NEW PRECISION ORBITS OF BRIGHT DOUBLE-LINED SPECTROSCOPIC BINARIES. III. HD 82191, ω DRACONIS, AND 108 HERCULIS

Young (1942) reported the discovery of the duplicity of HD 82191 [α = 09^h31^m1739, δ = 27°23'141 (2000)]. He remarked that its spectrum is undoubtedly double lined although it was barely resolved on the 66 Å mm⁻¹ photographic plates that were obtained at the David Dunlap Observatory (DDO). The combined spectral class was estimated as being A0. Six follow-up spectra were obtained between 1946 and 1948. However, over two decades would pass before an extended observational effort at DDO by Heard & Hurkens (1973) resulted in 43 additional spectrograms and an analysis of the star system. They computed an orbital period of 9.0119 days and determined that the orbit is essentially circular. Comparing the line ratios of the iron lines of the sharp-lined components, they concluded that since the Fe ii lines of the two components are more equal in intensity than the Fe i lines, the secondary star has the earlier spectral type. Their derived minimum masses for the components are so large, ∼2 M_☉, that Heard & Hurkens (1973) suggested that the system is eclipsing. Based on the orbital prediction, Fernie (1974) detected a primary eclipse that lasted approximately 3 hr. However, because he observed a V mag depth of only 0.03, Fernie (1974) suggested that the eclipse should be verified. Gulliver (1971) noted that HD 82191 is an Am star. Abt (2004) did not confirm the Am spectral classification, but instead gave a combined spectral type of A0 Vs.

The naked eye star ω Dra [α = 17^h36^m5709, δ = 68°45'287 (2000)] was first observed spectroscopically at the very end of the 19th century. From four radial velocities obtained at Lick Observatory, Campbell (1899) announced that ω Dra was a single-lined spectroscopic binary with rapid variability. However, it was not until seven years later that an extensive series of plates was acquired at that observatory, enabling Turner (1907) to determine orbital elements from 26 observations. He characterized the star as F-type with rather broad, fuzzy lines and found an orbital period of 5.27968 days and an eccentricity very close to zero. Both Luyten (1936) and Lucy & Sweeney (1971) reexamined the orbital velocities used by Turner (1907) and adopted a circular orbit. As part of a survey of spectroscopic binaries among F- and G-type dwarfs and subgiants, Abt & Levy (1976) reobserved ω Dra at Kitt Peak National Observatory (KPNO) and were the first to detect lines of the secondary. They noted that a faint visual companion, which is over 70'' away, seems to have a common proper motion with the brighter system. In a survey for additional companions to 25 known binary systems, at Haute-Provence Observatory (HPO) Mayor & Mazeh (1987) obtained a third set of radial velocities for ω Dra. The center-of-mass velocities derived for the three data sets are quite similar, indicating no close companion to the binary.

Both Roman (1950) and Slettebak (1955) classified the combined spectrum of ω Dra as F5 V, similar to the more recent spectral type of F4 V given by Cowley (1976). Herbig & Spalding (1955) estimated a projected rotational velocity of <20: km s⁻¹, while Slettebak (1955) found a value of <25 km s⁻¹, and Levato (1975) determined 13 km s⁻¹. Favata et al. (1995) measured v sin i values of ⩽14 km s⁻¹ for both components.

The star 108 Her [α = 18^h20^m5697, δ = 29°51'321 (2000)] was discovered to be a binary early in the twentieth century. From plates taken at Mount Wilson Observatory in 1911, Adams (1912) listed four radial velocities that showed a significant variation. Using velocities from 17 plates acquired at the Astrophysical Observatory, Potsdam, Ludendorff (1914) determined a circular orbit with a period of 5.1460 days and found evidence of lines of the secondary. Shortly thereafter, Daniel & Jenkins (1916) made a much more extensive analysis with 93 spectrograms that were obtained at Allegheny Observatory from 1912 through 1914. While they reported that lines of the primary were fairly easy to measure, they stated that lines of the secondary were faint and hard to measure. Nevertheless, they were able to determine velocities of the secondary from the majority of their spectrograms. Nearly 70 years later Abt & Levy (1985) obtained 22 new observations at KPNO. They concluded that their velocities provided a small improvement in the period and produced an essentially circular orbit. While such properties of the orbit were in agreement with the results of Daniel & Jenkins (1916), Abt & Levy (1985) found a substantially smaller semiamplitude velocity for the secondary that resulted in a mass ratio of 1.11.

Cowley et al. (1969) classified 108 Her as A5m: or a mild metallic-lined star, where their subclass is a measure of the Ca K line. Bidelman (Abt & Bidelman 1969), however, called it a definite Am star. Bertaud (1970) found A5 for the Ca K line, and F0 for the metallic spectrum. More recently, Abt & Morrell (1995) also noted that the composite spectrum was that of an Am star, classifying it as A3/F0/F0 for the Ca K, Balmer, and metal lines, respectively.

Stickland (1973) determined abundances for the components of 108 Her, confirming the enhancement of iron in both components. However, only the primary exhibited a deficiency of calcium. Burkhart & Coupry (1991) also examined the calcium and iron abundances of the components of 108 Her, confirming that the primary is an Am star, but they concluded that the secondary has normal abundances of those two elements. Both components are slowly rotating, with v sin i ⩽ 20 km s⁻¹ (Abt 1975).

The 18 radial velocities of the primary that we obtained from the McDonald Observatory spectra are the most precise, and so we have used them to compute both eccentric and circular orbits. The eccentric solution produces e = 0.0028 ± 0.0008, and taken at face value, the tests of Lucy & Sweeney (1971) indicate that the eccentric solution should be adopted. However, the eccentricity is extremely small and may have resulted from observational errors. In addition, the distribution of the velocities is not as uniform as one would like. In fact, only five of the 18 velocities are on the descending branch of the velocity curve. Thus, we have chosen to adopt a circular orbit solution for HD 82191.

In addition to using our new velocities from McDonald Observatory and KPNO, we have also investigated the possibility of combining those observations with the earlier photographic ones from DDO. For the primary we made individual circular orbit solutions, which resulted in weights of 1.0, 0.1, and 0.005 for the McDonald, KPNO, and DDO velocities. Then a combined solution of the McDonald and KPNO primary velocities, appropriately weighted, was computed and compared with a solution containing velocities from all three observatories. In the latter solution the inclusion of the DDO velocities extensively extends the time baseline, but the only orbital element with an improved uncertainty is the period. However, the period in the three-observatory solution changed by less than 1σ, and so we have chosen not to include the DDO velocities in our analysis. A final circular orbit solution included the velocities of the secondary, for which we assigned weights of 0.5 and 0.07 for the McDonald and KPNO velocities, respectively. The large difference between these two weights, as well as those for the primary component, 1.0 versus 0.1, reflects the fact that for HD 82191 the spectral types of its two components are significantly earlier than most of the other stars that we are observing in this program. This puts the KPNO velocities at a disadvantage, in part because of the very limited 84 Å wavelength range that we observe but also because the Fe i lines in the 6430 Å region, which are generally measured in the later-type stars, are very weak in strength, and the small number of Fe ii lines in this region are also not particularly strong. The 18 McDonald Observatory and 12 KPNO observations used for this orbital solution are given in Table 2.

Table 3 lists the resulting elements for our final circular orbit, as well as the elements of Heard & Hurkens (1973). Figure 1 compares our new primary and secondary velocities with the calculated velocity curves, and zero phase is a time of maximum velocity for the primary. Inspection of Table 3 shows that our new orbital elements are generally consistent with those of Heard & Hurkens (1973) but are much more precise.

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To determine whether an eccentric or circular orbit is more appropriate for ω Dra, we have examined the 58 Fairborn Observatory observations of the primary, which are our most precise velocities. The eccentric solution results in e = 0.0027 ± 0.0008. Compared with a circular orbit solution of the same data, the tests of Lucy & Sweeney (1971) indicate that the eccentric solution should be adopted. However, once again, the eccentricity is extremely small and may simply result from observational errors. Thus, we also computed circular and eccentric solutions using the Fairborn observations of the secondary. For that eccentric solution we find e = 0.0009 ± 0.0009, an even smaller value than that for the solution of the primary. In this case the tests of Lucy & Sweeney (1971) indicate that the circular orbit should be adopted, a conclusion opposite to that found for the primary. Help in resolving this apparent contradiction is provided by the ω values of the two eccentric solutions. The difference for the two components is only 2°, compared to the expected value of 180°, if the orbit were truly eccentric. Because of this result and the very small eccentricities found for both components, we have chosen to adopt a circular orbit for ω Dra.

In addition to the large number of spectrograms from Fairborn Observatory, we also obtained 21 observations at KPNO and three at McDonald Observatory, one of which was acquired at single-lined phase. Because of their small number, we have chosen to treat the McDonald observations as if they are part of the data obtained at KPNO. Another set of velocities, those of HPO (Mayor & Mazeh 1987), were also considered for possible inclusion in the final orbital solution. Thus, we computed individual orbital solutions to determine the weights for the various sets of velocities. For the primary component those weights are 1.0, 0.8, and 0.04 for the Fairborn, KPNO/McDonald, and the HPO velocities of Mayor & Mazeh (1987), respectively. A combined solution with those three data sets, compared to a solution with just our Fairborn and KPNO/McDonald velocities, resulted in a slightly more precise period because of the longer time span of the data. However, the periods that were determined in the two solutions differ by less than their 1σ uncertainties, and the uncertainties of the other elements were not significantly improved with the addition of the Mayor & Mazeh (1987) HPO velocities. Thus, we have chosen not to include any of the HPO velocities in our later solutions.

We next determined weights for the secondary component, which are 0.6 and 0.3 for our Fairborn and KPNO/McDonald velocities, respectively. With the velocities for both stars appropriately weighted, we computed a final combined circular orbit solution. The Fairborn and KPNO/McDonald Observatory observations used for this orbital solution are given in Table 4. Table 5 lists our orbital elements and those of Mayor & Mazeh (1987). Their period, which has a slightly better uncertainty than ours, was determined by combining their elements with the T₀ value of Luyten (1936), who based that result on an orbital solution of the radial velocities of Turner (1907). The elements of the two solutions are generally consistent but our resulting minimum masses are much more precise. Figure 2 compares our primary and secondary velocities with the calculated velocity curves. Zero phase for that orbit is a time of maximum velocity for the primary.

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For 108 Her the 14 radial velocities of the primary that we obtained from the McDonald Observatory spectra are the most precise, and so we have used them to compute both eccentric and circular orbits. The eccentric solution produces e = 0.0016 ± 0.0005, and taken at face value, the tests of Lucy & Sweeney (1971) indicate that the eccentric solution should be adopted. However, the eccentricity is extremely small, and just as in the case of HD 82191, the distribution of the velocities is not as uniform as one would like. In fact, only five of the 14 velocities are on the ascending branch of the velocity curve. Because we have almost twice as many KPNO velocities, we also computed an eccentric solution of the primary with those velocities. That solution gave an even smaller eccentricity, e = 0.0008 ± 0.0009, than with the McDonald velocities. In this case, the precepts of Lucy & Sweeney (1971) indicate that the circular solution should be adopted. Because of this result and the possible bias introduced by the very unequal phase distribution of the McDonald Observatory velocities, we have chosen to adopt a circular orbit solution for 108 Her.

The velocities of Ludendorff (1914) and Daniel & Jenkins (1916) are not precise enough to improve our orbital solution. To see whether the velocities of Abt & Levy (1985) warrant inclusion in our combined orbital solution, we reexamined the orbit of Abt & Levy (1985), using their primary velocities alone. Adopting their period, which is substantially different from the one computed by Daniel & Jenkins (1916) as well as the one determined in this paper, produces an extremely poor fit to their data. Reanalysis of their primary velocities with the period as a free parameter results in a period that is similar in value to ours. Thus, perhaps the period given by Abt & Levy (1985) is a transcription error.

We computed individual orbital solutions to determine the weights for each set of velocities. For the primary those weights are 1.0, 0.4, and 0.004 for the McDonald, KPNO, and Abt & Levy (1985) KPNO velocities, respectively. A combined solution with those three data sets, compared to a solution with just our McDonald and KPNO velocities, resulted in a slightly more precise period because of the longer time span of the data. However, the periods that were determined in the two solutions differ by less than their 1σ uncertainties, and the uncertainties of the other elements were not improved with the addition of the Abt & Levy (1985) velocities. Thus, we have chosen not to include any of the Abt & Levy (1985) velocities in our later solutions. We next determined weights for the secondary component, which are 0.3 and 0.1 for our McDonald and KPNO velocities, respectively. With our McDonald and KPNO velocities for both stars appropriately weighted, we computed a final combined circular orbit solution (Table 7). The 14 McDonald Observatory and 26 KPNO observations used for this orbital solution are given in Table 6.

Table 7 lists the resulting elements for our final orbit, as well as the orbital elements of Abt & Levy (1985). The much smaller uncertainties of our elements are obvious. The problem with the period derived by Abt & Levy (1985) has been discussed above. In addition, although our mass ratio is very similar to theirs, our minimum masses are more than 20% larger. Finally, Figure 3 compares our new primary and secondary velocities with the calculated velocity curves. Zero phase for that orbit is a time of maximum velocity for the primary.

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Gulliver (1971) identified HD 82191 as an Am star, and Heard & Hurkens (1973) judged the system to have A1, mid A, and F0 spectral classes for its calcium, hydrogen, and metal lines, respectively. Such a classification is quite different from that of Abt (2004), who classified the combined spectrum as A0 Vs.

Figure 4 compares a spectrum of 68 Tau (panel (a)) to a blended spectrum (panel (b)) and a double-lined spectrum (panel (c)) of HD 82191. Although Cowley et al. (1969) and Abt & Morrell (1995) classified 68 Tau as A2 IV, Conti (1965) identified it as one of the prototypes for the extension of Am stars to early-A spectral types. Conti (1965) also discussed why visual identification of Am star anomalies is difficult for these hotter A stars. In the case of 68 Tau its Am nature has been confirmed by several abundance analyses, including those of Varenne & Monier (1999) and Pintado & Adelman (2003).

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The most numerous lines of 68 Tau in the 6430 Å region are Fe i lines. However, because of its effective temperature, the three strongest features of 68 Tau in this wavelength region are Fe ii lines, which are indicated, along with the strongest Ca i line, in Figure 4. Most of the lines in the spectrum of 68 Tau that are redward of the Fe ii line at 6457 Å are terrestrial water vapor lines. Ignoring those lines, the blended spectrum of HD 82191 (panel (b)) appears similar to that of 68 Tau except for the calcium line at about 6440 Å, which is significantly weaker in HD 82191. The spectrum of HD 82191 in panel (c), which shows lines of the individual components, enables us to identify the star with the stronger Fe ii lines and the weaker Fe i lines as the more massive primary. From spectrum addition fits with 68 Tau to the individual components of HD 82191 we estimate that the spectral classes for the iron lines of the primary and secondary are about A1 and A4, respectively. Relative to 68 Tau, previously identified as an Am star, the primary is clearly deficient in calcium, and the secondary probably is as well. Thus, we concur with the conclusion of Heard & Hurkens (1973) that both components are Am stars.

From the ratio of the line depths of the Fe ii lines the magnitude difference between the components is 0.2 mag at 6430 Å, essentially the same as that found by Heard & Hurkens (1973) from their blue spectrograms. Even adopting a larger magnitude difference, as discussed in Section 6.1, the Hipparcos parallax (Perryman et al. 1997) indicates that both stars are on the main sequence.

Both Roman (1950) and Slettebak (1955) classified the combined spectrum of ω Dra as F5 V, similar to the more recent spectral type of F4 V given by Cowley (1976). The reference stars θ Cyg (F4 V (Slettebak 1955) and mean [Fe/H] = 0.01 (Taylor 2005)) and λ Ser (G0 V (Keenan & McNeil 1989) and mean [Fe/H] = 0.00 (Taylor 2005)) produce an excellent fit to the components.

The continuum intensity ratio of the secondary/primary is 0.376, which results in a continuum magnitude difference of 1.06 at 6430 Å. The secondary has a significantly later spectral class than the primary, and so this is a minimum value. As discussed in Section 6.2, the Hipparcos parallax (Perryman et al. 1997) indicates that both stars are on the main sequence.

Classifiers have identified 108 Her as an Am star, with Abt & Morrell (1995) concluding that the combined spectrum has types A3/F0/F0 for the Ca i K line, the Balmer lines, and the metals. From our visual examination of the 6430 Å region, it is clear that the primary is an Am star. Although we are unable to find an Am reference star among our collection of spectra that reasonably approximates the primary's spectrum, comparing the ratio of the Fe ii and Fe i lines to those of several reference stars, we estimate that the spectral class of the iron lines is A7. The calcium lines of the primary are weak and thus, have an earlier spectral class, which we estimate as A3. The iron and calcium lines of the secondary in the 6430 Å region are well matched by the A9 V spectrum (Abt & Morrell 1995) of HR 1613, which has normal rather than peculiar abundances of those elements (Bikmaev et al. 2002). Thus, we conclude that the primary is an Am star, while the secondary has a spectral class of A9.

Comparing several Fe i lines, the average ratio of their equivalent widths is 0.57, which translates to a magnitude difference of 0.6 at 6430 Å. This is a lower limit to that difference because the Am star's iron line strengths are somewhat enhanced. With such a magnitude difference or even significantly larger ones (Section 6.3), the Hipparcos parallax (Perryman et al. 1997) indicates that both stars are on the main sequence.

To determine if the components of HD 82191 are synchronously rotating, we must first estimate their radii. Although the system is believed to be eclipsing, no light-curve solution is available. Thus, we obtain its radii using the Stefan–Boltzmann law. From the Hipparcos catalog (Perryman et al. 1997) the V magnitude and B − V color of the HD 82191 system are 6.64 and 0.08, respectively. The Hipparcos parallax of 7.11 ± 0.84 mas (Perryman et al. 1997) corresponds to a distance of 141 ± 17 pc. Although at such a distance there may be a slight amount of interstellar reddening, we have assumed that there is none.

While our magnitude difference from Section 5.1 indicates that the stars are nearly equal in brightness, the primary to secondary mass ratio of 1.2 suggests otherwise. Thus, we have adopted the 0.8 mag difference from the mass–luminosity calibration of Smith (1983), which increases the apparent magnitude of the primary by 0.4 mag. The parallax, the V magnitude, and the adopted V magnitude difference were combined to obtain absolute magnitudes M_V = 1.3 ± 0.3 mag and M_V = 2.1 ± 0.3 mag for the primary and secondary, respectively. We next adopted B − V colors of 0.06 and 0.12 for the primary and secondary, respectively, and then used Table 3 of Flower (1996) to obtain the bolometric corrections and effective temperatures of the two components. The resulting luminosities of the primary and secondary are L₁ = 24.8 ± 7.4 L_☉ and L₂ = 11.3 ± 3.4 L_☉, respectively, while the radii are R₁ = 2.1 ± 0.4 R_☉ and R₂ = 1.6 ± 0.3 R_☉, respectively. The uncertainties in the computed quantities are primarily due to the parallax uncertainty plus, to a lesser extent, the effective temperature uncertainty, which is estimated to be ± 300 K.

For HD 82191 our v sin i values, averaged from eight spectra, are 11.7 ± 1.0 and 11.9 ± 1.0 km s⁻¹ for the primary and secondary, respectively. The minimum masses of the two components are relatively large, and Fernie (1974) detected a partial eclipse of the primary, indicating that the orbital inclination is not too far from 90°. Choosing a somewhat smaller inclination of 85° does not significantly increase our projected rotational velocities, and so we adopt 12 km s⁻¹ as the equatorial rotational velocity for both components. The estimated radii result in rotational velocities of 11.8 and 9.0 km s⁻¹ for the primary and secondary, respectively. Thus, the primary is synchronously rotating, while the secondary appears to be rotating faster than synchronous. However, given the uncertainty of the secondary's estimated radius, and the difficulty in measuring the broadening of the very weak lines of the secondary, it is possible that the secondary is also synchronously rotating.

Similar to HD 82191, the answer to the question of whether the components of ω Dra are synchronously rotating begins with estimates of the components' radii. From the Hipparcos catalog (Perryman et al. 1997) the V magnitude and B − V color of the ω Dra system are 4.77 and 0.43, respectively. The Hipparcos parallax of 42.62 ± 0.53 mas (Perryman et al. 1997) corresponds to a distance of 23.46 ± 0.29 pc. From a consideration of our spectral types and minimum magnitude difference, we adopted a V magnitude difference of 1.2, slightly larger than the canonical value given by Gray (1992). The parallax, the V magnitude, and the adopted V magnitude difference were combined to obtain absolute magnitudes M_V = 3.2 ± 0.1 mag and M_V = 4.4 ± 0.2 mag for the primary and secondary, respectively. We next assumed B − V colors of 0.40 and 0.58 (Gray 1992), for the primary and secondary, respectively, and then used Table 3 of Flower (1996) to obtain the bolometric corrections and effective temperatures of the two components. The resulting luminosities of the primary and secondary are L₁ = 4.0 ± 0.4 L_☉ and L₂ = 1.4 ± 0.3 L_☉, respectively, while the radii are R₁ = 1.5 ± 0.1 R_☉ and R₂ = 1.1 ± 0.1 R_☉, respectively. These values indicate that both components are on the main sequence. The uncertainties in the computed quantities are dominated by the parallax and the effective temperature uncertainties. The latter is estimated to be ±200 K for the primary and ± 150 K for the secondary.

For ω Dra our v sin i values, averaged from eighteen KPNO spectra, are 7.2 ± 1.0 and 7.1 ± 2.0 km s⁻¹ for the primary and secondary, respectively. The estimated uncertainty for the secondary is larger because the lines of the secondary are significantly weaker than those of the primary and thus, are more susceptible to blends that would increase the line broadening. The minimum masses of the components are very small, and so we adopt the canonical masses (Gray 1992) for our spectral types, which produce an orbital inclination of 29°. Assuming this value for the rotational inclination increases the rotational velocities to 14 km s⁻¹ for both components. Our computed radii result in velocities of 14 and 10.5 km s⁻¹. Taken at face value, the primary is synchronously rotating, while the secondary is not. However, the errors for the various values produce a near overlap of the predicted and observed rotational velocities, so we do not completely rule out the possibility that the secondary is also rotating synchronously.

To see if the components of 108 Her are synchronously rotating, we once again begin by determining the radii of the components. Our spectral type for the secondary corresponds to a mass of 1.6 M_☉ (Gray 1992). That value and the primary to secondary mass ratio of 1.18 result in a mass of 1.9 M_☉ for the primary. With those masses and the mass–luminosity calibration of Smith (1983), we obtained a magnitude difference of 0.7, which increases the apparent magnitude of the primary by 0.46 mag. The parallax, the V magnitude, and the adopted V magnitude difference were combined to obtain absolute magnitudes M_V = 2.3 ± 0.3 mag and M_V = 3.0 ± 0.3 mag for the primary and secondary, respectively. We next assumed B − V colors of 0.14 and 0.26 for the primary and secondary, respectively, and then used Table 3 of Flower (1996) to obtain the bolometric corrections and effective temperatures of the two components. The resulting luminosities of the primary and secondary are L₁ = 9.6 ± 2.7 L_☉ and L₂ = 5.0 ± 1.4 L_☉, respectively, while the radii are R₁ = 1.6 ± 0.3 R_☉ and R₂ = 1.4 ± 0.2 R_☉, respectively. As is generally the case, uncertainties in our computed quantities are dominated by the parallax uncertainty. Additional uncertainty results primarily from the effective temperature uncertainty, which is estimated to be ± 300 K. These radii appear to be about 0.2 R_☉ smaller than expected canonical values for main-sequence stars of A spectral type (e.g., Gray 1992), but the uncertainties are large enough to produce an overlap of the values.

For 108 Her our v sin i values, averaged from 20 spectra, are 14.3 ± 1.0 and 12.8 ± 1.0 km s⁻¹ for the primary and secondary, respectively. Our adopted masses result in an inclination of 69° and so increase the rotational velocities to 15 and 14 km s⁻¹. Our computed radii result in synchronous velocities of 15 and 13 km s⁻¹ for the primary and secondary, respectively, so it appears that both components are synchronously rotating.