1957 Ap J. . .125. .719L the SPECTRA of WHITE DWARFS

1957 Ap J. . .125. .719L í<, spectra similartovanMaanen2,andoneistheheliumstar,L930-80. found formain-sequencestars.Threeofthewhitedwarfsobservedhavenostrongabsorptionfeatures ing B—Vcolorsofabout+0.1havethestrongesthydrogenlines,inkeepingwithsamecorrelation and areclassifiedascontinuous-spectrumstars.Ofthethreeremainingstarsobserved,twohave parison withS.Verweij’stheoreticalprofiles,indicateloggvaluesoftheorder7.0.Acorrelationisfound between thestrengthofhydrogenlinesandcolorswhitedwarfssuchthatthosestarshav- lar spectrograph,whichhasadispersionof430A/mmatH7.EastmanIIa-0plates, the LickObservatory.Seventeenofthesestarsshowstronghydrogenabsorptionlineswhich,byacom- preliminary values. baked for2daysat50°C,wereused.Thecalibrationwasputonaseparateplatefrom L 930-80.Forallstarsbut40Eri(B),Luyten’sfindingcharts(1949)wereused. his datagavenoevidenceofthis.Thereseemstobesuchacorrelation,asillustrated neously. Atleasttwospectraofeachwhitedwarfwereobtained,withtheexception the samepacket.Thecalibrationplateandspectralplatesweredevelopedsimulta- observed, whileHfwasalsomeasuredwhenpossible.Nocorrectionappliedfor and equivalentwidthsweremeasuredforH7,H<5,Heallthehydrogen-linestars in Figuret,whichtheequivalentwidthsofH7areplottedasafunctionB—V the profilesofsomethem,inspitelowdispersionspectra.Line C. R.LyndsfurnishedthecolorsofVR7andL1244-26.Allareunpublished Figure 2.TheequivalentwidthsofH7weretakenfromGünther(1933),andthecolors color ofthewhitedwarfs. gravity, g,ortheeffectivetemperature.Theprocedure adoptedhereisthatofdetermin- In thisrespectthemain-sequencestarsandwhitedwarfsaresimilar. are thoseofJohnson(1953).AmaximumisreachedatabouttheB—Vcolor+0.1. by theinteratomicelectricfieldsindenseatmospheres ofwhitedwarfs,andthus ing theeffectivetemperaturesofastarfromitscolor andthenusingtheprofilesof determining theStarkprofilesofanabsorption lines arethesurfacegravityand instrumental broadeningbecauseofthewidthlines. they mayberepresentedbyStark-broadenedprofiles. Sincethephysicalparameters temperature, theprofilesofhydrogenlinesoffer amethodofdeterminingthesurface © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem The spectraoftwenty-threewhitedwarfswereobtainedwiththeCrossleynebularspectrograph Twenty-three whitedwarfswereobservedwiththeLickObservatoryCrossleynebu- The hydrogenlinesinwhitedwarfsaresobroadthatithasbeenpossibletodetermine Luyten (1952)suggestedapossiblecorrelationbetweencolorandlinestrength,but The variationinhydrogenstrengthwithcolorformain-sequencestarsisgiven Colors ofseventeenwhitedwarfsobservedwerekindlysuppliedbyD.L.Harris. Kuiper (1939)foundthatthehydrogenlinesinwhite dwarfsareprimarilybroadened Berkeley AstronomicalDepartment,UniversityofCalifornia Received December10,1956;revisedJanuary7,1957 THE SPECTRAOFWHITEDWARFS THE HYDROGENLINESINWHITEDWARES DETERMINATION OFLOGg SPECTROGRAPHIC DATA Beverly T.Lynds ABSTRACT 719 1957 Ap J. . .125. .719L - of thetheoreticalprofilesHy,ascomputedbyVerweij,withtemperatureforvari- hydrogen linestodeterminelogg.Thetemperaturesadoptedaretheeffectivetempera- adopted teperatures.Thecurvesinthefigurerepresentvariationofhalf-width less thanorequalto10000°. as asourceofopacity.Actually,inwhitedwarfs,Hbecomesimportantattemperatures For lowertemperatures,however,hisresultsarenotvalid,becauseoftheneglectH“ sequently, itispossibletouseVerweij’stheoreticalprofiles(1936)withsomeconfidence. tures ofthemain-sequencestarshavingsameB—Vcoloraswhitedwarf.Once theory isavailable.ForverystrongfieldstheHoltsmarkdistributionmaybeused;con- the temperaturesaredeterminedforstars,logg’smaybeestimatedifasuitable 720 BEVERLYT.LYNDS Fig. 2.—Correlationbetween equivalentwidthsofH7andtheB—Vcolorsmain-sequence stars © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem In Figure3thehalf-widthofH7ataresidualintensity0.9isplottedagainst Fig. 1.—CorrelationsbetweenequivalentwidthsofH7andtheB—Vcolorswhitedwarfs E.A. 20 E A. 20 10 40 0.2 1 \^^—ir i 0.0 B-V +0.2 +0.4 WHITE DWARFS 721 ous log g values. Thus, if Verweij’s theory is applicable to the atmospheres of white dwarfs, one should be able to read off the appropriate value of log g for each point, once the temperature is known. The stars observed have similar log g values, most of them lying between 6.8 and 7.5 c.g.s. units. According to Verweij’s results, the sharp increase in width of Hy as the temperature increases and the temperature of maximum width are essentially independ- ent of log g, although the magnitude of the variation is sensitive to the surface gravity. This is probably the reason why the general variation of hydrogen strength with color or spectral type is the same as that of main-sequence stars with respect to the sharp rise before maximum as well as the location of the maximum intensity. The difference between main-sequence stars, with a maximum equivalent width of Hy of about 17 A, and white dwarfs, with a maximum equivalent width of Hy of about 50 A, is the result of the much higher surface gravities of the white dwarfs. The fact that there is a corre-

Fig. 3 —^Variation in the half-width of H7 at a residual intensity of 0.9 with the temperature The curves represent the variation in half-width of the theoretical profiles of Hy as computed by Verweij. The solid curve is the variation for log g = 7.0; the dashed curve, for log g = 60; the dashed portion of the curve above the log g = 7 0 curve is the interpolated variation for log g = 7.5. latíon bétween equivalent width and color of white dwarfs indicates that the values of the surface gravity for these stars are similar. One check on the determination of the temperature and surface gravity by this method is available in the case of 40 Eri (B). If the value of 13000° is adopted for the temperature (Berger, Chalonge, Divan, and Fringant 1952) and a mass of 0.43 solar mass (Popper 1954), then, since the parallax is known, the radius and consequently the surface gravity may be calculated. These values give a log g = 7.7 According to Verweij^ theory, such a combination should give a half-width for Hy of 60 A, while the observed half-width is 63 A. COMPARISON OP THEORETICAL AND OBSERVED PROPILES Using this method of determining log g, we are assured that the theoretical and observed profiles will fit at one point. Figure 4 contains a comparison of the entire profiles for three of the white dwarfs whose log g values are close to 7.0. Because of the approxi- mations in the theory, the central parts of the theoretical lines are not valid ; therefore,

© American Astronomical Society • Provided by the NASA Astrophysics Data System 722 BEVERLY T. LYNDS we require a fit only in the wings. We are limited in the direct comparison by the number of theoretical profiles computed by Verweij. In some cases it was necessary to plot the two theoretical profiles which bracket the observed temperatures. The agreement between the observed and the theoretical profiles is very good, except for the case of HZ 43, possibly caused by the extreme shallowness of the line or possibly due to a very high surface temperature, as suggested by Greenstein (1954). The two sharp-line stars have temperatures well into the region where H~ plays an important role, so that this analysis should not be used. Although it has not been possible to compare directly the profiles of 40 Eri (B) (log g = 7.7) and L 1244-26 (log g = 8.4), the wings of the theoretical profiles may be calculated to a first approximation by the relation given by Verweij : AX ^ gO-«)/5. This has been done, and the comparison is given in Figure 5. The agreement is surprisingly good.

100 a

Fig. 4 —Profiles of the H7 line for L 1512-34 (B) (top) ; VR 7 (left), and He 3 (right). The dashed lines are Verweij’s theoretical profiles of H7 for the same temperatures and surface gravities of the white dwarfs. too a

Fig. 5.—^Profiles of the H7 line for o2 Eri (B) (left) and L 1244-26 (right). The dashed curves are Ver- weifs theoretical profiles of H7 for the same temperatures and surface gravities of the two stars.

Since Verweij has calculated the profiles of the first four Balmer lines, it is possible to repeat this analysis for Hô. Figure 6 gives a plot similar to Figure 3—the half-width of H6 at a residual intensity of 0.9 as a function of the temperature. The observed points indicate lower surface gravities than those found for H7. A comparison of the theoretical curves for Hô having the log g values determined from the H7 lines shows that the theoretical profiles of H5 are much stronger than the observed ones. It is possible, however, to bring these profiles into closer agreement by raising the con-

Fig. 6.—^Variation in the half-width of H5 at a residual intensity of 0.9 with the temperature. The curves represent the variation in half-width of the theoretical profiles of H5 as computed by Verweij. The solid curve is the variation for log g — 7.0; the dashed curve, for log g = 6.0.

5040 T Fig. 7 —Difference between observed and theoretical profiles of H5 at a AX of 60 A, as a function of 0.

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1957 Ap J. . .125. .719L radiation; however,thisenergymaybere-emitted inthesurroundingregionsofline, dwarfs withJ5—Vcolors from—0.05to+0.2;however,inviewofthepreceding con- main-sequence stars.Itis probablethatsuchcorrectionsshouldbeapplied toallwhite so thattheaverageintensity intheblueregionwouldstillbeaboutsame asthatof on theassumptionthatenergyabsorbedin the Balmerlinesappearsasthermal from 8800°to10000°andaloggchange7.2 7.3.Thesecorrectionswerecalculated peratures inwhitedwarfsthanmain-sequence stars. Thereisanindicationofthis, white dwarfisdependentuponthechoiceofeffectivetemperature.IfU—B B —Vcolorischangedfrom+0.13to+0.06,corresponding toatemperaturechange region ofthespectruminwhichHyandH5arefound. Thesetwolinestakeoutamaxi- perature ofmain-sequencestarswiththesameB—Vcoloraswhitedwarfs,thereisno mum ofabout100Ainthecasewhitedwarfs, as comparedtoabout40Aformain- strong Balmerlinesinwhitedwarfs.Thetransmission bandforthebluefiltercovers as seenbycomparingFigures1and2.Furthermore, evenifthecontinuousopacitiesare H~ becomesappreciable,andconsequentlyinthisregiontheopacitiesmaydiffer.This we findlogg’softheorder9or10.However,theoreticalprofilesforgand of themain-sequencestarshavingsameU—Bcoloraswhitedwarf),anentirely becoming approximatelyunity,whichisaboutthevaluefoundformain-sequencestars. from Hy.Furthermore,theobservedratioofequivalentwidthsHytoHôisabout sequence stars.Ifwemakeallowancefortheexcess absorptioninwhitedwarfs,the should causeamoresuddendecreaseintheBalmer-linestrengthwithdecreasingtem- opacity arisesfromhydrogen;but,fortemperaturesoftheorder10000°andlower, in theeffectivetemperature.Althoughitseemsreasonabletoadopttem- different effectivetemperatureisdetermined,owingtotheultravioletexcessofwhite color isusedinthesamemannerasB—V(adoptingeffectivetemperature equal. Forthesecalculations,onlytheredwardhalfofHôwasused,onassumption By raisingthecontinuum,centralintensitiesofHyandH<5aremadeapproximately the sameforwhitedwarfsandmain-sequencestars, acorrectionshouldbemadeforthe sequence stars.Forwhitedwarfs,attemperaturesgreaterthan10000°,thecontinuous dependence ofthecontinuousopacityweresameinbothwhitedwarfsandmain- dwarfs relativetothemain-sequencestars.Theeffectivetemperatures,basedon by theoverlapofwingsHyandH5,wefindlowervaluesloggfromH5than found fromthehalf-widthofHy.Thus,owingtodepressioncontinuumcaused half-widths ofH<$arecorrespondinglyincreasedandindicateloggvaluessimilartothose the onescorrespondingtologgandTvaluesderivedfromU—Bcolor. and theobservedprofilesofHôisfoundatAX=60Aplottedagainst0forthese maximum atabout0.54,andthendecreaseinwidthuntilthereisnooverlap0=0.7. theoretical justificationforthisprocedure.Thiswouldbevalidonlyifthewave-length stars. TheresultsaregiveninFigure7. To seewhetherthisisthecaseinwhitedwarfs,differencebetweentheoretical Hy. Thetheorypredictsthat,as0increasesfrom0.4to0.7,thewingsoverlap,reacha Verweij’s theoreticalprofilesforlogg=7.0andvariousfl’s.For0.4<00.6,the that itwasuninfluencedbyHe. wings ofHyandHôoverlap,consequentlythecontinuumisnotreachedbeyond T valuesderivedfromtheB—Vcolorarefoundtofitobservedprofilebetterthan U —Bcolors,areabout20000°.UsingVerweij’stheoryandthesehighertemperatures, 1.5 forwhitedwarfs.IfthecontinuumisraisedinregionofH5,ratiodecreased, tinuum oftheobservedprofiles.Thisisindeednecessary,ascanbeseenbyplotting 724 BEVERLYT.LYNDSj es) American Astronomical Society •Provided bytheNASA Astrophysics DataSystem Even thechoicebetweentwocolors,however,doesnoteliminateuncertainty It shouldbepointedoutthatthismethodofdeterminingthesurfacegravitya If anattemptismadetobringthetwoprofilesintoagreementatAX=60A, DISCUSSION WHITE DWARFS 725

sidérations, the magnitude of these corrections is unknown. Harris (1956) published his colors of 40 Eri (B) after this paper was submitted. The J3 — F color of +0.03 indicates a temperature of 10400°; however, we found that a temperature of 13000° best fits the observed profiles. THE CONTINUOUS-SPECTRA WHITE DWARFS Of the six remaining white dwarfs observed on this program, three are classified as continuous. Kuiper (1939) and Luyten (1952) have observed W 1516 and found it to have a continuous spectrum. No lines can be detected on the present spectra of this star. This is not the case for the other two stars. Luyten reported that LDS 678 (A) has a continuous spectrum, but Greenstein (1954) has found very broad and shallow hydrogen lines, similar to, but even weaker than, HZ 43. The three spectra obtained at the Crossley show no indication of hydrogen lines. There exists, however, the possibility of losing extremely weak features in the plate grain. There is an indication of a weak feature at about X 4462; this coincides with one of the Minkowski bands of the star Grw +70°8247. Minkowski (1938) found two broad, shallow bands centered at X 4475 and X 4135 in the spectrum of Grw +70°8247. Figure 8 shows the profiles of these bands, the mean of three Crossley spectra. The wave lengths indicated in the figure are only approximate;

Fig. 8 —Profiles of the absorption bands in Grw -f-70°8247 they were determined from microphotometer tracings; no attempt was made to measure the plate directly. Greenstein (1956) has also determined the profiles of these bands and has suggested that they may be the result of pressure broadening of He i. E. M. and G. Burbidge (1954) identify the Minkowski bands with Si n and Mg n. The intensity distribution of the continua of the “continuous-spectrum” white dwarfs is similar to the hydrogen-line stars, but their spectra are so obviously different that a separate classification must be maintained for them. Since these two types of white dwarfs are not readily distinguished from each other by their colors, the question arises as to why these stars are different spectroscopically. If a star were to evolve without any cataclysmic changes occurring during the evolution, then it would retain a surface layer of hydrogen, even if the interior were depleted of all its hydrogen. On the other hand, if, during the evolutionary sequence, a star explodes, then if the interior is void of hydrogen, even the surface layers would contain no hydrogen after the outburst. Such may be the case with the “continuous-spectrum” white dwarfs, which, on this hypothesis, are tentatively related with supernovae. The hydrogen-line white dwarfs would then be stars which have managed to reach the white-dwarf stage in a less spectacular way. This might help to explain the discrepancy between the frequencies of white dwarfs and of supernovae. LATE-TYPE WHITE DWARFS The final group of white dwarfs studied are of the later types, having van Maanen 2 as their prototype. Two spectra of L 745-46 (A) obtained at Lick show weak hydrogen lines as well as the characteristic H and K lines. Table 1 summarizes the data on the white dwarfs observed.

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1957 Ap J. . .125. .719L o L 997-21 L 1244-26 L 1512-34(B) L 870-2. “SA,” SelectedArea Oxf 4-25°6725 L 930-80 LDS 678(A). 40 Eri(B) VR 16t He 3 VR 7Î L 745-46(A) BD —7°3632 HZ 43. SA 29-130 W 1346 vMa 2.. R 198 Grw+70°5824 Grw+73°8031 R137 Grw -|-708247 W 1516. © American Astronomical Society •Provided bytheNASA Astrophysics DataSystem *“L” indicatesLuyten;“R,”Ross;“VR,”vanRhijn;“He,”Hertzsprung; “W,”Wolf;“HZ,”HumasonandZwicky; f Thehalf-widthofHyataresidualintensity090 t Hyadesmember Star* -f- 27 +0™34 +0 32 +0 56 +0 05 +0 12 + 01 4- 04 + 13 + 17 + 02 - 09 - 07 - 03 -0 21 - 10 - 06 - 02 B —V -0 55 -1 01 -0 97 -0^50 -1 13 -0 87 -0 90 -0 91 -0 84 -0 66 -0 56 -0 68 -0 58 U-B White Dwarfs TABLE 1 Continuous-Spectrum 39 47 41 46 H andK;possiblelinesalso 40 25 31 32 36 He Iinabsorption 37 41 52 Minkowski bands Weak featureatX4470 No linesinspectrum 27 24 Strong HandK;Felinesinultraviolet 12 13 5 Hydrogen-Line Helium-Line Later-Type Equivalent Widths 31 31 29 23 22 28 27 27 24 29 21 22 27 16 m 6 5 7 (A) 16 11 12 17 19 12 14 16 11 14 17 14 He 9 0 4 0 3 5 8 5 6 3 6 3 6 4 5 4 7 9 6 8 9 2 4 6 2 7 2 7 3 1 4 nr AXf (A) 45 48 47 63 80 22 62 64 63 25 52 60 63 64 73 72 10 WHITE DWARFS 727

Grateful acknowledgment is made to Professor Otto Struve, under whose direction this work was done, and to Dr. G. H. Herbig and Dr. N. U. Mayall, for their kind assist- ance with the observations. The author is also indebted to Dr. Su-shu Huang and to Dr. C. R. Lynds for many helpful discussions.

REFERENCES Berger, J., Chalonge, D., Divan, L., and Fringant, A. M. 1952, Contr. Inst. Ap. Paris, Ser. A, No. 128 Burbidge, E. M. and G. 1954, Pub. A.S P., 66, 308. Greenstein, J. L. 1956, Third Berkeley Symposium on Mathematical Statistics and Probability, 3, 11. Günther, S. 1933, Zs.f. Ap., 7, 106. Harris, D. L. 1956, Ap. J., 124, 665. Johnson, H. L , and Morgan W. W. 1953, Ap. J., 117, 313. Kuiper, G. P. 1933, Colloque international d'astrophysique: Les Novae et les naines blanches, Vol. 3. Luyten, W. J 1949, Ap. J., 109, 528. . 1952, ibid., 116, 283. Minkowski, R. 1938, Ann. Kept. Mount Wilson Obs., p. 28. Popper, D. M. 1954, Ap. J., 120, 316. Verweij, S. 1936, Pub. Amsterdam U., No. 5.