NEW PRECISION ORBITS OF BRIGHT DOUBLE-LINED SPECTROSCOPIC BINARIES. V. THE AM STARS HD 434 AND 41 SEXTANTIS

HD 434 (α = 00^h09^m0016, δ = 28°14'512 (2000)) was not included in the Bright Star Catalogue (Hoffleit 1982), which has a nominal magnitude limit of V = 6.5. However, in Appendix III of that catalog it is noted as one of a number of stars that modern photoelectric photometry has shown to be slightly brighter than the catalog limiting magnitude (Hoffleit 1982). Interest in HD 434 came slowly. Shajn (1951) discovered that it had radial velocity variations and classified its spectrum as A2s. However, Walker (1966) identified it as an Am star. Palmer et al. (1968) observed HD 434 as part of a spectroscopic survey of 633 bright, northern A stars and confirmed its velocity variations. Eventually, Hube & Gulliver (1985) obtained over three dozen additional radial velocities from which they computed a preliminary single-lined orbit with a period of 34.2601 days. Both Sreedhar Rao & Abhyankar (1992) and Margoni et al. (1992) collected additional observations, and using previous velocity observations, the two groups independently revised the preliminary orbit of Hube & Gulliver (1985). As part of an extended project on Am binaries, Iliev et al. (2001) reobserved HD 434 and announced the discovery of its secondary spectrum. From those spectra, Budaj et al. (2003) obtained a mass ratio of 1.19 for the primary relative to the secondary.

Walker (1966) used the strength of the Ca K line relative to the Balmer lines to estimate a spectral class of A4, which was repeated by Palmer et al. (1968). Bertaud (1970) classified the Ca K and metal lines as A3 and F0, respectively. More recently Abt (2004) also identified the combined spectrum as that of a classical Am star and provided spectral classes for its Ca K, hydrogen, and metal lines of A2, A6, and F0, respectively. Examining their red wavelength spectra where both components of the binary were in evidence, Iliev et al. (2001) concluded that both stars have Am peculiarities.

Walker (1966) estimated a v sin i value of 60 ± 25 km s⁻¹. However, the significantly higher resolution observations of Iliev et al. (2001) resulted in values of about 32 and 27 km s⁻¹ for the primary and secondary, respectively.

Cowley et al. (1969) included 41 Sex (α = 10^h50^m1806, δ = −08°53'519 (2000)) in a study of the spectral classifications of bright A stars. They characterized its spectrum as that of an Am star and found its Ca K line to have an A3 spectral class. Because most Am stars are binaries (Abt 1961; Abt & Levy 1985), Worek et al. (1978) obtained radial velocities of the system and, as expected, found it to be a spectroscopic binary. They determined an orbital period of 6.1670 days and concluded that it had a nearly circular orbit. Abt & Levy (1985) made 41 Sex part of their improved study of Am stars. From their spectroscopic observations they computed a new orbit that confirmed the results of Worek et al. (1978). Shortly thereafter, Worek et al. (1986) also published an improved solution of 41 Sex, which generally agreed with the previous two. Over the next dozen years, there were two additional attempts to upgrade the orbital solution of 41 Sex. Sreedhar Rao & Abhyankar (1992) combined all previously published velocities with an extensive number of newly obtained measurements to produce another revised orbit. Meanwhile, Worek (1998) continued his work on 41 Sex, computing the most recent revision of its orbit.

After the initial recognition of 41 Sex as an Am star by Cowley et al. (1969), Abt & Levy (1985) in their improved study of Am binaries classified the star as A2, A8, and F0 from its Ca K, hydrogen, and metal lines, respectively. Later, Abt & Morrell (1995) included 41 Sex in an extensive survey of A stars that examined the relationship between rotational velocity and spectral peculiarities. From their new analysis they estimated spectral classes of A3, A7, and A9, very similar to the results of Abt & Levy (1985). They also measured a v sin i value of 18 km s⁻¹ for the primary. Royer et al. (2002) rescaled that result to 26 km s⁻¹, while Fekel (2003) obtained a value of 21 km s⁻¹.

From moderate dispersion photographic plates, Sreedhar Rao et al. (1990) announced the discovery of phase-modulated variations of the Ca K, hydrogen lines, and various metal lines in the spectrum of 41 Sex. They interpreted their results as surface abundance inhomogenities similar to the Sr, Cr, and Eu line enhancements found in Ap stars and suggested that the characteristics of the abundance peculiarities linked the heretofore separate Am and Ap stars. Although Sreedhar Rao & Abhyankar (1992) concluded that 41 Sex is a prototype for a new class of spectrum variables among Am stars, they did caution that higher resolution CCD spectra would be useful to confirm the spectral line variations. Worek (1998) took up their challenge and obtained CCD spectra of 41 Sex. His careful analysis of the new spectra did not confirm the line variability claims of Sreedhar Rao et al. (1990).

For HD 434 the line broadening and modest velocity amplitudes of its components, combined with its roughly 1 month orbital period, caused us to obtain the vast majority of our observations at Fairborn Observatory, where from 2003 through 2010 we acquired 39 spectra that had resolved or mostly resolved spectral lines of the two components. At McDonald Observatory and KPNO we collected only three additional double-lined spectra, one from McDonald and two from KPNO. All our velocities are listed in Table 2. Using the Fairborn velocities for the two components, we computed single-lined orbital solutions, which resulted in weights of 1.0 and 0.5 for the Fairborn primary and secondary velocities, respectively. Because of their small number, we simply adopted the same weights for the primary and secondary velocities of our three McDonald and KPNO observations. A simultaneous solution of the weighted primary and secondary velocities produced a period of 34.2624 days.

The spectral resolution of the various earlier photographic plate data sets was not sufficient to separate the components. Thus, the earlier velocity measurements are blends of the primary and secondary, and so we have not attempted to use those velocities to improve the orbit. Table 3 lists the orbital elements from our simultaneous solution of the two components with only our data. Figure 3 compares our primary and secondary velocities with the calculated velocity curves. Zero phase is a time of periastron passage.

Zoom In Zoom Out Reset image size

In addition to our new elements, Table 3 lists the preliminary elements of Hube & Gulliver (1985), and there are significant differences between the two solutions. Our center-of-mass velocity is more than 4 km s⁻¹ greater than that of Hube & Gulliver (1985), which is probably mostly due to their measurement of blended lines. In addition, our eccentricity is 20% smaller than that of Hube & Gulliver (1985), while our semiamplitude of the primary is 6% larger.

For 41 Sex we acquired 34 observations at KPNO and 49 at Fairborn Observatory between 2001 and 2010 (Table 4). After measuring the primary and secondary velocities we computed four independent single-lined orbital solutions for the four data sets. Comparing the variances of those solutions, the KPNO velocities are the most precise, and we adopted weights of 1.0, 0.3, 0.04, and 0.01 for the KPNO primary, Fairborn primary, KPNO secondary, and Fairborn secondary velocities, respectively. The center-of-mass velocities of the four data sets are in good agreement except for that of the KPNO secondary. However, given that its velocities typically come from the measurement of just one or two very weak secondary lines, the 1 km s⁻¹ difference between the primary and secondary center-of-mass values is not overly troubling. A simultaneous solution of the appropriately weighted primary and secondary velocities produced a period of 6.167019 days.

From their initial orbital analysis, Worek et al. (1978) concluded that the orbit of 41 Sex is essentially circular. Follow-up work generally validated that result. However, Sreedhar Rao & Abhyankar (1992) concluded that the very modest eccentricity of 0.034, which they obtained for their combined solution, is real. Our independent KPNO and Fairborn orbital solutions of the primary produce extremely small eccentricities of 0.0016 ± 0.0017 and 0.0009 ± 0.016, respectively. Thus, following the precepts of Lucy & Sweeney (1971) we have concluded that the orbit is indeed circular.

In principle, the older literature velocities of the primary could improve the precision of the period. However, the vast majority are from photographic plates that have significantly lower resolution than our observations. Nevertheless, we have examined two different older data sets. The 22 KPNO photographic plate velocities of Abt & Levy (1985) were obtained between 1976 and 1978, extending the time baseline by 25 years. However, from a comparison of orbital solutions the weights of those velocities, relative to our KPNO CCD velocities, are just 0.01. The resulting combined solution of the two data sets does not significantly change the orbital period. We also examined the six CCD velocities of Worek (1998) to see how they compare with our orbit for the primary. Although they appear to be consistent with our orbit, they have residuals that on average are 0.9 km s⁻¹ too positive. This is not overly surprising because such a value is similar to the difference between our systemic velocity and his (−5.7 and −4.5 km s⁻¹, respectively). Therefore, we have chosen to list in Table 5 the circular orbital solution determined with the new velocities from our two observatories. Figure 4 compares our primary and secondary velocities with the calculated velocity curves. For a circular orbit, the element T, a time of periastron passage, is undefined. Thus, as recommended by Batten et al. (1989), T₀, a time of maximum velocity for the primary, is used instead.

Zoom In Zoom Out Reset image size

In addition to our elements, Table 5 lists those of Abt & Levy (1985) and Worek (1998). The derived periods and semiamplitudes of the three solutions are in excellent accord. The three values of the systemic velocity are −6.2, −4.5, and −5.7 km s⁻¹ according to Abt & Levy (1985), Worek (1998), and this work. The uncertainties of the values indicate that the difference between the systemic velocity of Abt & Levy (1985) and our work is slightly more than 1σ. The 1.2 km s⁻¹ difference between the results of Worek (1998) and our work is a 6σ result, but nevertheless, perhaps is simply a difference in observatory zero points rather than an indication of a third star in the system. We note that our velocities cover 10 years and are more precise than those previously obtained, yet they show no systematic, long-term velocity change attributable to a third star.

Despite being unable to determine spectral classes for the components of HD 434, we have compared the spectrum of this binary with several reference star spectra and have the following comments.

Abt (2004) classified the combined spectrum of HD 434 as an Am star with A2, A6, and F0 spectral classes for its Ca K, hydrogen, and metal lines, respectively. We find that in the 6430 Å region, the spectrum of the Am star HR 7431, which Abt & Morrell (1995) classified as A2, A7, and F0, is a reasonable fit to the relative strength of the primary's iron and calcium lines. Thus, we adopt A2 and F0 for the calcium and metal spectral classes of the primary. The iron lines of the secondary are more consistent with those of HR 5075, classified as F2 V by Abt & Morrell (1995), than with those of HR 7431, but the calcium lines of the secondary are much weaker than those of HR 5075, and so we adopt A2 and F2 for the calcium and metal spectral classes of the secondary. Thus, we confirm the conclusion of Iliev et al. (2001) that both components are Am stars. From our various spectrum fits to the iron lines, we estimate a V mag difference of 0.8 ± 0.2. This assumes that the surface abundances of the two stars are the same, which, because both components are Am stars, is not necessarily the case. However, a similar or identical magnitude difference can be estimated from the mass ratio of HD 434 and the canonical properties of A and early-F stars, if one assumes that the spectral type of the primary is somewhat earlier than the composite hydrogen type of Abt (2004) and that the secondary type is somewhat later. For example, in his Table B1, Gray (1992) lists masses for A5 V and F1 V stars of 1.86 M_☉ and 1.51 M_☉, respectively. This combination results in a mass ratio of 0.81, identical to our mass ratio for HD 434 from Table 3. Those two spectral types have corresponding M_v magnitudes of 2.0 and 2.8, resulting in a magnitude difference of 0.8, which is the value that we have estimated from our spectrum fits to the iron lines.

Because the primary of 41 Sex, like both components of HD 434, is an Am star, we are unable to determine its hydrogen line spectral class. The large magnitude difference between the primary and the secondary means that the secondary spectral class is not well determined. Nevertheless, we discuss the results of our comparison of the spectrum of 41 Sex with several reference star spectra.

Abt & Morrell (1995) classified the combined spectrum of 41 Sex as an Am star with A3, A7, and A9 for its Ca K, hydrogen, and metal lines, respectively. We find that in the 6430 Å region, the spectrum of the Am star HR 7431, which Abt & Morrell (1995) classified as A2, A7, and F0 for its Ca K, hydrogen, and metal lines, respectively, is a reasonable fit to the relative strength of the primary's Fe i and Fe ii lines but its calcium lines are not nearly as strong as those of 41 Sex. From a comparison with several other reference stars we adopt A5 and F0 for the primary's calcium and metal spectral classes, respectively. The very weak spectrum of the secondary is consistent with that of a late-F or an early-G star.

For HD 434 we begin by adopting a V mag of 6.47 and a B − V color of 0.242 mag from the Hipparcos catalog (Perryman et al. 1997). With our magnitude difference of 0.8, the individual V magnitudes are 6.89 and 7.69 for the primary and secondary, respectively. The new Hipparcos parallax reduction by van Leeuwen (2007) produces a value of 9.02 ± 0.49 mas and corresponds to a distance of 110.9 ± 6.0 pc. Even though there may be a slight amount of reddening at this distance, we assume that it is negligible. The resulting absolute magnitudes are M_V = 1.7 ± 0.2 mag and M_V = 2.5 ± 0.2 mag for the primary and secondary, respectively. From Johnson (1966) we assume B − V colors of 0.17 for the primary and 0.36 for the secondary, which, when combined for the two stars, produce a B − V color similar to the observed value. Then, from Table 3 of Flower (1996), we obtain the bolometric corrections and effective temperatures of the two components. Finally, with the use of the Stefan–Boltzmann law, the luminosities of the primary and secondary are L₁ = 16.7 ± 3.6 L_☉ and L₂ = 8.0 ± 1.7 L_☉, respectively, while the radii are R₁ = 2.2 ± 0.3 R_☉ and R₂ = 2.0 ± 0.3 R_☉, respectively. The uncertainties in the computed quantities are dominated by the parallax uncertainty, the magnitude difference uncertainty, and the effective temperature uncertainty with the latter estimated to be ± 300 K.

Stockton & Fekel (1992) concluded that binaries with mass ratios as small as 0.6 and magnitude differences somewhat greater than 2.5 mag can be detected at 6430 Å. With a smaller mass ratio of 0.5, the components of 41 Sex have an even greater magnitude difference. Because of the faintness of the secondary, that component will have only a very slight effect on the V mag and color of the primary. For example, if the ΔV mag between the primary and secondary is assumed to be 3.0 mag, then the V mag of the primary is 5.87, while increasing the magnitude difference to 3.5 makes the V mag of the primary 5.84. As discussed below, in the following computations we adopt ΔV = 3.2 mag, which with a V mag of 5.80 for the combined system from Hipparcos (Perryman et al. 1997) results in V = 5.86 mag for the primary. The new reduction of the Hipparcos parallax produces a value of 10.50 ± 0.34 mas (van Leeuwen 2007), which corresponds to a distance of 95.2 ± 3.1 pc. At such a distance we assume that the system is not significantly reddened. Our assumed magnitude difference and the parallax result in an absolute magnitude of M_v = 0.97 ± 0.12 mag for the primary. From the Hipparcos catalog (Perryman et al. 1997), the B − V color of the 41 Sex system is 0.156. Given the very modest effect of the secondary, we adopt a slightly smaller value of 0.15 for the primary. The bolometric correction and effective temperature come from Table 3 of Flower (1996). Then from the Stefan–Boltzmann law the luminosity of the primary, L₁, is 31.9 ± 3.6 L_☉, while the radius is R₁ = 2.9 ± 0.2 R_☉.

The properties of the secondary are much less secure. We compare the M_v of the primary and the components' mass ratio with the canonical stellar properties listed in Table B1 of Gray (1992) and conclude that the secondary is most probably a late-F or early-G star, which is in agreement with our rough classification of this star. From that table we estimate a V mag difference of 3.2 ± 0.3. This leads to L₂ = 1.8 ± 0.5 L_☉ and R₂ = 1.3 ± 0.2 R_☉. The uncertainties in the computed quantities of the primary and secondary are dominated by the parallax and the effective temperature uncertainties as well as the magnitude difference for the secondary. The temperature uncertainty is estimated to be ±200 K for the primary and secondary.

To determine whether the components of HD 434 are rotating pseudosynchronously, we compare our observed velocities with the predicted pseudosynchronous velocities. For HD 434 our v sin i values, averaged from two spectra, are 33 ± 2.0 and 30 ± 3.0 km s⁻¹ for the primary and secondary, respectively. These values are in good agreement with those of Iliev et al. (2001), who estimated projected rotational velocities of about 32 and 27 km s⁻¹ for the two stars. The minimum masses of the two components are relatively small; both are less than 1 M_☉. From our comparison with the solar-abundance evolutionary tracks of Girardi et al. (2000) we adopt a mass of 1.9 M_☉ for the primary (Figure 5). Then that mass, combined with its m sin³ i value (Table 3), results in an orbital inclination of 54°. If the rotational inclination is the same as that of the orbit, then the observed equatorial rotational velocities are 40 and 33 km s⁻¹ for the primary and secondary, respectively. The pseudosynchronous rotation period of HD 434 is 20.9 days. This value plus our computed radii from the Stefan–Boltzmann law produces pseudosynchronous rotational velocities of 5 km s⁻¹ for both the primary and secondary. Thus, the two components of HD 434 are rotating 6–8 times more rapidly than their pseudosynchronous values.

Zoom In Zoom Out Reset image size

To determine whether the components of 41 Sex are synchronously rotating, we compute equatorial velocities from our projected rotational velocities and then compare them with the predicted pseudosynchronous velocities. For 41 Sex our v sin i values, averaged from 35 spectra for the primary and 29 spectra for the secondary, are 20 ± 1 and 7 ± 3 km s⁻¹, respectively. Fekel (2003) obtained a v sin i value of 21 km s⁻¹ from a small subset of our spectra. The minimum masses of the two components (Table 5) are relatively small compared to the expected masses for their spectral types (Gray 1992). Thus, we compare the position of the primary in the H-R diagram with the solar abundance evolutionary tracks of Girardi et al. (2000), which produces a mass estimate of 2.18 M_☉. That value, combined with the m sin³ i value of the primary, results in an orbital inclination of 54°, which by chance is the same value that we have estimated for HD 434. If the axes of the rotational and orbital inclinations are parallel, then the observed equatorial rotational velocities are 25 and 9 km s⁻¹. The synchronous rotational velocities for the primary and secondary, computed with our radii from the Stefan–Boltzmann law, are 24 and 10 km s⁻¹, respectively. Thus, we conclude that both the primary and secondary are rotating synchronously. This result accords with theory, since the binary orbit is already circularized.