A COMPREHENSIVE SPECTROSCOPIC ANALYSIS OF DB WHITE DWARFS

Our model atmospheres and synthetic spectra are built from the model atmosphere code described in Tremblay & Bergeron (2009) and references therein, in which we have incorporated the improved Stark profiles of neutral helium of Beauchamp et al. (1997). These detailed profiles for over 20 lines of neutral helium take into account the transition from quadratic to linear Stark broadening, the transition from the impact to the quasi-static regime for electrons, as well as forbidden components. In the context of DB stars, these models are comparable to those described by Beauchamp (1995) and Beauchamp et al. (1996), with the exception that at low temperatures (T_eff < 10,800 K), we now use the free–free absorption coefficient of the negative helium ion of John (1994). For the hydrogen lines in DBA stars, we rely on the improved calculations for Stark broadening of Tremblay & Bergeron (2009). Our models are in LTE and include convective energy transport treated within the mixing-length theory. The theoretical spectra are calculated using the occupation formalism of Hummer & Mihalas (1988) for both the hydrogen and helium populations and corresponding bound–bound, bound–free, and pseudo-continuum opacities.

An important issue related to the modeling of DB spectra is the inclusion of van der Waals broadening at low effective temperatures (T_eff ≲15,000 K), where Stark broadening is no longer the dominant source of line broadening. Beauchamp et al. (1996, see their Figure 6) show the effect of this broadening mechanism in a log g versus T_eff diagram for DB stars with parameters determined from optical spectroscopy. The neglect of van der Waals broadening results in spuriously high log g values at low effective temperatures. In this series of synthetic spectrum calculations, we include the treatment of this broadening mechanism provided by Deridder & Van Rensbergen (1976).

Our model grid covers a range of effective temperature between T_eff = 11,000 K and 40,000 K by steps of 1000 K, while the log g ranges from 7.0 to 9.0 by steps of 0.5 dex. In addition to pure helium models, we also calculated models with log H/He = −6.5 to −2.0 by steps of 0.5. In order to explore the effect of varying the convective efficiency on the predicted emergent fluxes, models have been calculated with the ML2 version of the mixing-length theory, which corresponds to the prescription of Böhm & Cassinelli (1971), with various values of α = ℓ/H, i.e., the ratio of the mixing length to the pressure scale height, ranging from 0.75 to 1.75 by steps of 0.25.

The determination of the atmospheric parameters, T_eff, log g, and H/He, of DB stars represents an inherent difficulty in any analysis of their properties. While the atmospheric parameters for DA stars derived from various studies agree generally well (see, e.g., Figure 9 of Liebert et al. 2005), a similar comparison for DB stars is less than satisfactory, as shown for instance in Figures 3 and 4 of Voss et al. (2007), which compare the values obtained from the SPY survey with those obtained from independent studies (Beauchamp et al. 1999; Friedrich et al. 2000; Castanheira et al. 2006).

In addition to being rarer than their hydrogen-line DA counterparts, the hotter DB stars are characterized by an optical spectrum where the neutral helium transitions exhibit little sensitivity to effective temperature. As an illustration, we show in the left panel of Figure 1 the model spectra⁷ for various values of T_eff (shown in blue), compared to a model template at T_eff = 24,000 K (shown in red). There is a wide range in temperature, between T_eff ∼ 20,000 K and 30,000 K, where the optical spectra are virtually identical. This underscores the need to secure well calibrated, high signal-to-noise spectroscopic observations to study these stars. Equivalently, we show in the left panel of Figure 2 the variation of the equivalent width of He i λ4471 as a function of effective temperature for various hydrogen abundances. In all cases, the variation of the equivalent width shows a wide plateau, about 10,000 K wide, that inhibits the determination of accurate effective temperatures from the optical spectrum of DB stars in this particular range of temperature. Also shown in this figure are the measured equivalent widths in our sample of DB stars, arbitrarily located at T_eff = 22,000 K. Interestingly enough, the DB stars in our sample with the strongest lines have equivalent widths that are larger than predicted by any of our models shown in this panel.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Luckily, we fare somewhat better with gravity indicators, as illustrated in the middle panel of Figure 1. The large gravity sensitivity of several segments containing neutral helium transitions (notably the 2³P − 6³D λ3819 line, the 4100–4200 Å region that contains the 2³P − 5³S λ4121, 2¹P − 6¹D λ4144, and 2¹P − 6¹S λ4169 lines, as well as the strong 2¹P − 5¹D λ4388 transition; Wickramasinghe 1979) can be used successfully through the entire temperature range. We disagree in that respect with the statement of Voss et al. (2007, see Section 3.1) that the dependence of line profiles on log g is smaller for the cooler DB stars. Interestingly, the variation of the He i λ4471 equivalent width with T_eff is also strongly log g dependent, as can be observed in the middle panel of Figure 2. For low-gravity DB white dwarfs, the maximum is now strongly peaked near 22,000 K, while for high-gravity DB stars, the plateau becomes even wider, and the maximum equivalent width is reached at temperatures near 33,000 K. Again, variations of log g help very little in matching the maximum observed equivalent widths of the DB stars in our sample.

Less well documented is the sensitivity of the optical spectrum of DB stars to the convective efficiency. Helium atmospheres of white dwarfs become convective below T_eff ∼ 60,000 K, but it is not until the temperature drops below ∼30,000 K that the helium convection zone becomes sufficiently important, depending on the assumed convective efficiency (see Figure 10 of Tassoul et al. 1990). For completeness and future reference, we show in Figure 3 the extent of the helium convection zone in a 0.6 M_☉ DB white dwarf. Convective energy transport is generally treated in model atmosphere calculations within the mixing-length theory, and unless convection becomes adiabatic, the emergent model fluxes will depend on the assumed convective efficiency, parameterized in this case by the free parameter α. This additional parameterization was first introduced in the context of DB stars by Beauchamp (1995) on the basis of work carried out in the hydrogen-line DA stars (Bergeron et al. 1995).

Zoom In Zoom Out Reset image size

To illustrate this sensitivity, we compare in the right panel of Figure 1 model spectra calculated with α = 0.75 and 1.75. The effect is subtle and only noticeable between T_eff ∼ 18,000 K and 28,000 K. At higher effective temperatures, the atmospheres of DB stars become almost completely radiative (see Figure 3), while at lower temperatures convection becomes adiabatic, and the convective efficiency no longer depends on the specific value of α. Despite the apparent lack of sensitivity to variations of α, the effects on the normalized line profiles are more pronounced. This is illustrated in the right panel of Figure 2, where the equivalent width of He i λ4471 as a function of effective temperature is shown for model atmospheres calculated with various convective efficiencies. Once again, the line strength is sensitive to α for effective temperatures between 18,000 K and 28,000 K and, in contrast to the results shown in the previous panels, the largest predicted equivalent widths (achieved with α = 0.75) are larger than the largest measured values. This means that, were we to overestimate α in our models, all the stars would be shifted toward the maximum of the curve (i.e., near 30,000 K for α = 1.75) and form a clump. In contrast, were we to underestimate α, the stars we fit would be lumped on respective sides of the maximum of the curve (i.e., near 18,000 K and 30,000 K for α = 0.75), and gaps would develop in the distribution of stars with respect to effective temperature. This behavior can be used to constrain α, as we show below.

We finally note that the results presented here are consistent with those of Voss et al. (2007) who mention that the helium lines in their models, calculated with ML2/α = 0.6 (i.e., a value even smaller than the smallest value used in Figure 2), reach a maximum strength around T_eff = 20,000 K.

Our fitting technique is similar to that outlined in Liebert et al. (2005, and references therein) for the analysis of DA stars. The first step is to normalize the flux from individual predefined wavelength segments, in both observed and model spectra, to a continuum set to unity. The comparison with model spectra, which are convolved with the appropriate Gaussian instrumental profile, is then carried out in terms of this normalized spectrum only. The most sensitive aspect of this approach is to properly define the continuum of the observed spectra. Here we rely on the procedure developed by Liebert et al. (2005), where the fluxed spectrum is first fitted with model spectra, multiplied by a high-order polynomial (up to λ⁵), in order to account for any residual error in the flux calibration. The nonlinear least-squares minimization method of Levenberg–Marquardt (Press et al. 1986) is used throughout. Note that the values of T_eff and log g derived in this first step are meaningless since too many fitting parameters are considered, and the model fit just serves as a smooth fitting function used to define the continuum of the observed spectrum. Normal points are then fixed at several wavelengths defined by this smooth function and used to normalize the spectrum. This method turns out to be quite accurate when a glitch is present in the spectrum at the location where the continuum is set. It also provides a precise value of the line center, which can be corrected to the laboratory wavelength. An example of continuum fitting using this procedure is illustrated in the top panel of Figure 9.

Zoom In Zoom Out Reset image size

Once the spectrum is normalized to a continuum set to unity, as shown in the bottom panel of Figure 9, we use our grid of model spectra to determine T_eff, log g, and H/He in terms of the normalized spectrum only. Our three-dimensional minimization technique again relies on the nonlinear least-squares method of Levenberg–Marquardt, which is based on a steepest descent method.

As shown in Figure 2, two solutions exist for a given DB spectrum, one on each side of the maximum strength of the neutral helium lines. In most cases, it is easy to distinguish these cool and hot solutions from an examination of our best fits, as displayed in the left panel of Figure 10 for the cool DB star LP 475-242 (0437+138). In addition, we also look at our spectroscopic solution in terms of absolute fluxes (not shown here) by normalizing both the observed and predicted model spectra at 4250 Å. In general, the slopes agree well, except in some cases where the object has been observed at high airmasses, in which case the slope of the observed spectrum might be distorted.

Zoom In Zoom Out Reset image size

However, when the star is close to the temperature where the helium lines reach their maximum strength—a temperature range that strongly depends on log g and on the assumed convective efficiency according to Figure 2—the cool and hot solutions cannot be distinguished, as shown in the right panel of Figure 10 for the hot DB star PG 1115+158. The comparison of the slopes of the energy distributions does not help either in this case. Fortunately, we discovered that this ambiguity could be resolved with the help of spectroscopic observations at Hα, which add an additional constraint in our fitting procedure. Since our Hα data are independent of our blue observations, we use an iterative procedure where we fit the blue spectrum with an assumed hydrogen abundance to obtain a first estimate of T_eff and log g. The Hα spectra are then used to determine the hydrogen abundance, or upper limits on H/He, at these particular values of T_eff and log g. The procedure is then repeated until the value of H/He has converged. An example of our solution for PG 1115+158 is displayed in Figure 11. The weak Hα absorption feature shown in the insert (from an SDSS spectrum, in this case) serves as an important constraint to determine the hydrogen abundance, which otherwise could only be inferred from the weak depression observed near Hβ. Interestingly, our final solution for this object lies between the cool and hot solutions displayed in Figure 10.

Zoom In Zoom Out Reset image size

The procedure described above works well when any hydrogen absorption feature (Hα or Hβ) is visible in the optical spectrum. When no such feature is present, only upper limits on the hydrogen abundance can be determined. These limits depend on the S/N of the observations, and on whether they are based on our blue spectra for Hβ, or our red spectra for Hα. We show, in Figure 12, the limits on the hydrogen abundance imposed by the absence of Hα and Hβ features in our spectra (we adopt a detection limit of 200 mÅ and 300 mÅ for the equivalent widths of Hα and Hβ, respectively); the results for Hα are qualitatively similar to those shown in Figure 9 of Voss et al. (2007). For high S/N spectra with no detectable hydrogen feature,¹⁰ we set the hydrogen abundance in our fitting procedure at the value given by these upper limits at the appropriate temperature. In cases where the spectrum is noisier, our fitting procedure may find an upper limit on the hydrogen abundance that is larger than those of Figure 12.

Zoom In Zoom Out Reset image size

Four DBZ stars in our sample have sufficiently strong calcium lines that the inclusion of the Ca ii H and K doublet is required to fit them properly. These are GD 40 (0300−013), CBS 78 (0838+375), KUV 15519+1730 (1551+175), and G241-6 (2222+683). We take a simple approach here of including only calcium in our equation of state and opacity calculations. A more detailed analysis of these DBZ stars, including additional heavy elements, will be presented elsewhere. A smaller grid of models between T_eff = 12,000 K and 17,000 K has been calculated for this purpose, with calcium abundances of log Ca/He =−7.5 to −6.0 by steps of 0.5, and the same log g and H/He values as above. For each star we adopt the calcium abundance that best reproduces the calcium doublet. Our best fits for these four DBZ stars are presented in Figure 13.

Zoom In Zoom Out Reset image size

The problem of the convective efficiency in the atmosphere of DA stars has been tackled by Bergeron et al. (1995) who used optical spectroscopic observations combined with UV energy distributions to show that the so-called ML2/α = 0.6 parameterization of the mixing-length theory provides the best internal consistency between optical and UV effective temperatures, trigonometric parallaxes, V magnitudes, and gravitational redshifts.¹¹ Similarly, Beauchamp et al. (1996, see their Figure 5) showed a comparison of optical and UV temperatures of DB white dwarfs using model atmospheres calculated with the ML1, ML2, and ML3 versions of the mixing-length theory; the authors only concluded then that ML2 and ML3 provided a more satisfactory correlation than ML1. The spectroscopic analysis of Beauchamp et al. (1999), however, relied on model atmospheres calculated with a convective efficiency of ML2/α = 1.25, although details of this particular choice were not provided in that study. The spectroscopic analysis of the DB stars in the SPY survey by Voss et al. (2007), on the other hand, relied on models calculated with ML2/α = 0.6, i.e., the same convective efficiency as for DA models. As shown in Figure 2, the strength of the helium lines in DB stars is significantly affected by the assumed parameterization of the mixing-length theory used in the model atmosphere calculations, in particular between T_eff ∼ 18,000 K and 30,000 K. It is thus of utmost importance to calibrate the convective efficiency in DB stars as accurately as possible.

The log g versus T_eff distribution of all DB stars in our sample is displayed in Figure 14 for three versions of the mixing-length theory, namely ML2/α = 0.75, 1.25, and 1.75. As expected, only objects with 18,000 K ≲ T_eff ≲ 30,000 K are affected by this parameterization. As discussed at the end of Section 2.2, if the convective efficiency is underestimated, the helium lines are predicted too strong near the maximum equivalent widths, and DB stars will have a tendency to be lumped on either side of this maximum. This is precisely what is observed in Figure 14 for α = 0.75 where the maximum occurs near 23,000 K according to Figure 2 (see also Figure 3 of Bergeron et al. 1995 for DA stars near the ZZ Ceti instability strip). On the other hand, if the convective efficiency is overestimated, helium lines are predicted too weak near the maximum, and DB stars in this case will tend to accumulate at this location. Again, this is what is observed in Figure 14 for α = 1.75 where DB stars form a clump at T_eff ∼ 25,000 K, even leaving a void near 20,000 K (see a similar result for DA stars in Bergeron et al. 1995). The results with α = 1.25, however, provide a smoother distribution and a uniform increase of the number of DB stars as a function of effective temperature, which is exactly what is expected in terms of the white dwarf luminosity function. Based on these results alone, a value around α = 1.25 seems entirely reasonable, even though we cannot easily rule out values between α ∼ 1.0 and 1.5 at this stage.

Zoom In Zoom Out Reset image size

Bergeron et al. (1995) went a step further to calibrate the convective efficiency in DA stars, by comparing optical temperatures determined from spectroscopy with those obtained from UV energy distributions. Such a comparison is displayed in Figure 15 for two versions of the convective efficiency, namely ML2/α = 1.25 and 1.75. Also shown in the bottom panel is a comparison of our UV temperatures, derived from fits to IUE spectra with ML2/α = 0.6 models, with those obtained by Castanheira et al. (2006) based on similar assumptions; note the almost perfect agreement here. In all UV fits, we simply assume log g = 8 and pure helium compositions for all objects. We first begin by examining the results for α = 1.25. Although there is a good overall agreement between optical and UV temperatures, there are also several discrepant results at the hot end of the sequence. The two objects with T_opt ∼ 30,000 K correspond to PG 0112+104, recently analyzed in great detail by Dufour et al. (2010b), and PG 1654+160. Although the IUE spectrum of the first object is of good quality, the spectrum of the second object suffers from a significant discontinuity between the SWP and LWP images. It is also possible that the UV energy distributions may become increasingly less sensitive to temperature at the hot end of the DB sequence, while interstellar extinction may have to be taken into account for the intrinsically brighter, and more distant, DB stars. Indeed, for PG 0112+104, Dufour et al. (2010b) found the energy distribution extending into the FUV region (∼925 Å) to be globally consistent with the ∼31,000 K effective temperature derived from the optical spectroscopy provided that a small amount of reddening were included in the fits (E(B − V) = 0.015). The most important outlier in Figure 15 is LP 497-114 (1311+129) with a ∼8000 K temperature difference; this peculiar white dwarf is further discussed in Section 5.4.

Zoom In Zoom Out Reset image size

More worrisome in the top panel of Figure 15 is the systematic offset between both temperature scales (with T_UV > T_opt) for 15,000 K <T_UV < 22,000 K. Note that a more efficient prescription of the mixing-length theory, shown in the middle panel of Figure 15, improves the agreement between both temperature scales near T_UV ∼ 22,000 K, but the agreement gets worse for hot DB stars, and the systematic shift still remains for 15,000 K <T_UV < 20,000 K. Hence, it is not clear that increasing the convective efficiency would improve the overall agreement.

Since UV temperatures may depend on surface gravity, hydrogen abundance, and convective efficiency, we explore in Figure 16 the effects of variations of these parameters on our temperature determinations. All in all, we see that UV temperatures are fairly independent of our initial assumption of log g = 8 and pure helium compositions in our fits.¹² The same conclusion applies to our particular choice of α. We thus conclude that the systematic shifts observed in Figure 15 with our ML2/α = 1.25 models cannot be explained in terms of inadequate assumptions in our fits to UV data. What the overall results suggest, instead, is that theoretical improvements probably need to be made at the level of the model atmospheres, perhaps even with the treatment of convective energy transport (see below).

Zoom In Zoom Out Reset image size

The internal uncertainties of the atmospheric parameters— T_eff, log g, and H/He—can be obtained directly from the covariance matrix of our fitting method. These depend mostly on the S/N of the observations and on the sensitivity of the models to each parameter. For DA white dwarfs, these internal errors can become negligibly small with sufficiently high signal-to-noise spectroscopic observations (S/N ≳ 50; Bergeron et al. 1992, Liebert et al. 2005). Since our DB spectra are rather homogeneous in terms of S/N (see Figures 5 and 6) and of sufficiently high quality (S/N > 50), the internal errors in our analysis will be mostly dominated by the sensitivity of the models to each fitted parameter. The theoretical spectra displayed in Figure 1 indicate that the internal errors will be relatively small for log g (similar conclusions apply to H/He), but can be relatively large for T_eff, particularly in the temperature range where the strength of the helium lines reaches its maximum.

The true error budget, however, must also take into account external uncertainties originating mostly from flux calibration, which can be estimated from multiple observations of the same star, as performed by Liebert et al. (2005, Figure 8) for DA stars, or by Voss et al. (2007, Figures 1 and 2) for DB stars. Even though we have not reobserved DB stars for that specific purpose (except in a few cases), we still managed to secure repeated observations of 28 DB stars in our sample, either because of flux calibration problems (e.g., objects observed at high airmass) or insufficient S/N. Hence the external errors determined below will tend to be overestimated, if anything.

We compare in Figure 17 the T_eff and log g measurements for the 28 DB stars in our sample with multiple spectra. As expected, the external error on T_eff is particularly large between ∼20,000 K and 25,000 K, where the helium lines reach their maximum strength. Otherwise, outside this temperature range, the temperature estimates are in excellent agreement. The spread in log g measurements is more significant, however, but some of the most extreme outliers are white dwarfs with a first spectroscopic observation at very low S/N; these include the DB stars reported by Lépine et al. (2011) for instance. If we take the average uncertainties of both parameters, we obtain 〈ΔT_eff/T_eff〉 = 4.6% and 〈Δlog g〉 = 0.069, but if we remove the obvious outliers, these numbers drop to 〈ΔT_eff/T_eff〉 = 2.3% and 〈Δlog g〉 = 0.052. Given that these are probably overestimated, as discussed in the previous paragraph, we adopt these values as conservative estimates of the external uncertainties of our atmospheric parameters. Note that these results are comparable to those obtained by Voss et al. (2007), 〈ΔT_eff/T_eff〉 = 2.03% and 〈Δlog g〉 = 0.058, based on multiple observations of 24 objects.

Zoom In Zoom Out Reset image size

The atmospheric parameters for the 108 DB and DBA stars in our sample are reported in Table 1; the values in parentheses for T_eff and log g represent the combined (in quadrature) internal and external errors of the fitting technique, while only the internal error is available for H/He. For DB stars without detectable hydrogen, upper limits on the hydrogen abundance are given in Table 1. The stellar mass (M) and white dwarf cooling age (log τ) of each star are obtained from evolutionary models similar to those described in Fontaine et al. (2001) but with C/O cores, q(He) ≡ log M_He/M_⋆ = 10⁻² and q(H) = 10⁻¹⁰, which are representative of helium-atmosphere white dwarfs. The absolute visual magnitude (M_V) and luminosity (L) are determined with the improved calibration from Holberg & Bergeron (2006), defined with the Hubble Space Telescope absolute flux scale of Vega. The V magnitudes¹³ are taken from the Villanova White Dwarf Catalog, which combined with M_V yield the distance D. Finally, for all PG stars in the complete sample, we also provide the 1/V_max weighting (pc⁻³) used in the calculation of the luminosity function, where V_max represents the volume defined by the maximum distance at which a given object would still appear in the sample given the magnitude limit of the PG Survey (see Liebert et al. 2005 for details).

Sample fits for both DB and DBA stars covering the full temperature range of our sample are displayed in Figure 18. The left panels show the blue portion of our spectroscopic fits, while the right panels show the corresponding region near Hα. The importance of the red coverage is clearly illustrated, with Hα being barely detected in several DBA stars, while Hβ remains spectroscopically invisible. In other objects, only an upper limit on H/He could be set, based on the absence of Hα. We also show in this figure the DBA star with the largest hydrogen abundance measured in our sample (LP 497-114; 1311+129). A trend for the coolest objects to have larger than average surface gravities is already apparent.

Zoom In Zoom Out Reset image size

As mentioned in the Introduction, the spectroscopic analysis of ∼70 DB and DBA stars in the SPY survey (Voss et al. 2007) represents the largest set of data against which our atmospheric parameter determinations can be compared. We have 44 white dwarfs in common with the SPY sample, 22 of which are DBA stars. The comparison of effective temperatures and surface gravities is displayed in Figure 19.

Zoom In Zoom Out Reset image size

Voss et al. (2007) also included van der Waals broadening in their models, in a simplified form. Even though they found a much better agreement with the observed line profiles and strengths, their fits were not completely satisfactory according to the authors; they also mention that a fit in which log g is actually allowed to vary converges to very high values. Hence a value of log g = 8 was simply assumed for the coolest DB stars in their sample (shown as open circles in Figure 19). The comparison of log g values is thus meaningless for these stars, although we note that the corresponding temperatures are in excellent agreement, except for the two coolest white dwarfs for which our values of log g ∼ 9 are likely overestimated. Worth mentioning in this context are the results shown in Figure 5 of Kepler et al. (2007) for the DB stars identified in the Data Release 4 of the SDSS, where the masses gradually increase to very large values (M > 1.0 M_☉) at low effective temperatures. Whether this increase is due to an inappropriate treatment of van der Waals broadening, or to the neglect of this broadening mechanism altogether, is not discussed in their analysis.

For T_eff ≲ 19,000 K, the T_eff determinations displayed in Figure 19 are in good agreement, although our log g values in this temperature range appear systematically larger than those of Voss et al. by 0.15 dex, on average. The log g values agree much better at higher temperatures, however, with the exception of PG 1115+158 (labeled in the figure) for which we get a surface gravity 0.4 dex higher than the value derived by Voss et al. (log g = 7.52). This white dwarf is of particular interest because of its low inferred mass of only 0.385 M_☉, and also because it is a member of the pulsating V777 Her class. Beauchamp et al. (1996) found no low-mass DB stars in their sample and argued that evolutionary scenarios that could produce such low-mass degenerates could simply not form DB white dwarfs. Both spectroscopic solutions for PG 1115+158 are compared in Figures 11 and 20. While the effective temperatures agree well within the uncertainties, the low surface gravity obtained by Voss et al. predicts helium lines that are much shallower than observed. Hence we believe that our solution at log g = 7.91 (or M = 0.56 M_☉) is more appropriate for this star.

Zoom In Zoom Out Reset image size

The differences in temperature for T_eff > 19,000 K are significantly more important, partly due to the use of different versions of the mixing-length theory (ML2/α = 0.6 versus α = 1.25), but also because of the intrinsic difficulty of measuring T_eff precisely in this particular temperature range. The most extreme case here is for KUV 03493+0131 (0349+015; labeled in Figure 19) for which we obtain an effective temperature ∼6000 K higher than that found by Voss et al. Both spectroscopic solutions for this object are displayed in Figures 18 and 20. Note that if we rely only on the blue spectrum for this object, we find a cooler solution at T_eff = 22,760 K, still significantly hotter than that of Voss et al. We find that our solution at T_eff = 24,860 K reproduces the widths and overall strengths of the neutral helium lines, as well of the observed slope of the spectral energy distribution (not shown here), much better than a solution at 18,740 K.

Beauchamp et al. (1996) showed that the mass distribution of DB stars was relatively narrow, with the mass of 73% of their 41 DB stars above T_eff = 15,000 K (excluding DBA stars) lying between 0.5 and 0.6 M_☉, for an average mass of 〈M_DB〉 = 0.567 M_☉. The 13 DBA stars were found at slightly larger masses, with an average mass of 〈M_DBA〉 = 0.642 M_☉, suggesting that more massive white dwarfs may have a tendency to show hydrogen, perhaps through an increased hydrogen accretion from the interstellar medium or through a decreased dilution of the accreted hydrogen throughout a thinner helium convection zone (Beauchamp et al. 1996). One significant distinction between the mass distributions of DB and DA stars, noted by Beauchamp et al., was the almost complete absence of the low- and high-mass tails in the mass distribution of DB stars, suggesting that the formation of double degenerates and mergers, which are often invoked to explain, respectively, these low- and high-mass tails for DA stars, are not producing DB stars. The picture drawn by Voss et al. (2007) using ∼50 DB stars from the SPY survey differs significantly from the one described above. While the results of Beauchamp et al. (1996) indicate that 25% of all DB white dwarfs are DBA stars, the high-resolution spectroscopic observations at Hα of the SPY survey revealed a much larger fraction of 55% of DBA stars in their sample, as discussed above. The resulting mean mass of each subsample, 〈M_DB〉 = 0.584 M_☉ and 〈M_DBA〉 = 0.607 M_☉, is now in much closer agreement, suggesting that both populations have a common origin. Furthermore, Voss et al. found a significantly larger mass dispersion, with several low-mass (M ≲ 0.5 M_☉) and high-mass white dwarfs in their sample, in line with the results for DA stars.

The distribution of mass as a function of effective temperature for all 108 DB and DBA stars in our sample is displayed in Figure 21. Our final sample comprises 47 DBA stars, or 44% of the DB white dwarf population. Based on our discussion above, it is clear that this fraction represents only a lower limit since we are lacking the red spectral coverage for many of the DB stars in our sample, the cool ones in particular. In contrast to the mass distribution of DB stars in the SDSS obtained by Kepler et al. (2007, see their Figure 5), our mass distribution does not show this overwhelming increase in mass at low effective temperature, even though we do find several stars with masses in excess of 1 M_☉. These are (below T_eff = 15,000 K) 0249+346, 1419+351, 1542−275, 2058+342, 2147+280, and 2316−273, all of which are shown in the last panel of Figure 5. Note that there are additional white dwarfs in the same range of temperature that have more normal masses (M < 0.8 M_☉), for instance 0517+771, 1056+345, 1129+373, and 1542+244, also shown in this last panel, with the exception that these have well-defined helium absorption features—the log g-sensitive He i λ3819 line in particular—as opposed to the very massive ones. Instead of invoking a problem with the model spectra, our results suggest that we have probably reached the limit of the spectroscopic technique for these objects. They are probably cooler, more normal mass DB stars, with extremely weak absorption features (see further evidence below).

Zoom In Zoom Out Reset image size

Even if we ignore the most massive objects in Figure 21, we still note a trend for DB stars in the range 13,000 K ≲ T_eff ≲ 18,000 K to have larger masses, up to ∼0.9 M_☉ in some cases, a problem usually attributed to the treatment of van der Waals broadening (Beauchamp et al. 1996). What is more intriguing, however, is that white dwarfs with normal masses, M ∼ 0.6 M_☉, are also found in the same range of temperature as these massive stars, which implies that the large dispersion in mass that occurs at these temperatures might be real after all. This point has already been made by Limoges & Bergeron (2010) who show in their Figure 7 the spectroscopic fits for two DB stars with nearly identical temperatures (T_eff ∼ 15,000 K), but with log g values that differ by 0.33 dex (log g = 8.03 and 8.36). The comparison reveals that the He i λ3819 and λ4388 lines, which are the most gravity sensitive in this range of temperature, differ markedly in both stars, indicating that the high log g value measured in one of these stars is probably real, and not a simple artifact produced by the models.

The problem thus rests on our ability to confirm independently the atmospheric parameters obtained here within the current theoretical framework. To do so we rely on independent distance estimates obtained from trigonometric parallax measurements taken mostly from the Yale parallax catalog (van Altena et al. 1995, hereafter YPC) and from the new Hipparcos-based parallaxes from Gould & Chanamé (2004). We found good trigonometric parallaxes for 11 DB white dwarfs in our sample. The parallax and corresponding distance for each object are reported in Table 2 together with our atmospheric parameter solution, including the spectroscopic distance. The comparison of spectroscopic distances and those obtained from trigonometric parallaxes is displayed in Figure 22. The agreement is surprisingly good, especially given the fact that white dwarfs with the closest match are found in the temperature range where the mass dispersion is large in Figure 21 (T_eff ∼ 15,000 K; see Table 2). We are thus fairly confident that our surface gravity and mass values measured spectroscopically are fairly accurate.

Zoom In Zoom Out Reset image size

We also observe some discrepant distance estimates, labeled in Figure 22. For Feige 4 (0017+136; label 1), we obtain a spectroscopic distance twice as large as that inferred from the trigonometric parallax. Our fit to this DB star is excellent, and we find no easy way to reconcile the two distance estimates. GD 358 (1645+325; label 2) is a pulsating white dwarf, the only hot DB star in Table 2. Again we do not have an easy explanation for the discrepancy. G188-27 (2147+280; label 3) has a spectroscopic distance significantly smaller than that inferred from the parallax. In this case, however, the spectroscopic log g value of 8.85 (or M = 1.12 M_☉) is certainly overestimated, and this object corresponds to one of the (almost) featureless DB stars discussed earlier. A value of log g = 8.2 would actually reconcile both distance estimates perfectly. This corresponds to a mass of ∼0.7 M_☉, i.e., the average mass of the bulk of DB white dwarfs near 15,000 K.

The mass distribution of all DB and DBA stars in our sample, regardless of their temperature, is displayed in Figure 23. If we exclude from this distribution the most massive objects near ∼1.2 M_☉, which all correspond to the almost featureless cool DB stars discussed above, we find a mean mass for our sample of 〈M〉 = 0.671 M_☉ with a standard deviation of only σ_M = 0.085 M_☉. In contrast to our preliminary conclusion presented in Beauchamp et al. (1996), we now find that there is no significant mass difference between the DB and the DBA samples—〈M_DB〉 = 0.657 M_☉ and 〈M_DBA〉 = 0.688 M_☉—in agreement with the conclusions of Voss et al. (2007). This result was already apparent from a quick examination of Figure 21. Note that the hottest white dwarfs in this figure are all of the DB type, and that their masses are slightly below 0.6 M_☉, thus contributing to an average mass for the DB white dwarfs that is only slightly lower than the mean for DBA stars.

Zoom In Zoom Out Reset image size

We also compare, in Figure 23, the mass distribution of DB stars with that of DA stars from the PG Survey, reanalyzed with our improved models for hydrogen-atmosphere white dwarfs (see Tremblay et al. 2011, and references therein), and for which we obtain 〈M_DA〉 = 0.631 M_☉ and σ_M = 0.133 M_☉. While the peak of the mass distribution of DB stars agrees with that of DA stars, the former distribution is shifted toward higher masses, resulting in an average mass ∼0.03 M_☉ higher. The peak value for the DB stars, between 0.60 and 0.65 M_☉, also agrees with the peak value determined by Voss et al. (2007, see their Figure 8), although their mean mass of 〈M〉 = 0.596 M_☉ is much smaller than ours. This result is consistent with our log g determinations being larger than their values by about 0.15 dex in the temperature range where the bulk of DB white dwarfs is found (see Figure 19).

Also of interest is the absence of low-mass DB stars in our sample, in contrast with low-mass DA stars, which are present in large numbers in all surveys, including the PG Survey shown in Figure 23. Voss et al. (2007, see their Figure 8) identified three objects¹⁴ in the SPY sample with M ≲ 0.5 M_☉, the lowest mass DB white dwarf being PG 1115+158, with a mass of only 0.385 M_☉ (or log g = 7.52). This object has already been discussed in Section 5.1, and we find instead a significantly larger value of M = 0.56 M_☉ for the same star. Similarly, Voss et al. report a mass of M = 0.481 M_☉ (T_eff = 16,904 K) for HE 0423−1434, while we find 0.64 M_☉ (T_eff = 16,900 K). Hence we reaffirm the conclusion of Beauchamp et al. (1996) that low-mass DB stars are rare, or absent, a conclusion also reached by Bergeron et al. (2001). These authors found, in their photometric analysis of 152 white dwarfs with trigonometric parallax measurements, that all low-mass degenerates probably possess hydrogen-rich atmospheres. As discussed in that study, since common envelope evolution is required to produce white dwarfs with M ≲ 0.5 M_☉—the Galaxy being too young to have produced them from single star evolution—we must conclude that this particular evolutionary channel does not produce helium-rich atmosphere white dwarfs. This could be the case because the objects which go through this close-binary phase end up with hydrogen layers too massive to allow the DA to DB conversion near T_eff ∼ 30,000 K or below.

Liebert et al. (2005) presented spectrophotometric observations of a complete sample of 348 DA white dwarfs identified in the PG Survey and obtained robust values of T_eff, log g, masses, radii, and cooling ages for all stars in their sample using the spectroscopic technique. They also calculated the luminosity function of the sample, weighted by 1/V_max, where V_max represents the volume defined by the maximum distance at which a given object would still appear in the sample given the magnitude limit of the PG Survey. An overall formation rate of white dwarfs in the local Galactic disk of (1 ± 0.25) × 10⁻¹² pc⁻³ yr⁻¹ was also reported.

Since we observed all DB stars in the PG Survey, we can calculate their luminosity function in the same fashion as for DA stars using the 1/V_max values given in Table 1.¹⁵ Our results are reported in Table 3 and shown in Figure 24. Note that we rely here on bolometric magnitudes rather than absolute visual magnitudes—as Liebert et al. (2005) did (see their Figure 10)—since DA and DB stars have different M_V values at a given effective temperature and surface gravity. Also shown in Figure 24 is the contribution from the DA stars in the PG Survey, again reevaluated using our updated grid of DA model spectra. In the bolometric magnitude range over which DB stars are detected (roughly M_bol = 7–11), the DB/(DA+DB) ratio is of the order of 0.2. We note, however, a large and significant increase in the value of log ϕ in the range from M_bol = 9 to 10, which corresponds to an effective temperature near 20,000 K. Thus, the DB/DA ratio is lower than the nominal value of 1 out of 4 white dwarfs at high effective temperatures, but increases sharply for stars below 20,000 K. This, it turns out, is also the temperature at which the bottom of the helium convection zone sinks sharply into the envelope along the cooling sequence (see Figure 3). It is also the temperature below which DBA stars start to appear in large numbers in Figure 21, and also where the average mass of all DB stars increases by ∼0.1 M_☉.

Zoom In Zoom Out Reset image size

The total space density of DB stars in the PG Survey can be obtained by summing the values in Table 3 over all magnitudes bins. We obtain a space density of 5.15 × 10⁻⁵ DB star per pc³. Hence we expect in a volume defined within 20 pc from the Sun around two genuine DB stars, yet none have been identified in our sample (see also Holberg et al. 2008).

About 44% of all DB stars in our sample show traces of hydrogen, or 50% if we consider only the objects for which we have spectroscopic data covering the Hα region. Voss et al. (2007) obtained an even higher fraction of 55% based on the SPY data. Hence the DBA phenomenon is quite common among DB stars. The hydrogen abundances as a function of effective temperature for all DBA stars in our sample are displayed in Figure 25. Also shown are the upper limits on the hydrogen abundance for DB stars, as determined from the absence of Hα or Hβ. In general, these DB stars are aligned on the observational limits reproduced here from Figure 12, but some objects have noisier data and these limits are simply not reached. The first striking result is that almost all white dwarfs above T_eff ∼ 20,000 K are DB stars, with the exception of three objects (KUV 05134+2605, PG 1115+158, and PG 1456+103).

Zoom In Zoom Out Reset image size

There are two possible origins for hydrogen in these helium-dominated atmospheres. First, hydrogen could be residual, originating from the thin hydrogen atmosphere of the DA progenitor, convectively diluted into the more massive helium envelope during the DA to DB transition that occurred at higher effective temperatures. MacDonald & Vennes (1991) showed that the exact temperature at which this process occurs depends on the thickness of the hydrogen layer (see their Table 1). For their S1 models, which correspond to the Schwarzschild criterion with a value of α = 1, a DA star with hydrogen layer masses of M_H = 10⁻¹⁵, 10⁻¹⁴, and 10⁻¹³ M_☉ would, respectively, mix at temperatures of T_eff = 27,400 K, 17,900 K, and 11,700 K. The main effect of adding more hydrogen on top of the helium convection zone is to delay the time it takes for helium to develop a sufficiently deep convection zone, thus reducing the temperature at which mixing occurs. Upon mixing, it is then assumed that the thin hydrogen atmosphere will be thoroughly mixed with the more massive helium convection zone and that the resulting photospheric hydrogen abundance will simply correspond to the ratio of the total hydrogen mass M_H to that of the helium convection zone, M_He-conv. One problem immediately arises when trying to account for the hot DB stars above T_eff ∼ 20,000 K in Figure 25. Indeed, for convective mixing to occur at these temperatures, the required hydrogen layer mass has to be of the order of 10⁻¹⁵ M_☉ according to MacDonald & Vennes. This mass, it turns out, is comparable to the mass of the helium convection zone in this temperature range (see Figure 3). The complete dilution of hydrogen should thus lead to an H/He ratio ∼1 instead of the observed limits of H/He ∼10⁻⁴ to 10⁻⁵.

We can explore this problem more quantitatively by converting the hydrogen abundances from Figure 25 into total hydrogen masses by assuming that hydrogen is indeed homogeneously mixed in the helium convection zone (see also Dufour et al. 2007b; Voss et al. 2007). For simplicity, we assume evolutionary models at 0.6 M_☉ (as in Figure 3) and also ignore the feedback effect of the presence of hydrogen on the depth of the mixed H/He convection zone.¹⁶ The total hydrogen mass as a function of effective temperature for all DBA stars in our sample is displayed in Figure 26. Again, the values for DB stars represent only upper limits. Above T_eff = 22,000 K, these upper limits imply M_H ≲ 10⁻¹⁷ M_☉. Such small hydrogen layer masses are simply unable to maintain a hydrogen-rich atmosphere at higher temperatures. The only way to account for the existence of these hot DB stars in our sample is thus to conclude that they must have maintained a helium-dominated atmosphere through their entire life history. This interpretation is consistent with the existence of hot DB stars in the DB gap, i.e., 30,000 K ≲ T_eff ≲ 45,000 K (Eisenstein et al. 2006). Even the three DBA stars near 24,000 K have hydrogen layer masses (M_H ∼ 10⁻¹⁶ M_☉) too small to have been DA stars in the past according to the results shown in Figure 1 of MacDonald & Vennes (1991). However, our estimates are sufficiently approximate such that larger masses of the order of M_H ∼ 10⁻¹⁵ M_☉ can probably be accommodated in these objects, in which case they would have undergone the DA to DB transition near ∼27,000 K according to Table 1 of MacDonald & Vennes (1991).

Zoom In Zoom Out Reset image size

We note that a similar evolutionary channel is required to explain the existence of the Hot DQ stars, whose atmospheres are dominated by carbon, with only traces of helium and no hydrogen (Dufour et al. 2008). Since the hottest DQ stars known have temperatures around 24,000 K, their immediate progenitors must necessarily be DB stars with no hydrogen. Hence it is tantalizing to suggest that some of the hot DB stars observed here, as well as the hot DB stars in the gap identified in the SDSS, are the immediate progenitors of the Hot DQ stars. If this interpretation is correct, what fraction of DB stars between T_eff ∼ 30,000 K and 24,000 K are progenitors of Hot DQ stars remains to be determined.

The situation is even more complicated below T_eff ∼ 20,000 K where the inferred hydrogen layer masses in the DBA stars are in the range 10⁻¹² ≲ M_H/M_☉ ≲ 10⁻¹⁰. According to MacDonald & Vennes (1991), DA stars with such large amounts of hydrogen would only mix at temperatures below 12,000 K. In other words, we observe much more hydrogen in those stars than would be expected on the basis of the complete mixing of the hydrogen layer in the underlying helium convection zone. Hence, the hydrogen abundances in these DBA stars are too high to have a residual origin, and external sources of hydrogen must be invoked, either from the interstellar medium or from other bodies such as comets, disrupted asteroids, small planets, etc., a conclusion also reached by Voss et al. (2007; see also MacDonald & Vennes 1991). It is important to recall that hydrogen can only accumulate in the photospheric regions, as a result of accretion, while heavier elements will slowly diffuse at the bottom of the helium convection zone on timescales of the order of 10⁵ yr or less (see Table 1 of Dupuis et al. 1993). Since the bottom of the helium convection zone grows deeper with time (see Figure 3), hydrogen becomes diluted in a larger volume. The measured hydrogen abundances in cool DB stars, and eventually DC white dwarfs, are thus governed by this balance between accretion and dilution within the helium convection zone. It is thus important to connect the constraints imposed by DBA stars with independent determinations of the hydrogen abundances in cooler white dwarfs, such as DZA stars (Dufour et al. 2007b).

We show in Figure 27 the same results as in Figure 25, but we added the H/He abundance ratios predicted from continuous accretion from the interstellar medium at various rates from 10⁻²¹ to 10⁻¹⁷ M_☉ yr⁻¹ (see also Figure 10 of Voss et al. 2007 for a similar calculation). Also shown are the hydrogen abundances for the DZA stars determined by Dufour et al. (2007b). As can be seen, with the exception of the three hottest DBA stars, this range of accretion rates can easily account for the amount of hydrogen observed in DBA and DZA stars. However, some of the upper limits on the hydrogen abundance below ∼20,000 K are quite stringent, H/He <10⁻⁶. These DB stars are observed in the same range as some DBA stars, characterized by hydrogen abundances of the order of H/He ∼10⁻⁴, or a factor 100 higher. It is thus difficult to understand why accretion of hydrogen could be effective for some DBA stars, and not for other white dwarfs at the same temperature. The existence of such cool, hydrogen-deficient DB stars in our sample, and probably a significant fraction of cool DC and DZ stars as well, can only be interpreted as having evolved from hotter DB stars that contain negligible amounts of hydrogen in their atmospheres, without invoking any accretion mechanism whatsoever.

Zoom In Zoom Out Reset image size

If this interpretation is correct, the presence of hydrogen in DBA stars must be residual. Perhaps then, it is time to question the assumption of complete mixing of the hydrogen layer: in that case, it remains conceivable that the amount of hydrogen present is indeed of the order of ∼10⁻¹⁴ M_☉, i.e., the amount expected for the convective dilution of the hydrogen atmosphere to occur below T_eff ∼ 20,000 K according to MacDonald & Vennes (1991), but that it somehow floats on top of the photosphere rather than being forcefully mixed by the helium convection zone.

One particular object in our sample is LP 497-114 (1311+129), the DBA star with the largest hydrogen abundance, H/He ∼10⁻³ (at T_eff ∼ 19,000 K in Figure 25). We have three independent spectroscopic observations for this object, one of which is an SDSS spectrum (which serves also as our Hα spectrum). Our best fit to these spectra is displayed in Figure 28. The two bottom fits are clearly at odds with what we can usually achieve in this temperature range, especially given the high S/N of these observations. In particular, the region around He i λ4471, as well as the core of most neutral helium lines, is poorly reproduced. If we consider only the blue spectra, we can achieve much better fits at T_eff ∼ 23,000 K, but then the line cores of Hα and He i λ6678 are predicted much too shallow. Note that the fit to the SDSS spectrum (top) is less problematic, although the line cores are also predicted too shallow. Incidentally, LP 497-114 shows the worst agreement between optical and UV temperatures (T_UV ∼ 27,000 K in Figure 15). Perhaps the problem with the modeling of this star is the assumption of a homogeneously mixed hydrogen and helium atmospheric composition. This star might be in the process of being convectively mixed, with hydrogen constantly trying to float back to the surface. This could even explain the small spectroscopic variations from spectrum to spectrum observed in Figure 28. If this is the case, the chemically homogeneous models used here no longer apply. This might also be the case, but to a lesser extent, with other DBA stars in our sample.

Zoom In Zoom Out Reset image size

Our first assessment of the instability strip of the pulsating DB (V777 Her) stars was presented in the spectroscopic study of Beauchamp et al. (1999). However, only blue spectroscopic observations were available at that time, and the insufficient constraints on the hydrogen content in these stars did not allow us to choose the most appropriate solution. Hunter et al. (2001) presented an update of the instability strip of the V777 Her stars using new spectroscopic observations at Hα, with the specific aim of constraining the hydrogen abundance in these stars. The results, shown in Figure 2 of Hunter et al., reveal an instability strip that contains at least one non-variable white dwarf, as well as a significant number of unknowns. Since this last report, one object in this sample, PG 2246+121, has been identified as a new variable DB white dwarf by Handler (2001).

We show in Figure 29 the results from our revised spectroscopic analysis. The V777 Her stars are identified in Table 1. We distinguish in this plot variable and non-variable white dwarfs, but also DB and DBA stars. Above T_eff ∼ 20,000 K, there are only three DBA stars in our sample with hydrogen abundances around H/He ∼10^−3.5, i.e., about 1 dex larger than the upper limits derived for DB stars in the same range of temperature, and all three are pulsating white dwarfs. Given our results presented so far, DB and DBA stars in this range of effective temperature seem to form two distinct classes of objects, with probably different progenitors: hot DB stars that once resided in the gap in one case, DA stars with thin hydrogen layers (M_H ∼ 10⁻¹⁵ M_☉) in the other case. Our results displayed in Figure 29 are consistent with this idea, in the sense that we can easily identify two distinct pure instability strips, within the uncertainties, one for the pure helium-atmosphere DB stars and one for the DBA stars.

Zoom In Zoom Out Reset image size

Also displayed in Figure 29 are the theoretical blue edges for pure helium envelope models reproduced from Figure 3 of Beauchamp et al. (1999), based on the nonadiabatic calculations of Brassard & Fontaine (1997a, 1997b), for various versions of the mixing-length theory. For DB stars, the observed blue edge near T_eff ∼ 30,000 K suggests a convective efficiency somewhere between the ML2 (α = 1.0) and ML3 (≡ ML2/α = 2.0) versions of the mixing-length theory, a parameterization entirely consistent with that adopted in our model atmosphere calculations (ML2/α = 1.25). The location of the red edge of the DB instability strip is located near T_eff ∼ 25,000 K, for a corresponding strip about 5000 K wide. Two objects, shown as black open circles, are located at the red edge—KUV 03493+0131 (0349+015) and PG 2354+159—but only the latter has been confirmed as a non-variable, to our knowledge (Robinson & Winget 1983).

The boundaries of the instability strip for the DBA stars are not as well defined as for the DB white dwarfs since we lack non-variable DBA stars both hotter and cooler than the DBA pulsators studied here, which would allow us to empirically define the edges of the instability strip (for instance, there is no DBA star in our sample between T_eff ∼ 23,000 K and 20,000 K). Nevertheless, the existence of DBA pulsators cooler than the coolest variable DB stars suggests that the presence of small traces of hydrogen (H/He ∼10⁻³) in the partial ionization zone would lower the temperature at which helium-atmosphere white dwarfs can pulsate. Interestingly, the effect produced by the presence of small amounts of hydrogen on the theoretical blue edge of the instability strip has been presented in Figure 10 of Fontaine & Brassard (2008). Indeed, the blue edge becomes cooler, but the effect is rather small (∼500 K), although the authors considered a trace of only H/He = 10⁻⁴ in their calculations, and it is expected that the effect would be considerably more important with the higher hydrogen abundances inferred in our analysis.

What finally comes out of these results is that DB white dwarfs cannot be considered as a homogeneous class of objects when studying the location of the instability strip because of this additional parameter, the hydrogen abundance.

HE 2149−0516 is a DAB star discussed briefly by Voss et al. (2007), who describe its spectrum as exhibiting strong Balmer lines and weaker but strong neutral helium lines. The authors had difficulty fitting this object with either pure hydrogen or pure helium models, and only a pure hydrogen fit to Hα suggested a temperature near T_eff ∼ 30,000 K, with an extremely low surface gravity of log g ∼ 7. Our normalized spectrum for this peculiar white dwarf is displayed in Figure 30. The absolute energy distribution (not shown here) is almost flat in the wavelength range displayed here, so this cannot be a hot white dwarf. Our best solution with our grid of DB models indeed yields T_eff = 11,370 K, log g = 7.6, and log H/He =−4.5, but our spectroscopic fit completely fails to reproduce both the helium and hydrogen lines adequately. Instead, we could achieve a much better fit by assuming that HE 2149−0516 is an unresolved DA + DB (or perhaps DBA) composite system. In this case, each component of the system dilutes the absorption features of the other component. Given that there are simply too many free parameters to fit and that the observed features are relatively weak, we kept both values of log g fixed in our fitting procedure, as well as the value of H/He for the DB star, and experimented with various values of these parameters. Our best fit is displayed in Figure 30. This is admittedly not a perfect fit, especially in the blue region of the spectrum, but given that both the DA and DB components fall in a temperature range that is problematic in terms of the modeling (i.e., the high log g problem), we are rather satisfied with the quality of our fit. Note that the combined model fluxes also reproduce the slope of the observed energy distribution perfectly (not shown here).

Zoom In Zoom Out Reset image size