STELLAR ASTROPHYSICS WITH A DISPERSED FOURIER TRANSFORM SPECTROGRAPH. II. ORBITS OF DOUBLE-LINED SPECTROSCOPIC BINARIES

Our RV measurements for the double-lined spectroscopic binary ι Pegasi (HR 8430, HD 210027, and HIP 109176) are plotted in Figure 1. The most recent published RV work on this system comes from Fekel & Tomkin (1983) whose orbital parameters are listed in Table 3 along with the values that we derive from our dFTS2 observations. In addition to adopting their value of the system's orbital period, we also followed their lead in assuming a circular orbit, because our RV points only covered half of the orbital phase, and CURVEFIT could not place meaningful constraints on e or ω. Our values for K₁ and K₂ are compatible with those of Fekel & Tomkin, although our solution for V₀ differs by a statistically significant amount. This discrepancy may indicate the gravitational influence of an unseen and distant third stellar component of the system, although Tokovinin et al. (2006) did not find any close tertiary companions in Two Micron All Sky Survey images of ι Peg, and the astrometric observations of Boden et al. (1999) saw no evidence for a companion either. Alternatively, the difference in V₀ might merely be a result of different RV zero points between Fekel & Tomkin's observations and ours—unfortunately, we did not make any RV observations of ι Piscium, the RV standard star that they used as their reference spectrum.

Zoom In Zoom Out Reset image size

Although the rms scatter of our RV points around the best-fit orbital curves is small (56 m s⁻¹ and 158 m s⁻¹ for the A and B components, respectively), the scatter is larger than would be expected from the error bars on each individual RV measurement, and is significantly above the instrumental RV error floor of ∼10 m s⁻¹ that we determined in Behr et al. (2009). To account for this discrepancy, we multiply the RV error bars by 3.11 for the primary and 1.83 for the secondary, such that the mean per-measurement error bar matches the rms deviation σ_RV for each stellar component. The orbital fits are then recalculated using these scaled error bars, and the resulting orbital parameters are listed in the rightmost column of Table 3. This same procedure is applied to all subsequent binary systems as well.

The additional RV variability, if real, may be a result of stellar activity on both the primary and secondary, driven by tidal interactions between the two stars. Fekel & Tomkin measure vsin i = 7 ± 2 km s⁻¹ for the primary, very close to an estimated synchronous rate of 6.5 km s⁻¹, and vsin i = 9 ± 3 km s⁻¹ for the secondary, which is well above the estimated synchronous rate of 4.5 km s⁻¹. Gray (1984) finds vsin i values of 6.5 ± 0.3 km s⁻¹ (primary) and 5 ± 1 km s⁻¹ (secondary), suggesting that the system is synchronized. Our preliminary analysis of line broadening indicates vsin i = 7.6 and 7.2 for the primary and secondary, respectively. If the secondary is indeed spinning more rapidly than the synchronous rate, then above-average surface activity could result, which would add significant astrophysical RV "jitter" to our measurements. A synchronously rotating component would be less susceptible to tidal effects, but activity might still be enhanced by the proximity of a massive companion. However, Konacki et al. (2009) measured RVs of ι Peg with three different spectrographs and found no jitter greater than 17 m s⁻¹ (primary) and 85 m s⁻¹ (secondary), suggesting that the jitter observed by dFTS2 was instrumental rather than astrophysical.

Boden et al. (1999) measured an inclination angle for this system of i = 9567 ± 022 (based on their primary data set). Using this value along with our orbital parameters, with the fundamental parameters recommended by Torres et al. (2010), we derive stellar masses of M₁ = 1.3241 ± 0.0018 M_☉ and M₂ = 0.8251 ± 0.0010 M_☉, which represent relative (statistical) errors of 0.14% and 0.12%, respectively. With scaled error bars, the mass estimates are the same, albeit with larger error bars, for relative uncertainties of 0.19% and 0.15%. These values agree reasonably well with the calculations of Boden et al. who used Fekel & Tomkin's K₁ and K₂ values to determine M₁ = 1.326 ± 0.016 M_☉ and M₂ = 0.819 ± 0.009 M_☉. For our mass estimates, the largest component of the error budget is due to the uncertainty in i, although the uncertainties in the K values are also significant contributors.

The spectroscopic orbit of the ω Draconis system (HR 6596, HD 160922, and HIP 86201) was measured by Mayor & Mazeh (1987) and more recently by Fekel et al. (2009). Their derived orbital parameters are shown in Table 4, along with our values. Our K velocities agree closely with those of Fekel et al. We find a small but non-zero eccentricity for the orbits, 0.0023 ± 0.0002. Fekel et al. derived e = 0.0027 ± 0.0008 for the primary, with ω₁ = 401 ± 178 (F. C. Fekel 2009, private communication), but their e and ω values for the secondary did not agree with those of the primary, so they adopted a circular orbit for the system. (Our ω₁ = 137.86 ± 13.48, as described below.) Despite the similarity between our e value and their non-zero e value, the measurements of ω₁ are substantially different, so we cannot plausibly claim that an orbital eccentricity has been clearly detected.

As an additional test of the non-zero eccentricity, we follow the Fekel et al. procedure of fitting orbits to the A and B components separately and comparing the derived values for ω₁ and ω₂, which should differ by 180°. Using the formal error bar data, we calculated e₁ = 0.0020 ± 0.0003 with ω₁ = 7416 ± 1274, and e₂ = 0.0027 ± 0.0005 with ω₂ = 24314 ± 1305. The eccentricity values agree reasonably well, and the ω angles differ by ∼169°, which is within 1σ of 180°. However, this ω₁ value does not agree with the ω₁ value from the combined fit, which is puzzling. This discrepancy may be related to the apparent systematic trends in the secondary RV residuals which are evident in Figure 2. Further observations with better phase coverage will be required to validate or refute our measured eccentricity for ω Dra.

Zoom In Zoom Out Reset image size

As with ι Peg, our value for V₀ differs from the prior work by a statistically significant amount, although the magnitude of the difference is not as large. Differences in the RV zero point are the most likely explanation.

No visual orbit or estimate of the inclination angle i has been determined for this binary, despite efforts to resolve it using speckle interferometry (Isobe 1991; Miura et al. 1995). We are therefore unable to calculate the true masses of the stellar components. We find M₁sin ³i = 0.16054 ± 0.00011 M_☉ and M₂sin ³i = 0.13030 ± 0.00007 M_☉, in moderately good agreement with Fekel et al. (With the scaled RV error bars, our mass estimates are virtually unchanged, with error bars approximately three times larger.) We hope that long-baseline interferometers will soon be able to resolve the astrometric orbit of this system and determine the inclination angle.

The spectroscopic binary 12 Boötis (HR 5304, HD 123999, and HIP 69226) has received recent attention from both Boden et al. (2005), who combined spectroscopic and astrometric data, and Tomkin & Fekel (2006), who performed a high-precision spectroscopy-only assessment of the orbit. Orbital parameters are shown in Table 5, and our RV data are plotted in Figure 3. The derived quantities for e and ω₁ are in excellent agreement among all three studies. Our K₁ and K₂ values, on the other hand, are smaller than those of Boden et al. and Tomkin & Fekel by several standard deviations, and our derived systemic velocity is different as well. The discrepancy in V₀ may simply be ascribed to a different RV zero point, but the difference in K_1/2 deserves further scrutiny. Due to the premature conclusion of our observing program, our RV data do not fully cover the region of maximum absolute velocities around phase =0.15, so the velocity amplitudes are not as reliably constrained as they might be. When dFTS observations resume, 12 Boo will be one of our highest priority targets, so that this issue can be addressed.

Zoom In Zoom Out Reset image size

Given smaller K amplitudes than prior publications, we derive smaller masses as well. Using i = 107990 ± 0077 from Boden et al., we determine M₁ = 1.4013 ± 0.0025 M_☉ and M₂ = 1.3607 ± 0.0024 M_☉, for a relative statistical uncertainty of 0.18%. These values are several σ smaller than the masses derived by Boden et al. and Tomkin & Fekel.

The eclipsing SB2 system of V1143 Cygni (HR 7484, HD 185912, and HIP 96620) was previously analyzed by Andersen et al. (1987). Their orbital parameters are compared to ours in Table 6, and our RV data are plotted in Figure 4. There is a broad agreement between the two sets of orbital elements, although the error bars that we derived for K₁ and K₂ are relatively large, partly because of the small number of observations, partly because the individual RV measurements had larger error bars due to larger rotational broadening of the absorption lines and lower signal-to-noise ratio. Of particular interest is the comparison of the periastron angle ω₁. From precise photometric timing of the system's eclipses, Gimenez & Margrave (1985) detected apsidal motion (precession of the periastron point) with a period of 10,750 years, which would imply a change in the value of ω₁ of 076 during the ∼22.6 years that elapsed between their last observations (1985 October) and our first observations (2008 May). The actual measured change in ω₁ is +039 ± 025. The predicted periastron precession is therefore not ruled out, but is not solidly confirmed either. With more extensive observations of V1143 Cyg, we hope to place more useful constraints on the magnitudes of the classical gravitational quadrupole and general relativity effects which cause the precession.

Zoom In Zoom Out Reset image size

Andersen et al. (1987) adopt an inclination angle of 870 ± 1° based upon eclipse photometry by Wood (1971), Popper & Etzel (1981), and van Hamme & Wilson (1984). Using that same value for i, we estimate M₁ = 1.3815 ± 0.0114 M_☉ and M₂ = 1.3451 ± 0.0100 M_☉. The error bars on K₁ and K₂ dominate the error budget for the masses, so further high-accuracy spectroscopic observations of this system are clearly called for.

β Aurigae (HR 2088, HD 40183, and HIP 28360) is another eclipsing double-lined binary, consisting of two A2 subgiants in a close four-day orbit. Smith (1948) measured the RV curves of both components, and Pourbaix (2000) reanalyzed these data in conjunction with interferometric astrometry data from Hummel et al. (1995) to refine the orbital parameters. Our RV curve is displayed in Figure 5. The phase coverage was insufficient to constrain e or ω₁, so we assumed a circular orbit. Our derived parameters differ from the prior two analyses (Table 7), with K₁ and K₂ semi-amplitude values intermediate between those of Smith and those of Pourbaix. As with V1143 Cyg, this system exhibits a rotational line broadening of 30–40 km s⁻¹, which increases the uncertainty of each RV measurement and thus the derived orbital parameters.

Zoom In Zoom Out Reset image size

Adopting i = 760 ± 04 from Hummel et al. (1995), we calculate M₁ = 2.3885 ± 0.0134 M_☉ and M₂ = 2.3270 ± 0.0130 M_☉. (Pourbaix uses i = 750 ± 073; the source of this value is unclear.) The majority of the 0.54% relative error in our mass values is due to the inclination angle uncertainty, so this system would be a prime follow-up target for further long-baseline spatial interferometry.

The brighter component of the visual binary Mizar (HR 5054, HD 116656, and HIP 65378) is itself a spectroscopic binary, with two early-A dwarfs in an elliptical 20 day orbit. Table 8 lists the orbital parameters measured by Fehrenbach & Prevot (1961) and the subsequent revisions computed by Pourbaix (2000) with astrometry data from Hummel et al. (1998), along with the values computed from our RV data (Figure 6). We find smaller velocity amplitudes and a slightly larger eccentricity for this binary system than prior researchers. Like the prior two targets, Mizar A's component spectra are moderately rotationally broadened, reducing the quality of the RV measurements.

Zoom In Zoom Out Reset image size

According to Hummel et al., i = 605 ± 03 for this binary. Using this value, we determine that M₁ = 2.2224 ± 0.0221 M_☉ and M₂ = 2.2381 ± 0.0219 M_☉, for a relative mass error of 1.00% and 0.98%, respectively. The uncertainty in i is responsible for most of the mass error; if σ_i could be reduced to 005 and the errors on K₁ and K₂ could be cut in half, then the mass uncertainty would drop below 0.25%.

The κ Pegasi system (HR 8315, HD 206901, and HIP 107354) is a hierarchical triple, with two bright components (A and B) in an 11.5 year orbit, and a fainter unseen component in a six-day orbit around the B component. The canonical published orbit for this system comes from Mayor & Mazeh (1987), with more recent observations by Konacki (2005) (with orbit analyses published in Muterspaugh et al. 2006 and Muterspaugh et al. 2008) and our dFTS1 prototype (Hajian et al. 2007). Table 9 displays the orbital parameters as measured by Mayor & Mazeh, dFTS1, and dFTS2. Following Mayor & Mazeh, we assume that e = 0 for the short-period orbit. The dFTS2 observations of this system were made during two observing runs separated by ∼0.64 years, so we expect the V₀ value of the short-period binary to change due to the long-period orbit. To account for this change, we treated the data from the two observing runs completely separately, and the results are given in two separate columns in the table. For the RV plot in Figure 7, we shifted Bb component's RV values from the first observing run by −1.198 km s⁻¹ so that the two different epochs would share the same V₀.

Zoom In Zoom Out Reset image size

With only four RV measurements in the second observing run, the value for the K₁ amplitude should be considered provisional, but the change in V₀ is quite clear. We see an even larger change in V₀ as compared to the mid-1981 observations of Mayor & Mazeh, although differences in RV zero point must be considered. Unfortunately, our prior dFTS1 observations did not yield a value of V₀, because the template spectra were not referenced to an absolute wavelength standard.

RV measurements of the A component are not as precise as those of the B component, because its lines are much broader: we estimate vsin i = 47.9 km s⁻¹ for A and 7.1 km s⁻¹ for B. Even taking this fact into account, however, we find a much larger scatter of our RV measurements for A than expected from χ² statistics. One possible explanation for this discrepancy is that the A component is also a close binary, as proposed by Beardsley & King (1976). We phased our RV data to their claimed 4.77 day period, but did not find any coherent cyclic pattern in the A component velocities. (Muterspaugh et al. 2006 see no evidence for a fourth component either.) The binarity of A is a possibility that we might explore with future data, but for the time being, this hypothesis is not supported.

The η Virginis triple system (HR 4689, HD 107259, and HIP 60129) was studied extensively by Hartkopf et al. (1992) who combined spectroscopy and speckle interferometry to determine the orbits of both the short-period (72 day) pair and the long-period (13.1 year) grouping. Hummel et al. (2003) made additional observations of this system with the NPOI interferometer, refining the orbital parameters and determining the inclination angle of the close binary orbit. Table 10 compares their parameters for the short-period Aa–Ab pair to our derivation. The parameters are in general agreement, except that the change in V₀ is larger than previously seen, and is likely due to the gravitational influence of the third component of the system. Figure 8 shows the RV curves for the close binary, as measured by dFTS2. Note that the residuals for the secondary RV points all lie above the dotted line denoting zero residual. This offset may indicate a significant difference in the gravitational redshift or convective blueshift between the two component stars, or it may be an effect of the third component. Interestingly, Hartkopf et al. see a similar effect, but with the opposite sign, in that the V₀ that they derive from the Aa RV curve is ∼0.4 km s⁻¹ larger than V₀ from the Ab component.

Zoom In Zoom Out Reset image size

Hartkopf et al. made a tentative spectroscopic detection of a blended Mg ii 4481 feature from the faint tertiary component, which appeared to be rotationally broadened by about 160 km s⁻¹. Our instrument bandpass does not include this line, so we were unable to verify their detection, but we performed a crude three-dimensional cross-correlation using two narrow-lined template spectra plus a broad-lined A2V template. We found no evidence of a consistent RV solution for the third component.

According to the observations of Hummel et al. (2003), the inclination angle of η Vir Aa–Ab is 455 ± 09. Combining this number with our orbital parameters, we determine that M₁ = 2.4818 ± 0.1158 M_☉ and M₂ = 1.8745 ± 0.0874 M_☉. The inclination uncertainty is the dominant contributor to the error budget, although the velocimetry results can certainly be improved with more data points.