Free Access
Issue
A&A
Volume 531, July 2011
Article Number L7
Number of page(s) 5
Section Letters
DOI https://doi.org/10.1051/0004-6361/201116887
Published online 20 June 2011

© ESO, 2011

1. Introduction

AA Dor is a close, eclipsing, post common-envelope binary system with an sdOB-type primary star and an unseen low-mass companion. The orbital period is 0.261 539 7363 (4) d (Kilkenny 2011) and the inclination is (Hilditch et al. 2003). A detailed introduction to the system and previous analyses is given in Rauch (2004), and we summarize results of previous spectral analyses of the primary in Table 1.

Table 1

Effective temperature and surface gravity of the primary of AA Dor, determined in previous and the present spectral analyses.

Rauch (2000) encountered the problem of his spectroscopically determined surface gravity log g = 5.21 ± 0.1 not matching log g = 5.53 ± 0.03 determined from light-curve analysis (Hilditch et al. 1996). Hilditch et al. (2003) present an improved photometric model and derive log g = 5.45−5.51. The reason for the log g discrepancy is unknown. Fleig et al. (2008) find a slightly higher log g = 5.3 ± 0.1 but the discrepancy remains. A recent analysis by Müller et al. (2010) has apparently solved the log g problem by finding log g = 5.51 ± 0.05.

Müller et al. (2010) do not consider that the He I lines (as well as other lines of low-ionized species, e.g. of Mg II, Fig. 1) are too strong in the models at their favored parameters and log g = 5.51 ± 0.05, as demonstrated in Fig. 1. Increasing the He abundance to better fit He II λ   4686 Å also results in a much stronger He I λ   4471 Å, which then disagrees with the observation. We mention that Fleig et al. (2008) evaluate the ionization equilibria of C III/C IV, N III/N IV, O III/O IV, P IV/P V, and S IV/S V in the FUV wavelength range and find to agree with the higher Teff concluded from the He I lines.

Since Kurucz (2009, http://kurucz.harvard.edu/atoms.html has substantially extended his database, and the model atoms in our Tübingen Model-Atom Database (TMAD1) have been updated as well, we decided to calculate an improved, extended, state-of-the-art NLTE model-atmosphere grid. This grid is described in Sect. 2. The re-analysis of our UVES spectra (105–180 s, which in total cover one orbital period and which were also used by Müller et al. 2010) that were obtained in 2001 at the VLT is described in Sect. 3. We conclude in Sect. 4.

2. Atomic data and model-atmosphere grid

The model atmospheres used here were calculated with the Tübingen Model-Atmosphere Package (Werner et al. 2003, TMAP). The models are plane-parallel, in hydrostatic and radiative equilibrium. TMAP uses the occupation-probability formalism of Hummer & Mihalas (1988) that was generalized to NLTE conditions by Hubeny et al. (1994). TMAP considers opacities of H+He+C+ N+O+Mg+Si+P+S using classical model atoms, and Ca+Sc+Ti+V+Cr+Mn+Fe+Co+Ni uses a statistical approach (Rauch & Deetjen 2003). All model atoms used in our calculations were updated to the most recent atomic data (Sect. 1), and 530 levels are treated in NLTE with 771 individual lines (from H–S) and 19 957 605 lines of Ca–Ni from Kurucz’ line lists (Kurucz 2009) combined to 636 superlines. The element abundances are summarized in Table 2.

The model-atmosphere grid spans (ΔTeff = 500   K) and log g = 5.15−6.20 (Δlog g = 0.05). In total this makes 638 models. Spectral energy distributions (SEDs) were calculated using the most recent line broadening data, e.g. H i line-broadening has changed in TMAP since Fleig et al. (2008) presented their analysis of AA Dor. The reason is that Repolust et al. (2005) found an error in the H i line-broadening tables (for high members of the spectral series only) by Lemke (1997) that were used before. These were substituted by a Holtsmark approximation. In addition, Tremblay & Bergeron (2009) provide new, parameter-free Stark line-broadening tables for H i considering non-ideal effects. These replaced Lemke’s data for the lowest ten members of the H i Lyman and Balmer series. In the parameter range of AA Dor, the new broadening tables have a significant impact on the line wings of higher Balmer-series members (narrower for H ϵ and higher, Fig. 2). As a consequence, our analysis results in a higher log g (Sect. 3).

thumbnail Fig. 1

Comparison of our synthetic spectra (full, blue line: , log g = 5.51; dashed, red: , log g = 5.46; He = 0.0027 by mass) around He I λ   4471 Å and Mg II λ   4481 Å (left) and He II λ   4686 Å (right) with the observation. The models are convolved with a rotational profile corresponding to vrot = 30 km s-1. Models and observation are smoothed with a Gaussian (0.1 Å FWHM) for clarity.

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In the framework of the Virtual Observatory2 (VO), all these SEDs (λ − Fλ) are available in VO compliant form via the VO service TheoSSA3 provided by the German Astrophysical Virtual Observatory (GAVO4).

3. Analysis and results

The light curve of AA Dor exhibits a reflection effect (e.g. Hilditch et al. 1996) that amounts to about 0.06 mag in the optical. To analyze the pure primary spectrum, we selected only those four observations that were taken closest to the occultation of the secondary. These were co-added in order to improve the S/N. In Fig. 3, we show a χ2 fit to all single UVES spectra. Our χ2 fit excludes the inner line cores of Hβ and Hγ, as well as obviously bad data points (quality flags given by Müller et al. 2010). Both the occultation (at φ = 0.5) and the transit (φ = 0.0) of the secondary are clearly visible in the determination of Teff and log g. Compared to a similar χ2 fit of Müller et al. (2010, their Fig. 3), we find the same log g = 5.45 but a significantly higher than for .

thumbnail Fig. 2

Synthetic spectrum calculated from a and log g = 5.45 model with different Stark line-broadening tables (L, blue line: Lemke 1997, T, red: Tremblay & Bergeron 2009, see text).

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thumbnail Fig. 3

Phase-dependent, best-fitting grid model determined by a χ2 fit. φ = 0.0 is the transit, φ = 0.5 is the occultation of the secondary. (The steps in Teff and log g represent the grid spacing.)

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For the analysis, we perform a detailed comparison in the classical way (χ-by-eye) and, for comparison in analogy to Müller et al. (2010) with a χ2 fit, used the same wavelength limits (Table 3) and lines, H β – H 11 and He II λ   4686 Å. Our χ2 fit yields and (T in Fig. 4). These errors are formal 1σ errors, and σ was calculated from the deviation of the model from the observed spectrum used in the χ2 fit. Compared to a similar χ2 fit with SEDs that were calculated with the previously used Stark broadening tables of Lemke (1997, L in Fig. 4, there is a significant deviation of ΔTeff = 600   K and Δlog g = 0.06.

thumbnail Fig. 4

Left: formal 1σ, 2σ, and 3σ contour lines of our χ2 fits in the Teff – log g plane. Right: reduced χ2 of our models depending on log g.

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A comparison of the best-fitting model from our χ2 fit and the best-fitting  χ-by-eye with the observations is shown in Fig. 5. It is obvious that the ionization equilibrium of He I / He II is reproduced not at but at . The theoretical line profiles of lower members of the Balmer series (H β – H δ) do not reproduce the observation perfectly. They fit slightly better at . Thus, a small Balmer-line problem (Napiwotzki & Rauch 1994; Werner 1996) due to additional metal opacities that are still not considered is apparently present. The inclusion of He I λ   4471 Å (Table 3) in the χ2-fit procedure results in higher . We finally adopt (cf. Fleig et al. 2008) and log g = 5.46 ± 0.05 because the previously evaluated ionization equilibria (Rauch 2000; Fleig et al. 2008) are an additional, crucial constraint. A χ2 fit at fixed (additional models were calculated with log g = 5.30 − 5.60 and Δlog g = 0.01) also has its minimum at log g = 5.46 (Fig. 4).

thumbnail Fig. 5

Comparison of synthetic line profiles of H and He lines calculated from a and log g = 5.46 model (left) and a and log g = 5.46 model (right) with the observation.

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A mass of Mpri = 0.4714 ± 0.0050   M is determined by comparing of Teff and log g with the evolutionary tracks of post-EHB stars (Fig. 6). From the same evolutionary calculations, we interpolate the primary’s luminosity. From our final model, we can determine the spectroscopic distance of AA Dor following Heber et al. (1984). We derive a distance of . The parameters of AA Dor are summarized in Tables 2 and 4.

thumbnail Fig. 6

Location of AA Dor in the Teff − log g plane compared to sdBs and sdOBs from Edelmann (2003). Post-EHB tracks from Dorman et al. (1998, labeled with the respective stellar masses in M are also shown.

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Table 4

Parameters of AA Dor compared with values of Hilditch et al. (2003).

thumbnail Fig. 7

Mass-radius relation for the primary of AA Dor. The dashed lines show the error ranges. The vertical lines show the primary mass, derived from comparison with post-RGB (Rauch 2000) and post-EHB (Fig. 6) evolutionary models.

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4. Conclusions

The so-called log g problem in AA Dor is solved (Fig. 7) and our results (Table 4) are in good agreement with the photometric model of Hilditch et al. (2003).

Four influences were identified on the log g determination.

  • 1)

    The major impact is the improvement in the Stark broadening tables, i.e. the difference between those of Lemke (1997) and of Tremblay & Bergeron (2009). This results in a systematic deviation of ΔTeff = 600   K and Δlog g = 0.06.

  • 2)

    The reflection effect is now eliminated by using only observed spectra that were obtained during the occultation of the secondary (Sect. 3).

  • 3)

    The improved atomic data makes the model-atmosphere more reliable thanks to a fuller consideration of the metal-line blanketing. The temperature stratification of the stellar models, however, is only marginally affected.

  • 4)

    The rotational velocity is lower than previously assumed (Müller et al. 2010). This only has little influence on the inner line core and is thus important for weak and narrow lines like He II λ   4686 Å (Fig. 1).

Since Vučković et al. (2008) identified spectral lines of the secondary in the UVES spectra and determined a lower limit (Ks > 230   km   s-1) of its orbital velocity amplitude, both components’ masses are known (Mpri = 0.45   M, Ms = 0.076   M, Vučković et al. 2008), albeit with large error bars. Müller et al. (2010) used the velocity amplitudes of both components (Kpri = 40.15 ± 0.11   km   s-1, Ks = 240 ± 20   km   s-1) to derive the masses and . This rules out a post-RGB scenario because post-RGB masses are significantly lower. The solution from mass function f(m) and light curve analysis, however, intersects with our result of log g = 5.46 ± 0.05 (Fig. 7) even for the higher post-EHB mass (Fig. 6).

From our mass determination of Mpri = 0.4714 ± 0.0050   M, we calculated (MpriKpri = MsKs) the secondary’s mass of Msec = 0.0725 − 0.0863   M. Since the hydrogen-burning mass limit is about 0.075   M (Chabrier & Baraffe 1997; Chabrier et al. 2000), the secondary may either be a brown dwarf or a late M dwarf.


Acknowledgments

We thank the anonymous referee, the editor R. Napiwotzki, and K. Werner for comments and discussions that helped to improve the paper. The UVES spectra used in this analysis were obtained as part of an ESO Service Mode run, proposal 66.D-1800. This research made use of the SIMBAD Astronomical Database, operated at the CDS, Strasbourg, France. We thank the GAVO team for support. T.R. is supported by the German Aerospace Center (DLR) under grant 05 OR 0806.

References

Online material

Table 2

Element abundances in our model-atmosphere grid.

Table 3

Lines and wavelength intervals used for our χ2 fits.

All Tables

Table 1

Effective temperature and surface gravity of the primary of AA Dor, determined in previous and the present spectral analyses.

Table 4

Parameters of AA Dor compared with values of Hilditch et al. (2003).

Table 2

Element abundances in our model-atmosphere grid.

Table 3

Lines and wavelength intervals used for our χ2 fits.

All Figures

thumbnail Fig. 1

Comparison of our synthetic spectra (full, blue line: , log g = 5.51; dashed, red: , log g = 5.46; He = 0.0027 by mass) around He I λ   4471 Å and Mg II λ   4481 Å (left) and He II λ   4686 Å (right) with the observation. The models are convolved with a rotational profile corresponding to vrot = 30 km s-1. Models and observation are smoothed with a Gaussian (0.1 Å FWHM) for clarity.

Open with DEXTER
In the text
thumbnail Fig. 2

Synthetic spectrum calculated from a and log g = 5.45 model with different Stark line-broadening tables (L, blue line: Lemke 1997, T, red: Tremblay & Bergeron 2009, see text).

Open with DEXTER
In the text
thumbnail Fig. 3

Phase-dependent, best-fitting grid model determined by a χ2 fit. φ = 0.0 is the transit, φ = 0.5 is the occultation of the secondary. (The steps in Teff and log g represent the grid spacing.)

Open with DEXTER
In the text
thumbnail Fig. 4

Left: formal 1σ, 2σ, and 3σ contour lines of our χ2 fits in the Teff – log g plane. Right: reduced χ2 of our models depending on log g.

Open with DEXTER
In the text
thumbnail Fig. 5

Comparison of synthetic line profiles of H and He lines calculated from a and log g = 5.46 model (left) and a and log g = 5.46 model (right) with the observation.

Open with DEXTER
In the text
thumbnail Fig. 6

Location of AA Dor in the Teff − log g plane compared to sdBs and sdOBs from Edelmann (2003). Post-EHB tracks from Dorman et al. (1998, labeled with the respective stellar masses in M are also shown.

Open with DEXTER
In the text
thumbnail Fig. 7

Mass-radius relation for the primary of AA Dor. The dashed lines show the error ranges. The vertical lines show the primary mass, derived from comparison with post-RGB (Rauch 2000) and post-EHB (Fig. 6) evolutionary models.

Open with DEXTER
In the text

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