Baltic Astronomy, vol. 7, 183-196, 1998.

BPM 37093: THE WAY TO THE INTERIOR OF CRYSTALLIZED

A.Kanaan1'2, S.O.Kepler2, O.Giovannini2·3, D.E.Winget4, M. Montgomery4 and A. Nitta4 1 Departamento de Matemätica, Universidade Federal de Santa Maria, Cidade Universitdria, Camobi 97119-900, Santa Maria - RS, Brazil 2 Instituto de Fisica, Universidade Federal do Rio Grande do Sul, 91501-970, Porto Alegre - RS, Brazil 3 Department of Physics and Space Sciences, Florida Institute of Technology, Melbourne, FL 32901, U.S.A. 4 Astronomy Department, University of Texas at Austin, Austin, TX 78712, U.S.A. Received January 27, 1998.

Abstract. BPM 37093 is a ZZ Ceti type of the mass ~ 1.1 MQ. Its temperature 11 000 K) and high mass imply that it should be crystallized throughout most of its core, the exact fraction depend- ing on the core composition. BPM 37093 is the first object where the results of crystallization theory can be probed observationally. If the star is crystallized, its pulsation spectrum should differ signifi- cantly from non-crystallized pulsating stars. Very high signal-to-noise high speed photometry will enable us to detect very low amplitude (

1. INTRODUCTION Since 1960 (Kirzhnitz 1960, Abrikosov 1960, Salpeter 1961) most astronomers have agreed that cool white dwarfs must crystallize. This process would start when the electrostatic interaction between the ions becomes much larger than the thermal energy. This conclu- sion is based on such well known physics that it has become widely accepted without ever having been tested. In measuring the function of white dwarfs there is hope of seeing a signature of crystallization. Crystallization is a phase transition which has a latent heat associated, therefore the cooling of a crystallizing should be slowed down. This should in turn imply a higher space density of white dwarfs at the corresponding luminosity (Wood 1990). However, the current lumi- nosity function is not good enough to show such a bump, which is expected to be small. More accurate luminosity functions should exhibit the bump, if it exists. Surveys like the Texas white dwarf survey (cf. Claver 1994) will increase the number of known white dwarfs by a factor of 10. When this survey is completed, a definitive answer about the existence of a bump will be reached. In 1987, Winget et al. used the white dwarf luminosity function to measure the age of the Galactic disk in the solar neighborhood. As pointed out by Mestel (1952), thanks to the lack of energy genera- tion in white dwarfs, there is a simple mapping between and ages. The connection between the two quantities comes from the cooling rates. These rates are, however, essentially theoretical val- ues. One excellent way of verifying the theoretical rates of cooling is the comparing them to the rates of period change for pulsating white dwarfs (Winget 1981). As these stars cool, their pulsation periods become longer, and the observational task is to measure the speed of this change. This is, of course, not a direct measure of cooling but is an independent way of computing it based on an observed quantity. The connection between the rate of period change and the cooling rates also depends on the I index of the pulsation mode. De- termination of I can be achieved through multicolor photometry by comparing the optical to UV amplitude as described by Robinson et al. (1995). The ZZ Ceti star G117-B15A provides us with obser- vational constraints on these cooling rates (Kepler et al. 1998). A value of Ρ = (1.2 ± 2.9) x 10~15 s/s has been found by Kepler et al. This number is consistent with the theoretical models of Bradley et al. (1992), and proves that G117-B15A is not currently in the BPM37093: the way to the interior of crystallized stars 185 phase of Debye cooling, where, owing to the rapid cooling, pulsation periods should change quickly. This is a reassuring result but it is no surprise. We do not expect a star like G117-B15A (Teff=11620 K, M= 0.59 MQ, Bergeron et al. 1995) to be even starting to crystal- lize. The two instability strips, DBV and DAV, will someday provide us with the cooling rates. However, both probe the same phase of cooling, namely the Mestel cooling phase. BPM 37093 is a ZZ Ceti star (Kanaan et al. 1992) of high mass (1.09 MQ, Bergeron et al. 1995; 1.01 M0, Giovannini 1996). Such massive white dwarfs are subject to much higher pressures in their core, and it is expected that for 1.0 MQ white dwarf crystallization starts at temperatures well within, or even hotter than, the ZZ Ceti instability strip (Wood 1990). In this paper we discuss the observed properties of BPM 37093 and explain why we consider it a special object. Then we review the evidence for its being crystallized and explain what can be learned from this object and any other high mass ZZ Ceti star to be identified in the future.

2. BPM 37093 AND THE OTHERS Before we get into a more detailed description of pulsations in BPM 37093, we want to put it in the context of other ZZ Ceti stars. Its light curve is dominated by a mode of period close to 600 s and of very low amplitude, of the order of 5 mmag. Among the DAVs, a clear correlation between temperature, am- plitude and period is observed: the cooler the star, the longer its pulsation period and the larger its pulsational amplitudes. Fig. 1 (based on data from the literature and from WET observations pre- sented by Clemens 1994) shows this in three panels: (a) temperature vs. period, (b) total power vs. temperature, (c) total power vs. pe- riod. These dependencies are understood as a consequence of the movement of the partial ionization zone of into deeper lay- ers of the star caused by evolutionary cooling (Winget 1981, Winget et al. 1982, Clemens 1994). As the partial ionization layer moves in deeper, the thermal timescale becomes longer and the amount of energy available for driving increases correspondingly. BPM 37093 is the only star which deviates significantly from the general trends shown on these plots. According to Bradley & Winget (1994), there should be an in- stability strip for each mass of ZZ Ceti. The more massive stars 186 Α. Kanaan, S. 0. Kepler et al.

I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I 1

·· a) £ 4 06 - t I - • \ • · - jj 4.08 • • · • • - • · - • · -I? 1 I , 1 , , , , .. 2 21 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 Log Weighted Mean Period (sec) π—I—I—I—I I I I—I—|—I—I—I—I J I—I—I—I—|—Γ-!—I—I—[—I—I—I—I—Γ~1—ΓΊ—I | I—Γ~Ι—I—[—ΓΤ—I 1 |—I—Γ~

1 • • • • I ' • * • I • • • ' I ' • • ' I ' ' • ' I • ' ' ' I ' • • • I • ' • • I • ' ' ' I ι ι ι I ι t ι ι - 3.1 3.2

Fig. 1. The period-amplitude-temperature relationship shown in three panels: (a) displays temperature against periods, (b) displays to- tal power against temperature and (c) shows total power against period. BPM 37093 is indicated by the star symbol. would start pulsating at higher temperatures and the less massive ones at lower temperatures. This would probably lead to a similar effect on the red edge, namely, the more massive ones would stop pulsating earlier than the less massive. However, from their models, they were unable to make such a prediction. Giovannini et al. (1998) have shown that the effect predicted by Bradley &; Winget (1994) for the blue and red edges can be seen in their extensive survey of photometric variability and temperatures of white dwarfs in and out of the ZZ Ceti instability strip. BPM 37093 defines the red edge of their 1.0 M© mass bin. While the temperature and mass of this star can always be ques- tioned, its pulsational period and amplitudes are measured quanti- ties, rather than derived (as the temperature and mass). One could argue that the deviation of BPM 37093 in Fig. lb is due to uncer- tainties in its temperature and/or mass determination. The plot (c), however, depends only on the period and amplitude, and BPM 37093 is a clear outlier on that plot as well. BPM37093: the way to the interior of crystallized stars 187

Independently of its temperature value, BPM 37093 does behave very differently in the amplitude vs. period plot. Since the star has a long period and a low amplitude and is close to the red edge of the observed instability strip, we may think that its pulsations are being shut off. However, it is known that other red edge ZZ Ceti stars pass through phases of low amplitude in their pulsations and then come back to high amplitude (Kleinmann 1995), which is their normal state. As the only data on BPM 37093 available were the data from the discovery paper (Kanaan et al. 1992), we decided to reobserve this object. Our first priority task is to verify if the star is a permanent, not temporary, low amplitude pulsator.

3. OBSERVATIONS We observed BPM 37093 for four hours in 1995 using the CTIO 1.5 m telescope with the Texas three-channel photometer. Cloudy skies prevailed during the rest of our five night observing run. We reobserved BPM 37093 in April 1996 for ten nights using the 0.9 m telescope at CTIO. This time we used one of the Cassegrain Focus CCD cameras with the Β filter. A filter is used to minimize the effects of differential extinction as well as the effects of seeing disk variations for stars of different colors. The Β filter was used mainly because of consistency: we have observed this star before with blue sensitive photomultipliers without filters, whose spectral response is roughly equivalent to the Β filter, and have observed all other pulsating white dwarfs with the same kind of equipment. Another reason for choosing the Β filter is that the amplitude of pulsations increases at shorter wavelengths (Robinson et al. 1982). We used a Tektronix 10242 chip and binned the pixels 2x2 resulting in pixels of 0.8 arcsec in size. The integration time was 20 s and the cycle time was 25 s resulting in a duty cycle of 80%. Such a high efficiency is possible only due to the use of four amplifiers which share the job of reading the whole chip simultaneously. From the very little data collected before, we had an impression that pulsations on this object were stable. We had observed it twice in 1991, once in 1992 and once in 1995. On every occasion we could gather only a few hours of data on different nights; these data showed two low amplitude modes having periods of about 614 and 560 s (see Fig. 2). We were in surprise. 188 Α. Kanaan, S. Ο. Kepler et al.

1 1 III! I I I I I 111 = .004 L' 199Ϊ .003 .002 .001 WfWiYftvwWYfflf f , Mmmim 0 = " 1 f III 1 Vffp1 1 1 I ^1 III: .004 1992 .003 .002 .001 _ 0 |.004 003 1.002 Ε .001 < ijfpi 0 bill Γ ι 1 1 1 1 1 1 I .004 199e .003 .002 .001 »^UiVUtwvMViMMLi^JWlMl J 0 Γ Γ Ί - 1 If la—r ι τ ι' ιJ .004 199Ϊ .003 .002 .001 0

Frequency (cycles/day)

Fig. 2. The Fourier transforms of our data for each year.

3.1. Analysis of the 1996 data In Fig. 3 we show the daily Fourier transforms. It is immediately apparent that something is happening to the pulsations. During the course of these ten nights, three pulsation modes can be identified: at 560 s (1.766 mHz), 583 s (1.716 mHz) and 614 s (1.634 mHz). The first and the last modes have been seen before and the 583 s mode is new. Even at the low resolution of our transforms, we should have seen it. Significant changes in amplitude and phase are seen in all of the identified modes. Even more impressive is the total BPM 37093: the way to the interior of crystallized stars 189 disappearance of pulsations after May 1. In our last night on May 2 we reobserved BPM 37093 and again found absolutely no varia- tions down to a limit of 1 mmag. Had we observed it for the first time on one of those two nights, we would have classified it is as a non-pulsating star. Note that McGraw in 1979 had classified this ob- ject as non-pulsating. However, his observations were not sensitive enough to have detected the 4-5 mmag modulations we normally see in this star.

BPM37093 -1996

:i 1 1 I 1 II | 1 1 1 | 1 II | II ι::ι ι ι | ι ι ι | ι ι ι | ι ι ι | ι ι ι: .004 .004 .003 .003 .002 .002 .001 .001 0 S 1 1 1] \ 1 1 II 1 1 1 II 1 1 1 ; 0 .004 .004 .003 .003 .002 .002 .001 .001 Hlllllllllllllllllllll l (Jll[llll|llll|llll|lll l 0 : I 1 1 1 1 I ΤI ιI ιI ιΫ'ΐ'Υ^κ'ΚϊΜΜII I I Τ II 1 1'ί1 0 .004 .004 .003 .003 .002 .002 α .001 .001 |IM |IIII|IMI|IIII|III I Ε ^^^Jmiliii i i-f/V-rV νΆ/ν ι ι iSA^rw-Jv^yV^n < 0 1 1 1 1 1 1 1 1 1 0 .004 !_' ι ' ι • • ι • ι .004 .003 .003 .002 .002 .001 .001

ν/ IUIjllll|lllljmi|lll l liuftlllllllllllllllll ! 0 ι ι ι ι ι ι! ΓτΎΜ 'Ν'Μ* :il 1 I 1 1 1 I 1 II | 1 1 1 I 1 I ι:0 .004 .004 .003 .003 .002 .002 .001 .001 0 ii^N^/NLw ι W V»i ι l/V %THMV r-ä 0 100 120 140 160 180 200 12014 0 160 180 200 Frequency (cycles/day)

Fig. 3. The daily Fourier transforms during our 1996 run on BPM 37093.

In Fig. 3, four modes are easily identifiable for the 1996 data set. Looking at the daily Fourier transforms we see that the 1.766 mHz mode is present from April 24 to April 29. The 1.716 mHz mode is present from April 25 till April 30. On April 30 a mode, compati- ble with being the same 1.634 mHz mode seen in previous years, is present and it disappears the next day. On May 1, there is a power in the same frequency region but the center of the peak is not at any frequency detected before. The next step in our analysis is a close look at the behavior of the phases and amplitudes of the two main modes. In Fig. 4a 190 Α. Kanaan, S. Ο. Kepler et al. we show the phase as a function of time for the 1.766 mHz mode. The phase is clearly shifting during the first four days and seems to reach a stable value on the fifth day and then turns back down. The amplitudes also vary during these four days but the change is not as clear (see Fig. 4b). We also present the phases and amplitudes for the 1.716 mHz mode in Figs. 4c and 4d. Neither of these plots can be explained in terms of simple beating between close modes. In particular, beating is unable to explain the disappearance of the mode for several days. If beating were the case, we should, first of all, see these modes in the Fourier transform since we have a long enough data set; what is more, the amplitude and phase changes should be correlated. In 1997 we obtained data over five nights with the 1.6 m tele- scope at the Laboratorio Nacional de Astrofisica in Itajuba, Brazil. The weather did not allow us to obtain enough data for a detailed analysis, as with the 1996 CTIO data set. However, we confirm the star was pulsating each of the five nights we could observe it for a few hours. The resulting Fourier transform for the 1997 data set is presented in Fig. 2.

4. A POSSIBLE EXPLANATION FOR THE UNUSUAL PULSATION PROPERTIES OF BPM 37093 We have shown that BPM 37093 is an outlier in the period- amplitude-temperature relation and that its pulsations are unusually unstable in a short timescale. Let us explore why this might happen.

4-1. Crystallization

According to Bergeron (1995), the mass of BPM37093 is 1.1 M©; similar results are obtained by Giovannini et al. (1998) using an in- dependent data set and model atmospheres. According to the evo- lutionary models of Wood (1990), this implies a crystallized core for any assumed internal composition heavier than . The per- centage of core crystallization depends on the internal stellar com- position. In Fig. 5 (based on models of Wood 1990) we show how much crystallization is expected for different (possible) combinations of the physical parameters of BPM 37093. Fig. 5 shows that BPM 37093 core must be at least 10% crys- tallized if its core composition is pure carbon and up to 90 % if its BPM 37093: the way to the interior of crystallized stars 191

I I I I I II I I I I I I I I I I II 1I I 5 I I I I I II I I I I I I II Ι ι ι ι ι I

i c> d)

.8 4 -

.6 | 3 Ε 1 4 ε 2 - ί Η i

I .2 1 -

ι ι ι I ι • ι I ι ι ι I ι ι ι I ι • ι I ι I ο Q I I I I I I I I I I I I I I I I I I I I I 198 200 202 204 206 208 198 200 202 204 206 208 JD(-2450000) JD(-2450000>

Fig. 4. (a) Phase versus time for the 1.766 mHz mode. Only the first six nights are on this plot because this mode disappears in the last four nights, (b) Amplitude versus time for the 1.766 mHz mode, (c) Phase versus time for the 1.716 mHz mode. We have plotted data from the second night till the seventh. For other nights this mode was not present, (d) Amplitude versus time for the 1.716 mHz mode. 192 Α. Kanaan, S. Ο. Kepler et al.

BPM37093 and Crystallization 30000

25000

20000

15000 -

10000

5000 1.05 1.1 1.15 1.2 1.25 1.3 Mass (solar masses)

Fig. 5. The rectangle in the center represents the range of masses and temperatures found for BPM 37093: the lower right corner is the determination of Bergeron et al. (1995), the top left corner is the determi- nation of Giovannini (1996). The formal temperature uncertainties from each author are much less than their discrepancies. The lines represent the limits where crystallization reaches 10 % (top line) and 90 % (bottom line). The continuous line is for an oxygen core, and the long-short dash line is for a pure carbon core. core is pure oxygen. For heavier compositions, the core should be entirely crystallized. At 1.0-1.1 MQ BPM 37093 is near the limiting mass for hav- ing an O/Ne core (Iben 1991, Garcia-Berro 1997a). Note that Dominguez et al. (1996) have shown that this approximation is valid for non-rotating stars while rotating stars should have higher limit- ing masses for O/Ne core. If the core is really composed of a mix of Ο and Ne, then BPM 37093 should be more than 98% crystallized. If this star is completely crystallized, its pulsation spectrum must be quite different from other non-crystallized ZZ Ceti stars, since a frac- tion of the outer layers, which takes part in the pulsation motions, will be crystallized. No detailed models for that kind of stars exist BP Μ 37093: the way to the interior of crystallized stars 193 yet, but Winget et al. (1997), and the only handle on the problem in the near future is to observe BPM 37093 and find as many pulsation modes as possible in order to compare its properties to those of other known pulsators. Another revealing way of studying this object would be the mea- surement of the rates of period change of its pulsation modes. It is expected that cooling rates would be greatly accelerated when the star enters the Debye cooling phase (Isern et al. 1997, Garcia-Berro et al. 1997b). We should in principle be able to distinguish between the phase of Debye cooling and the two other cooling regimes which are likely at this stage. Normal cooling is the phase in which the star spends most of its life and slowly radiates its internal heat away into space. After the normal cooling, the star will start crystallizing, and as the latent heat of crystallization is released, the temperature at the crystallization front stays almost constant (Isern et al. 1997); above the crystallization front, the star continues to cool normally, and the net effect is a very small decrease in the cooling rate. Our recent results show, however, that getting that kind of in- formation is going to be harder than we previously expected. For measuring Ρ it is imperative to have a stable mode. For G 29-38 we have seen that some of its modes come and go while others are sta- ble (Kleinmann 1995); the unstable modes are the highest amplitude modes, around 50 mmag, while stable modes have amplitudes of only a few mmag. If BPM 37093 is similar, we need to acquire data that allow us to see very low amplitude modes. We have observed this star for ten nights using a 0.9 m telescope and reached a sensitivity of 0.5 mmag, i.e., we could detect any pulsation of amplitude larger than 0.5 mmag. In two hours the sensitivity on the 0.9 m telescope is 2.5 mmag. On the 1.5 m telescope at CTIO we have reached a limit of 0.8 mmag in two hours. The use of a larger telescope will definitely be useful in improving the current limit.

4.2. Red edge Other ZZ Ceti stars near the red edge share with BPM 37093 the instability in their pulsation modes. Modes come and go and come back. Phase shifts are seen without change in amplitude. From another point of view, they are completely different from BPM 37093 in having many pulsation modes and large amplitudes. Also, the changes in the red edge pulsators happen on a time-scale of weeks to months, not days as we have seen in the case of BPM 37093. 194 Α. Kanaan, S. Ο. Kepler et al.

4-3. High mass

Other higher than average mass ZZ Ceti stars are known but they do not have anything in common with BPM 37093. Their pul- sational modes are just like other ZZ Ceti stars, and the pulsation models for more massive ZZ Ceti stars do not show any peculiarity when compared with less massive stars. It is true though that the next massive ZZ Ceti star (G 207-9, Bergeron et al. 1995) is only of 0.83 MQ and it is conceivable that strange effects only happen at much higher masses. Of course, the most important effect, which happens only at very high masses, is crystallization.

5. CONCLUSION We have now proven that BPM 37093 is a black-sheep among the herd of ZZ Ceti stars. Not only it does not fit in the period- luminosity-amplitude relation, but it has also an unstable amplitude spectrum, characteristic for the red edge pulsators with which it shares only a long period. Even its instability is not of the same kind as we see for the red edge pulsators because the latter objects are unstable in a timescale of months, not days. We are faced with a unique ZZ Ceti star in many respects. As BPM 37093 is the only ultra massive ZZ Ceti star, it is reasonable to think that the mass is the cause for all the difference. We expect the key to be in crystallization since a massive ZZ Ceti star like BPM 37093 should be either partly or completely crystallized. Very high signal-to-noise data gathered by large telescopes would allow to detect lower amplitude modes. Another possibility is the use of the Hubble Space Telescope to observe pulsations in the ultraviolet where the amplitudes are much higher. If we find several pulsation modes, we will be able to compare BPM 37093 properties to other normal ZZ Ceti stars. We hope then to find signatures of crystal- lization in its pulsations. If the stable modes will be found, we will be able to measure the rate of period change of the star and finally have a grip on the rates of cooling of crystallized white dwarfs. In the future, surveys for ZZ Ceti stars should turn up other above solar mass objects. These will be essential to test whether the behavior of BPM 37093 is common to the massive ZZ Ceti stars. Meanwhile, theoretical developments of pulsational models, includ- ing crystallization effects, allied with finding more normal modes in BPM 37093: the way to the interior of crystallized stars 195

BPM 37093, will help us to test whether crystallization has happened in BPM 37093 or not. This work was based on observations made at the Laboratorio Nacional de Astrofisica/CNPq (Brazil) and at the Cerro Tololo Inter- American Observatory/AURA (Chile - U.S.A.).

ACKNOWLEDGMENTS. We are grateful to IITAP at Iowa State University for providing the travel support to attend the WET Workshop. This work was partially supported by NASA, NSF and Brazilian institutions FAPERGS, CNPq, CAPES and FINEP.

REFERENCES

Abrikosov A. 1960, J. Exper. Theor. Physics, 39, 1797 Bergeron P., Wesemael F., Fontaine G., Liebert J. 1990, ApJ, 351, L21. Bergeron P., Wesemael F., Lamontagne R., Fontaine G., Saffer R. Α., Allard Ν. F. 1995, ApJ, 449, 258 Bradley P.A., Winget D.E., Wood Μ.A. 1992, ApJ, 391, L33 Claver C.F. 1994, Ph. D. Thesis, University of Texas at Austin Clemens C. 1994, Ph. D. Thesis, University of Texas at Austin Dominguez I., Straniero O., Tornambe Α., Isern J. 1996, ApJ, 472, 783 Garcia-Berro E., Isern J., Hernanz M. 1997a, MNRAS, 289, 973 Garcia-Berro E., Ritossa C., Ibenl. Jr. 1997b, ApJ, 485, 765 Giovannini O., 1996, Ph.D. Thesis, Universidade Federal do Rio Grande do Sul Giovannini O., Kepler S.O., Kanaan A. et al. 1998, Baltic Astronomy, 7, 131 (these proceedings) Iben I. 1991, ApJS, 76, 55 Isern J., Mochkovitch R., Garcia-Berro, Hernanz, Μ. 1997, ApJ, 485, 308 Kanaan Α., Kepler S.O., Giovannini Ο., Diaz Μ. 1992, ApJ, 390, L89 Kepler S.O. et al. 1995, Baltic Astronomy, 4, 221 KirzhnitzD. A. 1960, J. Exper. Theor. Physics, 38, 503 Kleinmann S. J. 1995, Ph. D. Thesis, University of Texas at Austin KleinmannS. J., NatherR.E., Phillips T. 1996, PASP, 108, 356 McGrawJ.T. 1976, ApJ, 210, L35 Mestel L. 1952, MNRAS, 112, 583 Robinson E.L., Kepler S.O., NatherR.E. 1982, ApJ, 259, 219 RobinsonE. L., MaillouxT. M., Zhang E., Koester D., Stiening R. F., Bless R.C., Percival J.W., Taylor M. J., van Citters G.W. 1995, ApJ, 438, 908 Salpeter Ε. 1961, ApJ, 134, 669 196 Α. Kanaan, S. Ο. Kepler et al.

Winget D.O. 1981, Ph. D. Thesis, University of Rochester Winget D.E., Robinson E.L., Nather E.R., Fontaine G. 1982, ApJ, 262, Lll Winget D.E., Hansen C. J., van Horn H.M. 1983, Nature, 303, 781 Winget D.E., Kepler S.O., Kanaan Α., Montgomery Μ., Giovannini Ο. 1997, ApJ, 487, L191 Wood M. A. 1990, Ph. D. Thesis, University of Texas at Austin