L I M I T S ON T H E 12C TO ~3C I S O T O P I C R A T I O IN T W O W H I T E

D W A R F S

G. W E G N E R

Department of Physics and Astronomy, Dartmouth College, Hanover, N.H., U.S.A.

(Received 22 February, 1984)

Abstract. A search for the molecular 12C13C isotopic bands in two white dwarfs is described. Spectroscopic observations of the two carbon band white dwarfs, BPM 27606 ( = 2153 - 5 t) and L 879 - 14 ( = 0435 - 08) have been obtained. These data have a resolution slightly better than 2 A~, higher than usually employed for white dwarfs and cover the Av = 1 vibrational Swan bands of the C 2 molecule where the isotopic shift is of order 8 A,. The isotopic bands have not been detected. However, upper limits to the 12C : J3C abundance ratio derived from the data yield Izc : 13C > 40 for BPM 27606 and ~2C : 13C > 8 for L 879 - 14. If these ratios are representative of the material in the interiors of the carbon band white dwarfs and taking the low apper limits on the N and O abundances relative to C, this is consistent with the carbon having been formed by the 3c~ process and not having undergone any subsequent mixing with H-rich material. In addition, the C z vibrational bandheads are blueshifted, most probably by pressure shifts. This shows that the employment of higher resolutions reveals additional physical effects in the spectra of the carbon band white dwarfs that may become important for interpreting the cool end of the helium rich white dwarf sequence.

1. Introduction

The origin of the white dwarf abundance classes, viz. the hydrogen- and helium-rich atmospheres, has still to be explained. The basic ideas with several individual modifi- cations are: (1) the current atmospheric abundances reflect details of the star's evolution prior to reaching the white dwarf stage, and (2) the present composition depends on how much interstellar material a white dwarf accretes. The subsequent proceses &convective mixing, downward diffusion, and element separation could also be important in the outer layers of these objects (cf. Vauclair etal . , 1979; Liebert, 1977; D'Antona and Mazzitelli, 1979). A resolution of this fundamental problem of the white dwarfs could, ultimately, lead to a better understanding of the late stages of stellar evolution.

One, hitherto, untried method for deciding about these two possibilities is the deter- mination of the isotopic ratio, 12C : 13C. In some cases, quite different ratios are to be expected, For example, accretion from the interstellar medium would yield 12C : 13C = 75 ~ 8 (Wilson etal . , 1981), with nearly solar proportions of N and O. However, if the 13C were produced by the CNO cycle, 12C : t3C could be as low as about 3 (Truran, 1973), and :if the carbon was produced by the 3e process, nearly pure 12C is to be expected.

For white dwarfs, 12C : ~3C is the only isotopic ratio that can be observed currently, because molecular features of N and O compounds do not appear in their spectra. Several of these objects do show Swan bands of C2, where in the case of the Av = + 1 vibrational bands near 24737, the isotopic shift is about 7.4 A, large enough to be detected. It is well known that these isotopic bands are easy to observe in the spectra of carbon stars (cf~ Climenhaga et al., 1977; and Yamashita et al., 1978) and comets (cf.

Astrophysics and Space Science 104 (1984) 347-355. 0004-640X/84/1042-03475 01.35. �9 1984 by D. Reidet Publishing Company.

348 G. WEGNER

Stawikowski and Greenstein, 1964) with ~2C : t3C varying about 2 to 20 with a majority of values smaller than 10 in the atmospheres of the former objects.

Up to the present, most white dwarfs have not been observed with resolution high enough to resolve the isotope shift. However, spectra of two Ca-band white dwarfs have been obtained with resolutions near 2 ,~, high enough to search for the 12C : ~3C isotopic bands. Both stars were chosen because they are among the brightest objects of this class and show relatively strong C: bands. Brief descriptions follow.

The object BPM 27606 ( = 2153 - 51) probably has the strongest Swan bands of any

known white dwarf. Wegner (1973) first observed the strong carbon features and Wickramasinghe and Bessell (1979) have published a low resolution scan of this star's

spectrum. The low velocity kinematical properties and d Me common proper motion companion are discussed in Wegner (1980). Atmospheric analyses by Koester et al.

(1982) based on the StrOmgren colors and Wegner et al. (1983) using visual and

ultraviolet spectra are in relatively good agreement, the latter finding: Tefr = 7000 K, tc = 7 x 10- s, and t N = t o -< 10 - 7 for BPM 27606, although the hydrogen abundance (tH = 7 x 10-3) derived from the presence of the 24300 CH band is somewhat higher

than usual. Numerous low resolution observations of the remaining white dwarf, L 879 - 14

(= LHS 194 = EG 41 = 0435 - 08) have been published including Greenstein and

Matthews (1957), Liebert (1977), Wegncr (1981), and Koester and Weidemann (1982). The Swan bands are not as strong in this star's spectrum as in that of the former, but

are more typical of the C2 white dwarfs. Atmospheric analyses have been carried out by Grenfell (1974), Koester et al. (1982)

and Wegner and Yackovich (1984), with relatively good agreement. The latter investi-

gators found that

T~er = 6600 K , t~-i < 2 x 10-3 ,

e c - - - 2 x 10 -6 and eN and t o < 1 0 -9

2. Observat ions

Portions of the spectra of the two carbon band white dwarfs have been observed with resolution high enough to resolve the laC12C and 12C13C bands in the vicinity of the Av = 1 transitions near 2 = 4700. These were derived from the two sources described

below. BPM 27606: Spectra were secured at the South African Astronomical Observatory

near Sutherland during 29 August to 4 September, 1978 using the image-tube spectro- graph attached to the 1.9 m reflector. Air-baked Eastman Kodak IIa,-O photographic plates and an EMI 9914 (1) three stage extended S-20 image intensifier were employed as the detector. In all, three spectra were obtained covering the wavelength interval 4200-5100 A centered on the Av = 1 bands. These had a plate factor of 30 A. mm 1 with a corresponding projected slit width of 0.6.3,_, were widened by 0.4 mm and required exposure times of 120 min. These spectrograms were subsequently scanned at

ISOTOPIC RATIO IN TWO WHITE DWARFS 349

the Max-Planck-Institut for Astronomie in Heidelberg with a Grant microdensitometer, converted to true intensity by means of calibration spectra of a stepped slit produced

by an auxiliary spectrograph on plates from the same box as the stellar spectrograms that had been developed with them.

In estimating the noise level of the final averaged spectrum of BPM 27606, it must be kept in mind that this quantity varies with wavelength. The raw spectrograms were well exposed in a region near their centers with the photographic density dropping to underexposure on each end. Thus, in the region 224400-4800 in the continuum, the signal to noise is about + 3 ~o, while near 24900 where the influence of the tail of the A V = 0 band can already be seen, this has dropped to about 4- 5 ~o. The resulting resolution is 1.6 A.

L 8 7 9 - 1 4 : Observations of this white dwarf were made on 21-29 November, 1982 with the intensified reticon scanner and the Mark II spectrograph attached to the 1.3 m telescope of the McGraw-Hill Observatory located on Kitt Peak. In all, 25 separate scans amounting to 22 hr of integration were used to construct this star's spectrum. In the data reductions, the sky contribution was subtracted, pixet to pixel variations eliminated by dividing with spectra from a continuous comparison lamp, and the instrumental response evaluated employing standard stars.

Near the center of these spectra, a total of abut 104 counts was obtained per channel,

but after data reduction, it appears that the signal to no e ratio achieved is close to + 2 .5~ in the continuum. These observations yielded a final resolution of 1.9 A as

judged from the widths of comparison lines.

3. Evaluation of the 12C to laC Ratio

3.1. FEATURES OBSERVED IN THE SPECTRA OF BPM 27606 AND L 879 - 14

The resulting spectral scans of BPM 27606 and L 879 - 14 in the wavelength interval 224450-4925 are shown in Figure 1 where the vibrational bandheads of the 12C12C

molecule can be seen. For this investigation, laboratory wavelengths and intensities of the 12C12C have been taken from Pearse and Gaydon (1976) and isotopic shifts for ~2C13C were evaluated using the relation for the vibrational isotopic shift and reduced

molecular mass (Herzberg, 1950). The spectra have been normalized to the continuum defined as a straight line connecting the points at 224450 and 4800.

In both cases, there is no evidence for the 12C13C bands, which if present should be seen as small depressions displaced redward by approximately 7.4 A.

Table I lists the observed wavelengths and central depths for the kv = + 1 vibrational bandheads observed in the spectra of BPM 27606 and L 879 - 14 and compares them with the laboratory data given in Pearse and Gaydon (1976). In the third column, I is the laboratory intensity according to Pearse and Gaydon (1976) and the Ra are the depths of the stellar bandheads relative to the continuum. These data show evidence for substantial blueshifls in the bandheads. For BPM 27606, the average is - 4 A while L 879 - 14 has quite large values near - 30 ,~. Examination of lower resolution observa- tions of L 879 - 14 and the quite similar star W219 confirm these wavelengths.

350 G. WEQNER

1.0

0.8

0.6

'-0.4 i11

t -

>, . -

" i .O

0.9

O.B

0.7

!

t l ~ i , * l t l i , l i , , I I , l ~ Li

L879-14

, I , , , , I [ , ~ , I , ~ , a [ ~ , L L I

4 5 0 0 4 6 0 0 4700 4800 4900 w a v e l e n g t h (~)

Fig. 1. Portions of the observed spectra of BPM 27606 and L 879 - 14 in the region of the Av = + 1 bands. Both scans have been normalized to the continuum at relative intensities of 1.0. Laboratory wavelengths for some of the molecular 12C 2 and 12C~3C features in this portion of the spectrum can be found in Table I

and in Figure 2.

TABLE I

Comparison of laboratory and observed bandheads in the spectra of BPM 27606 and L 879 - 14

U', V" ~Lab I BPM27606 L 879 - 14

Z. R z )~. Rz

1, 0 4737.1 9 4732 0.64 4709 0.18 2, 1 4715.2 8 4712 0.72 4680 0.28 3,2 4697.6 7 4692 0.68 4671 0.29 4~ 3 4684.8 4 4682 0.63 - - 6,5 4680.2 1 . . . . 5, 4 4678.6 2 4675 0.64 - -

ISOTOPIC RATIO IN TWO WHITE DWARFS 351

Most bandheads in Table I are well known from earlier lower resolution studies (cf. Liebert, 1977). Specifically, in the hv = 1 band of BPM 27606, the noise of the spectrum as normalized to the continuum is expected to be about _+_ 5~o, or + 0.02 in relative intensity, while the three strongest depressions have depths of at least 0.10 in relative intensity. Consequently, the reality of these features in the spectra of white dwarfs appears to be well established.

It is plausible that pressure shifts account for this. Since the atmosphere of BPM 27606 has the higher hydrogen content and Tee r, this produces lower atmospheric pressures, Pg, compared to L 8 7 9 - 1 4 . For a Rosseland depth of ~ = 5, model atmospheres with the parameters given above yield Pg = 1.1 x 109 and 4.9 x 109 dynes cm - 2 for BPM 27606 and L 879 - 14, respectively. Also, since the Cz

bands of B PM 27606 are considerably stronger, they should be representative of optical depths nearer the top of the atmosphere than in the case of L 879 - 14. Liebert and Dahn's (1983) interpretation of the features near 22 5000 and 4400-4700 in the spectrum of the cooler (T~f r = 5500 K) white dwarf LHS 1126 as blue pressure shifted Swan bands strengthens this conclusion. Large Zeeman-shifts seem to be ruled out at least in the case of L 879 - 14 by the 60 kG upper limit published by Angel et al. (1981) and such large Doppler shifts seems even more unlikely.

The possibility of using pressure shifts and observed band profiles as a means of probing the stratification of carbon in the white dwarf atmospheres immediately suggest itself.

In principle, the estimated 1 2 C : 13C can be affected by blending from the NH2 bands

near 24718. However, for helium-rich white dwarfs like BPM 27606 and L 789 - 14, this objection is invalid due to the strongly non-solar abundance ratios. As discussed in the introduction, H and N appear reduced by factors of order 10- 3 and 10 - 7 to 10 - 9

or more, respectively, which produces a vanishingly small amount of NH 2 in the atmospheres of these white dwarfs.

At higher resolution, additional details appear in the profiles of the Swan bands that need to be accounted for theoretically. Figure 2 compares the observed and calculated Av = + 1 bandhead region for C 2 in the spectrum of BPM 27606. The computed profile comes from Wegner et al. (1983) and shows how the models have difficulties in matching the depth and sharpness of the bandheads and do not account for pressure shifts when observed at higher resolutions.

Earlier studies of the C 2 white dwarfs (Grenfell, 1974; Wegner and Yackovich, 1983; Koester et al., 1982) used lower resolution data and employed the smeared line approxi- mation (Golden, 1967), which gave suitable agreement with the observations. As far as the derived carbon abundances are concerned, this method was sufficient, but at higher resolution when looking for the 12C13C bands, this approach does not reproduce the fine details of the bandheads.

Due to these difficulties, and in order to preserve the finer details observed in the C2 bands observed in the spectra of BPM 27606 and L 879 - 14, the upper limit to the 12C : 13C ratio has been estimated employing a semi-empirical method for the present exploratory study. Calculations taking the individual rotational band structure into

I'0

I I T ~ T ~ T ~

0.8

= m

e- @ *"0.6 c

. m

> = m

_ o.4

0"2

352 G. WEGNER

�9 i

�9 k I i " d

o, 0 4500 46oo 4zoo 48oo

w a v e l e n g t h

Fig. 2. Comparison between the empirical and calculated Av = + 1 band of BPM 27606. The observed (solid curve) is the same as Figure 1 and theoretical band structure (dashed curve downward displaced by 0.2 units) was computed, emplying the smeared line approximation as described in the text. A ~2C : ~3C isotopic ratio of 4 was used and dots mark the 12C13C bands. The greater sharpness of the observed

bandheads is noticeable. The atmospheric parameters given in Section 1 have been employed.

account are underway and when combined with additional new observations, should

further help to elucidate these problems.

3.2. THE 12C : 13C ISOTOPIC RATIO IN THE ATMOSPHERE OF B P M 27606

Inspect ion of Figure 1 showed no evidence for the ~2C13C features at the expected

positions in the spectra of BPM 27606 and L 879 - 14. Consequently, in order to make

an estimate of the upper limit to their strength, it was assumed that the observed

bandheads are due to 12C 2. A smooth curve was then drawn through the spectra and

ISOTOPIC RATIO IN TWO WHITE DWARF'~ 353

the band's absorption coefficient K~ estimated from the Minnaert's formula

1 I 1

R~ tc~ R c

where R;o and R c are, respectively, the observed depth at wavelength 2 and the limiting central depth of a line. Here, Rc was judged to be 0.78 from the depth of the (0, 0) band in BPM 27606. With a satisfactory choice of Re, Minnaert's formula gives a good approximation to line profiles, independently of the line formation mechanism (UnsOld, 1968) and has been employed in studies of the 12C : 13C isotopic ratios in carbon stars (cf. Climenhaga, 1960; or Climcnhaga et al., 1977).

With an estimate of ~ , it was then assumed that the Izc13c bands have an identical absorption coefficient, except displaced redward by the isotopic shift, the total absorp- tion coefficient then being their sum. From this, a series of band profiles was constructed with different ratios of 12C : 13C. Intercomparison of these band profiles with those from the model atmospheres show that the relative strengths of the 12C 2 and their corres- ponding 12C13C bands are in good agreement, thus providing a check on the suitability of this approach.

In order to more easily distinguish the weaker I2C13C bands against the strong

* 0 . 2

0 . 0

\ ,,r

,'," - 0 . 2 i

- 0 . 4

' I I I i I I

B P M 2 7 6 0 6

. AAA �9 ., ...-~ -.. \-~/ .. . . . \ / ..

'. . : v " " : "'" "" "v" ..'" V \ _ ",..." '. ~ I .- . . . . . : ." _

( 3 , 2 ) ( 2 , 1 } ( 1 , 0 1

. . . . . . . . 4 --~--4. 8 0

. . . . 2 0 ~ o b s e r v e d

. . . . 4 0

I I I I I I 4 7 0 0 4 7 2 0 4 7 4 0 4 7 6 0

Fig. 3. Comparison between the observed and computed residual spectra of BPM 27606 for the Av = + 1 band of C 2 using a range of ~2C : ~3C ratios. The 12C 2 band pattern has been removed by dividing with a

smoothed profile as described in the text.

354 0. WEGNER

observed bands, it is instructive to first remove the large amplitude background structure arising from the 12C 2 bands to help make any contribution from 12C13C more apparent. This was done by dividing the observed and calculated profiles by the smoothed one as shown in Figure 3. The fluctuations in the observed scan of BPM 27606 are taken to represent the noise in the region of interest, which has a mean value of + 0.03. For 12C: ~3C as low as 4, the diagram shows that the isotopic bands would be over- whelmingly visible and for 12C : ~3C = 20, they would still be easily seen. A value of 40 should still produce observable bands, but 80 or higher should not be distinguishable from the noise. Therefore, for BPM 27606, it is concluded that ~2C : ~3C > 40.

In the case of L 879 - 14, the situation is less favorable even though the signal to noise ratio is higher. Using the same procedure as above, only 12C : 13C > 8 can be ruled out.

Primarily, this is a result of the weakness of the C2 features and lower carbon abundance in the atmosphere of L 879 - 14, but were the pressure shifts in the C2 bands better understood, an improved estimate of the 13C content could perhaps be obtained from

their wavelengths.

4. Conclusions

Observations of the carbon and band white dwarfs BPM 27606 and L 879 - 14 reported here, bring two new facts about the spectra of the C2 Swan bands in degenerate stars: (1) Pressure shifts toward the blue can become important, particularly in modifying the bands of the coolest C2 white dwarfs. (2) There is no evidence for 12Ct3C bands in the atmospheres of these two objects. In all of the following, it has been assumed that the small difference in molecular weight between ~2C~3C and 12C a is insufficient to gravi-

tationally separate the two species. For BPM 27606, the large ratio, ~2C : 13C > 40 rules out the possibility that the

carbon in its atmosphere was produced in the same way as that in the carbon stars and some red giants where 12C : I3C values of order considerably below 20 are found (cf. Dominy etal., 1978; Richer etal., 1979). For the carbon stars in particular, the ~3C enhancement is explained by invoking processes that mix a2C rich material from the star's core into outer hydrogen-rich nuclear burning shells during the asymptotic giant branch phase (cf. Iben, 1981; Sackmann etaI., 1974; Scalo and Ulrich, 1973).

The range of possible stellar evolutionary processes producing a white dwarf is large. Estimates of the upper mass limit for white progenitors run from 5 M o (Wegner, 1980) to as high as 811//o (Weidemann and Koester, 1983). In order to achieve a core mass of near 0.6 M o, the white dwarf has had to have undergone substantial amounts of mass loss that removed the envelope and left the core. In that case, the processes producing carbon stars may not provide a directly relevant guide. Instead, the CNO abundances in the cores of evolved stars after the He-burning stage should be considered. Under those conditions, the 3~ process would be expected to produce mostly laC. This would also be consistent with the low abundances of N and O relative to C, where C : N and C : O are both larger than about 10 (Bues, 1979; Wegner and Yackovich, 1983; Yackovich, 1982), compared to solar values of C : N = 4.8 and C : O = 0.6 (Ross and

Aller, 1976).

ISOTOPIC RATIO IN TWO WHITE DWARFS 355

This preponderance of C over N and O lends weight to the argument against an interstellar origin for the carbon in these white dwarfs, for the current upper limit on 1;C : ~3C alone cannot eliminate this possibility. If future observations showed that I2C : 13C is considerably larger than 78, a much stronger demonstration could be made about the origin of carbon in the white dwarfs.

Acknowledgements

This work was partially supported by the National Science Foundation, grants AST 80-02677 and AST 82-19474. The author wishes to thank Drs John McGraw and David Dearborn for valuable discussions, and Harmut Schulz for aid in reducing the photographic data.

References

Angel, J. R. P., Borra, E. F., and Landstreet, J. D.: 1981, Astrophys. J. Suppl. 45, 457. Bues, I.: 1979, in H. M. Van Horn and V. Weidemann (eds.), 'White Dwarfs and Variable Degenerate Stars',

IAU Colloq. 53. Climenhaga, J. L.: 1960, Publ. Dominion Astrophys. Obs. 11, 307. Climenhaga, J. U, Harris, B. L., and Holts, J. T.: 1977, Astrophys. J. 215, 836. D'Antona, F. and Mazzitelli, I.: 1979, Astron. Astrophys. 74, 161. Dominy, J. F., Hinkle, K. H., Lambert, D. L., Hall, D. N. B., and Ridgway, S. T.: 1978, Astrophys. J. 223,

949. Golden, S. A.: 1967, or. Quant. Spect. Rad. Transf 7, 225. Greenstein, J. L. and Ma~:thews, M. S.: 1957, Astrophys. J. 126, 14. Grenfell, T. C.: 1974, Astron. Astrophys. 31, 303. Herzberg, G.: 1950, Spectra of Diatomic Molecules, Van Nostrand Book Co., New York. Iben, I.: 1981, Astrophys. J. 246, 278. Koester, D. and Weidemann, V.: 1982, Astron. Astrophys. 108, 406. Koester, D., Weidemann, V., and Zeidler, E.-M.: 1982, Astron. Astrophys. 116, 147. Liebert, J.: 1977, Publ. Astron. Soc. Pacific 89, 78. Liebert, J. and Dahn, C. C.: 1983, Astrophys. J. 269, 258. Pearse, R. W. B. and Gaydon, A. G.: 1976, The Identification of Molecular Spectra, Chapman and Hail,

London. Richer, H. B., Olander, N., and Westerlund, B. E.: 1979, Astrophys. J. 230, 724. Ross, J. E. and Aller, L. t:I.: 1976, Science 191, 1223. Sackman, I.-J., Smith, R. L., and Despain, K. H.: 1974, Astrophys. J. 187, 555. Scalo, J. M. and Ulrich, R. K.: 1973, Astrophys. J. 183, 15l. Stawikowski, A. and Greenstein, J. L.: 1964, Astrophys. or. 140, 1280. Truran, J. W.: 1973, Proc. Conf. Red Giant Stars, Indiana University Press, Bloomington, p. 434. Uns61d, A.: 1968, Physik der Sternatmosphiiren, Springer-Verlag, Berlin, 3rd edition. Vauclair, G., Vauclair, S., and Greenstein, J. L.: 1979, Aaron. Astrophys. 80, 79. Wegner, G.: 1973, Monthly Notices Roy. Astron. Soc. 163, 381. Wegner, G.: 1980, Astron. J. 86, 264. Wegner, G.: 1981, Astrophys. 3". 245, L27. Wegner, G. and Yackovich, F. H.: 1983, Astrophys. d. 275, 240. Wegner, G. and Yackovich, F. H.: 1984, Astrophys. J. (in press). Wegner, G., Schulz, H., and Yackovich, F. H.: 1983, in preparation. Weidemann, V. and Koester, D.: 1983, Astron. Astrophys. 121, 77. Wickramasinghe, D. T. and Bessell, M. S.: 1979, Monthly Notices Roy. Astron. Soc. 188, 841. Wilson, R. W., Langer, W. D., and Goldsmith, P. F.: 1981, Astrophys. 3". 243, L47. Yackovich, F. H.: 1982, Ph.D. Thesis, Pennsylvania State University, Pennsylvania. Yamashita, Y., Nariai, K., and Norimoto, Y.: 1978, An Atlas of Representative Stellar Spectra, John Wiley

and Sons, New York, p. 124.