDîi lies in the 0.9-1.20 range and that the emitting region is optically thin. If the masses of the red components of SS Cyg and RU Peg are ^1 3Jîo as well, the orbital inclinations would be in quite reasonable agreement with those derived by the argument of Section III. V. STATISTICAL PARALLAX The systemic velocities and corresponding peculiar radial velocities (i.e., radial velocities corrected for solar motion) are listed in Table 3, along with the proper motions. A rough statistical parallax can be obtained, following Smart (1938), from the radial velocities and proper motions of four stars: U Gem, SS Cyg, RU Peg, and EY Cyg. If TABLE 3 Magnitudes, Proper Motions, Peculiar Radial Velocities, Etc., for U Geminorum Variables

U* Outburst Star Mt MîV (min) Kind Period (km/sec) (sec of arc/yr) (days) RX And -12 13 6 Z 14 SS Aur +35 14 8 SS 54 U Gem +37 0 078 14 0 SS 103 EY Cyg '+13 062 15 0: SS 1000 SS Cyg +16 116 12 1 SS 52 RUPeg + 11 0 070 13 1 SS 70

* with solar motion removed t Mean of values given by Mannino and Rosino (1950) and by Miczaika and Becker (1948) r is the distance of any star, then, under the assumption that (log r> ^ log , we find (My) = +9.5 + 0.6 (m.e.) at minimum light. The quoted mean error is internal; a value of + 1 mag. would be more realistic. There are two direct checks on this value of (Tfy). Strand’s (1948) well-determined parallax for SS Cyg gives My — +9.5 at minimum light. From a study of the color of UZ Ser, Herbig (1944) concluded that the star is in front of an absorbing cloud not farther away than 200 pc. From this he found My ~ +10.1 at minimum. Both these values agree well with our statistical parallax. It must be admitted, however, that U Gem stars need not all have the same absolute magnitude. We have no way, at present, of determining the dispersion about the mean, if any. A further indication that {My) — +9.5 is approximately correct is found from a consideration of the colors at maximum light. At a mean distance of only 66 pc, little or no reddening would be expected. At maximum, the spectra of U Gem and SS Cyg are very nearly continuous (Elvey and Babcock 1943). (Occasionally, feeble emission or absorption lines of H and He n are seen [cf. also Adams and Joy 1922].) Thus we make the assumption that SS Cyg and U Gem radiate as black bodies at maximum light. The U — B, B — V colors of these stars (Grant and Abt 1959; Wallerstein 1959) may be compared with black-body radiators (Arp 1961). This was done earlier by Wallerstein (1959), but a slightly incorrect black-body trajectory in the color-color plot was used. With Arp’s new curve, we have the comparison shown in Figure 2. We conclude that, if

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1962ApJ. . .135 . .408K stars mustthereforebe = +12.5.Foreachgroup,82and123stars, respectively, been takentothelimitw g (min.)=+17.5;thecorrespondinglimitfor theWUMa computed byArp(1961)isshown. is concernedwithevidencesupportingtheproposition thataUGemvariablerepresents 414 ROBERTP.KRAFT 4; dataforthelatteraretakenfromcompilation byKitamura(1959). a laterstageintheevolutionofWUMastar.This viewhasbeenadvancedbySahade variables aresimilartothestarsoftypeWUMa. for theredcomponentsofthesesystems.Itwouldappearthatstarsaresignificant- disk aretheWUMastars(cf.Struve1950;Kitamura 1959).Theremainderofthepaper ly underluminousfortheirmasses.Inthisrespectandanumberofothers,theUGem with (M)in=+9.5. The onlyotherbinariesofcomparablyshortperiod whichalsobelongtothegalactic flattened stellarpopulation—thegalacticdisk.Theyarenotmembersofthe 12000° and15000°K,respectively,thereisnointerstellarreddening;thisconsistent (1959) andalsoindependentlybythewriterforsome . “halo”; neithercantheybedescribedasbelongingtoBaade’sclassicalpopulationII. SS CygandUGemradiateasblackbodiesatmaximumlightwithtemperaturesof P vm © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The physicalpropertiesoftheUGemandWUMa systemsaresummarizedinTable In Figure3weplotthes = rsinôdistributionforeachgroup.TheUGem stars have This resultisnot,however,compatiblewithaspectraltypeofG5-K0andSDÎ^1.0O The smallpeculiarvelocitiesofUGemstarsindicatethattheybelongtoamoderately Fig 2.—TheU—B,BVcolorsofGemandSSCyg atmaximumlight.Theblack-bodylocus VI. EVOLUTIONARYCONSIDERATIONS 1962ApJ. . .135 . .408K former didnothaveknownmagnitudesatminimum;theaveragerangeof4mag.was were foundintheVariableStarCatalogue(Kukarkinetal.1958).Twenty-fiveof finds thatthe2-distributionsareextraordinarilysimilar.Thisresult,coupledwithour and particularlytheratherdifferentbasisfordiscoveryofstarsintwogroups,one therefore appliedtothemagnitudesatmaximum.Consideringvariousuncertainties mura (1959)hasshownthatintheWUMastarsisitlikelyprimaryoverflows finding thatthetotalmassesandmeanpeculiarradialvelocitiesarecloselyalike,strong- underluminous byperhaps5mag.Butifourmodeliscorrect,thesealsolosemass lected bythesecondaryorlosttosystem.Themainpoint,however,isthatpri- its lobeoftheinnerLagrangiansurface.Thestarthereforelosesmass,whichmaybecol- ly suggestsagenericrelationbetweenthetwokindsofstars. kinds ofvariables,wenowturntothequestion:Areperiods,massratios,andtotal red componentsofUGemsystems,for,if+10butlO,thesestarsare mary isseriouslyunderluminousforitsmass(^3or4mag.).Thesametruethe through theinnerLagrangiansurface. (min.) =+17.5forUGemstars and=+12.5forWUMasystems. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem There is,however,alsoaphysicalpointofsimilaritynotcoveredinthetable.Kita- Having establishedthesimilarityinkinematicsandspacedistributionfortwo Fig. 3.—The^-distributionsof UGemandWUMastarscompared.Thelimitsofthesurvey are ä)h/ömi+2)?2> and wg=125,respectively.

^ ^ = ^ = 1035 erg/sec . (6)

With an ejection velocity of (say) 10 km/sec, the equation can be balanced if dm/dt = 2 X 1023 gm/sec = 6 X 1030 gm/yr. This would mean that W UMa stars last for only 500 years—a result unacceptable not only because of the excessively large number of W UMa stars it would imply but also because the change in period per unit time would greatly exceed that observed unless the amounts lost to the system and collected by the sec- ondary were very closely related. Evidence of the time scale that might be expected comes from the work of Morton (1960), who showed that the mass loss must proceed on the Kelvin time scale. In this case, = 1.5 X 106 years. Thus, even if the ejection velocity were 100 km/sec, we could not satisfy the Kelvin time scale and at the same time maintain the validity of equation (6). However, the Kelvin time is quite short compared with the age of Praesepe, viz., 1-5 X 108 years; there is strong evidence that Praesepe contains the W UMa star TX Cnc (Haffner 1937; Eggen 1961). This presumably means that the components of TX Cnc have only recently begun the activity presently identified with the W UMa characteristic. The mass of the primary is about 1.60 (Kitamura 1959). However, the masses of the stars now breaking off the main sequence and evolving to the right in the HR diagram are about 2.00. If the lifetime of TX Cnc is, indeed, significantly less than the age of the cluster, one could imagine that the original system consisted of an A or F primary of mass ^20, together with a much fainter and less massive secondary. At first, neither star filled its lobe of the inner Lagrangian surface. As evolution proceeded, the primary expanded to fill its lobe in a time of the order of 108 years; loss of mass has brought it rapidly to its present position in the cluster HR diagram. If this scheme is to be maintained, it will be necessary to explain how the primary can evolve along a line nearly parallel to the main sequence itself.

APPENDIX Journal of Observations, Velocity-Curves, and Discussion of Radial Velocities for Certain U Geminorum Variables I. RX And.—The emission spectrum of hydrogen is strong and shows the Balmer jump in emission. He i (X 4771, X 4026) and Ca n are present in emission; there is a faint indication of bright He n (X 4686). No trace of an absorption-line spectrum has been found. The journal of observations is given in Table 5, and the velocity-curve plotted in Figure 4. All spectrograms have dispersion ^180 A/mm. The star is unusual in having an of high eccentricity. The distortion of a sine-wave velocity-curve by streams of gas cannot, of course, be ruled out. II. SS Aur.—Only nine spectrograms (dispersion ^180 A/mm) are available. The emission lines of hydrogen are strong and have relatively sharp edges; the Balmer jump is in emission. Ca ii (K) is prominent in emission, but He i is weak. The underlying continuum is irregular and may correspond to the spectrum of a late-type star, but the match is not completely free from ambiguity. The journal of observations is found in Table 6. A period of about 3§ hours fits the velocities, but more observations are needed. III. U Gem.—The hydrogen emission lines and Ca u (K) are distinctly double. X 4471 and X 4026 of He i are feebly present, and there is a bright trace of X 4686 of He u. The difference in velocity at opposite elongations is illustrated in Figure 7. As was the case in the spectrum of DQ Her (Greenstein and Kraft 1959), the F/R ratio reverses at opposite elongations. When the spectra are lined up, as in Figure 8, some faint emission features at XX 4172, 4232, 43Ô1, 4512(?), and 4582 emerge which may correspond to the Fe n lines XX 4173, 4233, 4303, 4508 and 4522 (blended), and 4584.

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1962ApJ. . .135 . .408K respectively. p 6—Theradialvelocities ofRUPegFilledandopencirclesrefertoabsorption emission, IG> © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Km /sec o + 120 -160 -120 + 80 + 40 -80 -40 Fig. 4—Theradial-velocitycurve(emissionlines)ofRXAnd 08 0900010203 04 05060708P 418 1962ApJ. . .135 . .408K © American Astronomical Society Provided bytheNASA Astrophysics DataSystem 3888

1324 a 1326 a 1323 a 1324 b 1326 b 1276 a 1324 c 1326 c 1276 b 1325a 1276 c 1327 a 1325b 1327 b 1277a 1325c 1327 c 1277 b 1323 b 1277c 1323 c

Fig. 8. Spectra of U Gem around the cycle. No attempt has been made to show the radial velocity variation. Notice the change in visibility of the higher members of the Balmer series.

© American Astronomical Society • Provided by the NASA Astrophysics Data System o co « © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem

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♦Zero phase taken arbitrarily at J. D. a 2437173.0000 1962ApJ. . .135 . .408K N1165 a N1164 N 1218a N 1217a Plate No. JOURNAL OFOBSERVATIONSFORSSAUR © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem b b c b c 1960 Aug30.494 Date (U.T.) TABLE 6 (Mid-exp) Aug 31.381 Oct 17.389 420 31.409 17.520 17,502 17.479 17.448 17.420 (km/ sec) + 101 + 108 + 130 + 15 - 21 - 9 - 45 V 99 77 1962ApJ. . .135 . .408K N 1276a N1323 a N 1277a N1325 a N 1324a N 1327a N1326 a ♦Zero phasetakenarbitrarilyatJ. D.q=2437266.0000 Plate No, © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem JOURNAL OFOBSERVATIONSFORUGEM b b b c b c b b c c c b c c 266,9722 266,9270 266.9499 267.0416 267,0201 266,9978 (mid-exp) 340. 7820 340.6675 340. 6407 340. 6206 339.6428 340.8876 340.8668 340.8456 340. 7609 340,7383 340. 6914 340.9188 340. 7129 340.9397 340.9595 (Helioc.) 2437000+ J,D, TABLE 7 421 (km/sec) - 143 -237 -228 - 86 -252 - 39 - 160 -116 + 58 + 213 + 235 -250 + 290 + 325 + 117 + 135 + 153 + 332 + 259 + 238 + 108 V 0.328 Phase* 0.845 *460 .863 .987 .588 .704 .574 .304 .277 ,735 .428 .167 .013 .897 ,190 ,825 .611 .432 ,731 ,312 (P) 1962ApJ. . .135 . .408K N 1150a N1149 a N 1146a N1148a N1145 a N 1144a ♦Zero phasetakenarbitrarilyatJ.D.2437171,873,themomentof N1143a Plate No. max. positiveabsorption-linevelocity. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem b b b c b b b c c b c c c JOURNAL OFOBSERVATIONSFORRUPEG 2437000* (mid-exp) 172.9419 171.8360 171.8123 172.9099 172.8807 172.8582 172,8346 172.8061 171.9818 171.7613 171.7380 171.7137 172.9748 172,7842 172.7596 171,9995 171.9533 171.9311 171.9085 171.8585 (Helioc. ) J.D. TABLE 8 -187 - 24 -121 - 29 - 48 - 46 -124 -118 - 84 + 98 + 80 +129 + 95 +150 + 7 + 6 + 68 + 72 +109 + 3 em. (km/ sec) 422 V -132 - 43 - 71 -108 - 80 - 74 -107 - 40 - 97 - 14 - 54 + 96 +116 + 62 + 62 +100 abs. 84 54 31 0 0.566 Phase* 0*963 .836 .885 .584 .691 .633 .790 .708 .648 .210 .157 .961 ,906 .506 .453 .382 .328 .277 .092 (P) K0 Vn G8Vn G8IV n G8IV n G8IVn G8IV n G8IV n G8IV, Vn G8IVn G8 Vn KO IVn G8 IVn GSIIIn G8IV n G8 IVn G8Vn G8IV n G8Vn G8Vn G8 Vn Type Sp. 1962ApJ. . .135 . .408K 1 as radialvelocitiesarelistedinTable8.Theemissionlineshaveamorphousedgesat90A/mm Wallerstein, G1959,Pub.A S P.,71,316 1957,inI.A.U.Symposium, No.3,ed.GHHerbig(Cambridge:CambridgeUniversity Press). velocity-curve isillustratedinFigure6. and aredifficulttomeasure.Ca11(K)sometimesappearsdoubled;He1isratherweakinemis- between absorptionandemissionvelocities. The meanerrorsofmeasurementarelargeenoughthatthedifferenceinabsorption-linevelocity proaching toN1325cand1327c.ThevisibilityofthehighermembersBaimerseries members) tobemorepronounced,thestrongeremission.Thelargechangesincontinuum varies inthecycle;theyarestrongestnearelongation(1)andvirtuallydisappearatsuperior and c;superiorconjunction(bluestarbehind)toN1276elongation(2)withblueap- .1956,123,68 Walker, M.F.1954,Pub.A.S.P., 66,230. Schwarzschild, M1958,StructureandEvolutionoftheStars (Princeton:PrincetonUniversityPress), Joy, A.H.1940,Pub.AS.P.,52,324. Huang, S.-S.1956,AJ.,61,49. .1960,Ap.J,132,76. Herbig, G.H.1944,Pub.ASP,56,230. Haffner, H.1937,Zs.f.Ap,U,285. Adams, W.S.,andJoy,A.H.1922,Pop.Astr,30,103. between thetwoplatesisprobablynotsignificant. and —81km/sec,respectively.ForN1163a,b,wehave+18—8 Smart, W.M.1938,StellarDynamics(Cambridge:Cambridge UniversityPress),p.208 Petit, M.1959,PeremennyeZvezdy,12,4. Miczaika, G.,andBecker,W.1948,HeidelbergVeroff.,Vol. 15,No.8. .1959,ibid,130,110 .1956,Ap.J,124,317. Greenstein, J.L.,andKraft,R.P.1959,Ap.J.,130,99. Elvey, C.T.,andBabcock,H.W.1943,Ap.J.,97,412. .1959,PeremennyeZvezdy,12,18. Brun, A,andPetit,M.1952,Bull.Assoc,françaiseObs.étoilesvar.,12,1. Arp, H.C.1961,Ap.133,874. spectrum ofalate-typestarinthephotographicregion(IIa-0plates).MKspectraltypesaswell Eggen, O.J.1961,RoyalObs.Bull.,No31. sion. ThehigherBalmerlinesconverge,andthecontinuumisprobablyinemission. a, b,c,themeanvelocitiesofemission(H7+Hô)andabsorption(X4045X4226)are+26 intensity fromplatetoplate,thoughenhancedintheprocessofreproduction,areatleastpar- conjunction. Thereseemstobeatendencyfortheappearanceofduplicity(amonghigher shown inFigure5.Elongation(1)withthebluestarrecedingcorrespondstoplatesnearN1324b Struve, O1950,StellarEvolution (Princeton:PrincetonUniversityPress),p183 Strand, K.Aa1948,Ap.J.,107,106 Sahade, J.1959,LiegeSymposium:Modelesdétoilesetévolution stellaire,p76. Morton, DC.1960,Ap.J.,132,146. Kukarkin, B,Parenago,P.,Efremov,Y.,andKholopov, P. 1958,GeneralCatalogueofVariableStars, Kuiper, G.P.1941,Ap.J.,93,133 Kraft, R.P.1958,Ap.J.,127,625. Kitamura, M.1959,Pub.Astr.Soc.Japan,11,216. Grant, G.,andAbt,H.A.1959,Ap.J.,129,323. Mannino, G.,andRosino,L.1950,PaduaPub,No.14. Kuiper, GP,andJohnson,J.R1956,Ap.J123,90. Grant, G.1955,Ap.J.,122,566 tially duetochangesinstellarbrightness. Crawford, J.A,andKraft,R.P.1956,Ap.J.,123,44. (slightly) fortheeffectofexposuretime,whichisasmall,butsignificant,fractionperiod (cf. Herbig1960). © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem p. 233. The emissionlinesarequitenarrowforaUGemvariable.quotedvelocityismean V. RUPeg.—WiththeexceptionofSSCyg,thisisonlyotherstarshowingabsorption The journalofobservationsisgiveninTable7.radialvelocitieshavebeencorrected The cyclicalbehaviorofthespectrumisillustratedalsoinFigure8,andvelocity-curve Vol. 1(Moscow:AkademiiaNaukU.SS.R). IV. EYCyg.—Fromfivespectrograms,thereisnosignificantvelocityvariation.ForN1162 BINARY STARS423 REFERENCES