THE ASTROPHYSICAL JOURNAL, 455:L159–L162, 1995 December 20
© 1995. The American Astronomical Society. All rights reserved. Printed in U.S.A.

The Extremely Low Luminosity White Dwarf ESO 439-26

María Teresa Ruiz, 1, 2 P. Bergeron, 3 S. K. Leggett, 4 and Claudio Anguita 1, 2

Received 1995 September 13; accepted 1995 September 29


ABSTRACT

     We present a detailed analysis of the extremely low luminosity white dwarf ESO 439-26. The measured trigonometric parallax of &pgr; = 0&farcs;0237 ± 0&farcs;0030, together with the observed V magnitude of 20.52, yields an absolute visual magnitude of MV = 17.4 ± 0.3. ESO 439-26 thus lies more than 1 mag faintward of the observed cutoff of the white-dwarf luminosity function in the Galactic disk and could therefore be the coolest and hence oldest white dwarf ever detected. However, we show from a detailed analysis of the optical energy distribution that the intrinsic low luminosity of ESO 439-26 is the result of its small radius, or large mass. Our best solution is reached with Teff = 4560 ± 100 K, log g = 9.04 ± 0.14, and a pure-helium atmospheric composition. Evolutionary models are used to derive a mass of M = 1.21 ± 0.07 M&sun; and a cooling age of 6.4 ± 0.3 Gyr, a value that is smaller than the current estimates of the age of the Galactic disk.

Subject headings: stars: evolution—stars: individual (ESO 439-26)—white dwarfs

FOOTNOTES

     1 Visiting Astronomer, Cerro-Tololo Inter-American Observatory, National Optical Astronomical Observatories, which is operated by AURA, Inc., under contract with the National Science Foundation.
     2 Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago, Chile; canguita, mtruiz@das.uchile.cl.
     3 Département de Physique, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, PQ, Canada H3C 3J7; bergeron@astro.umontreal.ca.
     4 NASA Infrared Telescope Facility, P.O. Box 4729, Hilo, HI 96720; skl@galileo.ifa.hawaii.edu.

§1. INTRODUCTION

     It is now well established that the observed cutoff in the white-dwarf luminosity function is real and not due to some selection effect (Monet et al. 1992). This abrupt cutoff has been interpreted as being due to the finite age of the local Galactic disk, in which the coolest, and therefore the oldest, white dwarfs are still visible (Winget et al. 1987; Liebert, Dahn, & Monet 1988). For instance, the MV versus V - I diagram of Monet et al. (1992; their Fig. 10) indicates that there are no known white dwarfs fainter than MV ∼ 16.2. Similarly, Liebert et al. (1988) have determined that the white-dwarf luminosity function peaks roughly at log (L/L&sun;) = -4.3 and drops rapidly at lower luminosities. The shape of this luminosity function has been successfully used to infer the age of the Galactic disk (Winget et al. 1987; Wood 1992). Although there is still some controversy about the accuracy of the physics involved in the evolutionary models of cooling white dwarfs that use this method, the best current estimates range from 6.5 to 11 Gyr (Wood 1992, 1995). Since the Galactic disk (or the universe) cannot be younger than the oldest stars it contains, the discovery of even a single white dwarf with an age significantly larger than 11 Gyr would make the Galactic disk correspondingly older. Therefore, the search for very low luminosity white dwarfs is still very active.

     In this Letter, we report the discovery of the lowest luminosity white dwarf to date, ESO 439-26. The discovery of this object was first reported by Ruiz, Anguita, & Maza (1989; a finding chart for ESO 439-26 is provided as well), although their trigonometric-parallax measurement was still suffering from a large uncertainty. Since then, ESO 439-26 has remained on the CCD parallax program of faint, southern, nearby stars, and the uncertainty of the measured trigonometric parallax has been reduced significantly. We present a detailed analysis of this faint white dwarf, with the main goal of determining its age and whether ESO 439-26 represents the oldest known white dwarf in the local Galactic disk.

     In § 2 we describe the trigonometric-parallax determination, as well as the BVRI photometry, which are then used in § 3 to derive the atmospheric parameters, mass, and age of ESO 439-26. Concluding remarks follow in § 4.

§2. OBSERVATIONS

     The trigonometric-parallax determination was obtained by use of a CCD detector at the CTIO 1.5 m telescope with the f/13.5 secondary. The observations cover a period of 5 yr from 1989, during which two different CCD detectors were used: the first was an RCA (312 × 508) with a scale of 0&farcs;3 pixel-1 while the second was a TEK (1024 × 1024) with a scale of 0&farcs;24 pixel-1. In order to use all the good frames taken during this 5 yr period, we limited the reference frame to stars included in the small field of the RCA CCD (1&farcm;6 × 2&farcm;5). We note that the two CCD data sets produced consistent values for the trigonometric parallax and proper motion. Observations were carried out using an R filter, and 40 frames were used for the calculation, all with a seeing better than ∼1&farcs;2; the typical integration time was 500 s. Seven reference stars were used, selected for having magnitudes no brighter than 3 mag above the program star. The derived errors in the proper motions of these reference stars with respect to their barycenter are less than 0&farcs;001 yr-1, which indicates that the reference system is stable. Corrections for color refraction were obtained empirically by taking frames at different hour angles. Frames used in the parallax determination were always taken at small hour angles (<1 hr). By solving simultaneously for proper motion, the classical least-squares solution in right ascension yields the following values for the relative parallax and proper motion of ESO 439-26:











     Optical BVRI photometry was obtained with the CTIO 1.5 m telescope and TEK CCD on 1993 March 13 and with the CTIO 0.9 m telescope on 1994 April 17 and 1995 July 21 and 23, using the same detector. The accuracy of the photometry is approximately 4% in all filters. The average color indices for ESO 439-26 are given in Table 1.

§3. ANALYSIS

     The magnitude V from Table 1 combined with the trigonometric parallax given above yields an absolute visual magnitude of MV = 17.4 ± 0.3 for ESO 439-26. Hence, ESO 439-26 is more than 1 mag fainter than the faintest white dwarf identified in the parallax sample presented by Monet et al. (1992 and references therein). The existence of such an extremely low luminosity white dwarf may imply a larger value for the age of the local Galactic disk.

     Alternatively, the low luminosity of ESO 439-26 could be accounted for if it is a massive—not necessarily old—white dwarf with a correspondingly small radius. This is not an unexpected result since theoretical white-dwarf luminosity functions, such as those calculated by Wood (1992), do predict a low-luminosity tail composed of massive white-dwarf remnants. Very massive white dwarfs are not common, however (see, e.g., Bergeron, Saffer, & Liebert 1992), and the probability of discovering such an object in a proper-motion survey is small.

     Only a detailed comparison of the observed absolute flux distribution with theoretical predictions can resolve this ambiguity. In Figure 1, we show the location of ESO 439-26 in the MV versus V - I diagram together with the 0.6, 0.8, 1.0, and 1.2 M&sun; pure-hydrogen models, as well as the 1.2 M&sun; pure-helium model, of Bergeron, Wesemael, & Beauchamp (1995b). These photometric sequences are based on the new model atmosphere calculations of Bergeron, Saumon, & Wesemael (1995a) appropriate for cool hydrogen and helium white-dwarf atmospheres. For comparison, we also show the low-luminosity tail of the USNO trigonometric-parallax sample (Monet et al. 1992 and references therein). The location of ESO 439-26 in this diagram leads directly to the interpretation that it is a massive (M ∼ 1.2 M&sun;) and cool (Teff ∼ 4500 K) white dwarf. We note that this conclusion is independent of the assumed atmospheric composition. Therefore, the low luminosity of ESO 439-26 is a consequence of its small radius rather than the extremely low effective temperature of an old remnant.

Fig. 1

     We proceed next to a more detailed analysis of the energy distribution, using the BVRI photometry presented in Table 1. First, we convert every magnitude m into an average flux f$\mathstrut{^{m}_{{\lambda}}}$ using an equation similar to equation (2) of Bergeron et al. (1995b)



where



and where Sm(&lgr;) is the transmission function of the corresponding bandpass, f&lgr; is the flux from the star received at Earth, and cm is a constant determined by use of the fluxes from Vega (see Bergeron et al. 1995b for details). We then transform the monochromatic fluxes from the model atmospheres into average fluxes H$\mathstrut{^{m}_{{\lambda}}}$ by substituting f&lgr; in equation (2) for H&lgr;, the monochromatic Eddington flux. The average model and observed fluxes are of course related by the equation



where R/D is the ratio of the radius of the star to its distance from Earth. The &khgr;2 fit is then performed in terms of these average fluxes only. This method is more rigorous, and it is to be preferred to our previous technique, in which monochromatic (instead of average) Eddington fluxes were employed in the fitting procedure (see, e.g., Bergeron et al. 1994). The latter method can lead to large errors when the model fluxes vary rapidly over the filter bandpass, or when strong features, such as strong atomic lines, are present in the spectrum.

     In our fitting procedure, we consider Teff and the solid angle free parameters while the surface gravity (which can be expressed as a function of radius only) is constrained by the value of the trigonometric parallax. Since the atmospheric composition of ESO 439-26 is yet unknown, we consider both pure-hydrogen and pure-helium compositions. Our best fits to the observed photometry of ESO 439-26 are shown in Figure 2, and the derived atmospheric parameters are reported in Table 2. We obtain Teff = 4200 ± 200 K, log g = 8.89 ± 0.14 and Teff = 4560 ± 100 K, log g = 9.04 ± 0.14 for the pure-H and pure-He solutions, respectively. Although both fits are certainly acceptable, the pure-helium solution provides a somewhat better fit to the observed energy distribution. Infrared JHK photometry would help to constrain the atmospheric composition, and we are working on obtaining such data.

Fig. 2

     Even though H&agr; can be detected in ∼0.6 M&sun;, hydrogen-rich white dwarfs with effective temperatures comparable to that of ESO 439-26 (Bergeron, Ruiz, & Leggett 1996), the large surface gravity we derive for this object implies that collisional broadening will make any hydrogen lines present in the spectrum impossible to detect. Consequently, the absence of H&agr; in the spectrum of ESO 439-26 displayed in Ruiz et al. (1989) cannot be used to infer the chemical composition of its atmosphere.

     We rely on the evolutionary models of Wood (1990) 5 with pure-carbon cores (MHe = 10-4M*, MH = 0) to derive stellar masses for each composition. We obtain M = 1.13 ± 0.07 M&sun; and M = 1.21 ± 0.07 M&sun; for the pure-H and pure-He solutions, respectively. Note that the pure-He solution at Teff = 4560 K, M = 1.21 M&sun; is more consistent with the location of ESO 439-26 in Figure 1 (with respect to the theoretical photometric sequences) than the pure-H solution at Teff = 4200 K, M = 1.13 M&sun;, in agreement with the conclusion reached from our detailed fits to the energy distribution (Fig. 2).

     In Figure 3, we show the location of ESO 439-26 in the mass-Teff diagram for both atmospheric compositions. Also shown are the isochrones from the models of Wood (1990) with carbon core compositions. The onset of crystallization in the more massive sequences is clearly visible. Since crystallization considerably reduces the cooling timescales, the more massive stars evolve faster in this temperature range than their low-mass counterparts, which leads to the parabola-shaped isochrones shown in Figure 3. The isochrone shown as a dotted line corresponds to the last data point in the 1.2 M&sun; evolutionary sequence (&tgr; = 6.7 × 109 yr, Teff ∼ 3500 K) where our interpolation remains reliable. For greater cooling ages our interpolation relies on a smaller number of models, which leads to the incomplete isochrones seen in Figure 2. However, one expects intuitively that these parabola-shaped isochrones shift rightward in Figure 3, with the turning point of the parabola moving to lower masses as crystallization gradually occurs in these models.

Fig. 3

     From Figure 3, we estimate for ESO 439-26 cooling ages of 6.8 ± 0.3 Gyr and 6.4 ± 0.3 Gyr for the pure-hydrogen and pure-helium solutions, respectively. We therefore conclude that ESO 439-26 is not a particularly old white dwarf. White dwarfs with comparable effective temperatures but normal masses (M ∼ 0.6 M&sun;) would be considerably older (&tgr; ∼ 9 Gyr).

FOOTNOTES

     5 We refrain from using the new models of Wood (1995) with thick hydrogen layers since these do not reach low enough temperatures for our purposes. The effect of using thick hydrogen layer models to derive stellar masses from log g determinations is discussed at length in Bergeron et al. (1995c). Briefly, a thick hydrogen layer (MH = 10-4M*) would increase the derived mass by ∼0.03 M&sun;.

§4. CONCLUDING REMARKS

     Even though infrared JHK photometry will help us constrain the chemical atmospheric composition of ESO 439-26, we are still able to conclude that this white dwarf is relatively cool and that its intrinsic low luminosity is the result of its large mass and small radius.

     Our age estimates for ESO 439-26 are based on the pure-carbon core models of Wood (1990). Wood (1992, 1995) discusses at length the effects of various core compositions and thicknesses of the helium—and, to a lesser extent, hydrogen—layers. The carbon core models used in this study yield an upper limit to the age of ESO 439-26. The use of carbon/oxygen core models, for instance, would reduce the age by ∼2.5 Gyr, while models with helium layers 100 times thicker than those used here would reduce our estimate by ∼1.5 Gyr. With such a high mass, ESO 439-26 may even possess a higher metallicity core—oxygen, neon, and magnesium, for instance—in which case the age could be further reduced.

     Figure 3 also indicates that ESO 439-26 is in an advanced stage of crystallization. To our knowledge, ESO 439-26 is unique in this respect. No additional cool and massive white dwarfs have been identified in the photometric and spectroscopic survey of Bergeron et al. (1996).

ACKNOWLEDGMENTS

     This work was supported in part by the NSERC Canada, the Fund FCAR (Québec), FONDECYT grant 1950588, NSF grant 93-15372, and a Chrétien International Research Grant.

REFERENCES

FIGURES


Full image (6kb) | Discussion in text
     Fig. 1.—Location of ESO 439-26 in the MV vs. V - I diagram (filled circle) compared with the observed sequence of Monet et al. (1992; open circles). Also shown are the 0.6, 0.8, 1.0, and 1.2 M&sun; pure-hydrogen and 1.2 M&sun; pure-helium photometric sequences of Bergeron et al. (1995b). Effective temperatures are marked by squares on each sequence and correspond to Teff = 4000, 4500, 5000, and 5500 K (starting from the right).

Full image (6kb) | Discussion in text
     Fig. 2.—Our best fits to the observed energy distribution of ESO 439-26 (in units of ergs cm-2 s-1 Å-1) under the assumptions of pure-hydrogen and pure-helium compositions. The data are indicated by 1 σ error bars and the average model fluxes by filled (pure He) and open (pure H) circles. Both the effective temperature and the solid angle are considered free parameters while the surface gravity is constrained by the trigonometric parallax. The pure-helium solution provides the best fit, although both solutions are acceptable.

Full image (6kb) | Discussion in text
     Fig. 3.—Pure-hydrogen (open circle) and pure-helium (filled circle) solutions for ESO 439-26 in the M-Teff diagram. Also shown are the isochrones from the evolutionary models of Wood (1990) for pure-carbon core compositions, labeled in units of 109 yr. The dotted line corresponds to the 6.7 Gyr isochrone. For our preferred pure-helium solution, the age of ESO 439-26 is ∼6.4 Gyr.

TABLES

TABLE 1
Optical Color Indices for ESO 439-26
V B - V V - R V - I Nobs
20.52... 1.03 0.63 1.11 4
     Note.— Only two observations were secured for B - V.
Image of typeset table (9kb) | Discussion in text
TABLE 2
Pure-H and -He Solutions for ESO 439-26
Model Teff
(K)		 log g M
(M&sun;)		 Mbol log (L/L&sun;) Age
(Gyr)
Pure H... 4200 8.89 1.13 17.12 -4.95 6.8
Pure He... 4560 9.04 1.21 17.06 -4.93 6.4

Image of typeset table (12kb) | Discussion in text