THE PHASES DIFFERENTIAL ASTROMETRY DATA ARCHIVE. II. UPDATED BINARY STAR ORBITS AND A LONG PERIOD ECLIPSING BINARY

HD 5286 (36 And, HR 258, HIP 4288, and WDS 00550 + 2338) is a pair of subgiant stars with spectral types G6 and K6. The total system mass of 1.86 ± 0.15 M_☉ is in reasonable agreement with this classification (Cox 2000).

HD 6811 (ϕ And, 42 And, HR 335, HIP 5434, and WDS 01095 + 4715) is a pair of B stars (B6IV and B9V). The total mass is 6.5 ± 2.8 M_☉; while not well constrained, this value is reasonable for these stars.

HD 17904 (20 Per, HR 855, HIP 13490, and WDS 02537 + 3820) was reported to have a 1269 day subsystem by Abt & Levy (1976). The companion was further investigated by Scarfe & Fekel (1978) and Morbey & Griffin (1987) who found no evidence of such a companion, nor is such an object found by astrometry. The single-component velocities from those works were consistent with constant velocity, providing no constraint on the binary orbit, and were not used for the present orbit fitting. HD 17904 is a pair of mid F dwarfs; the total system mass of 3.88 ± 0.58 M_☉ is a bit high for such stars, though the uncertainty in this is large enough to still be in reasonable agreement.

While the orbital parameters of HD 44926 (HIP 30569, WDS 06255 + 2327) are not well constrained due to few observations covering a short fraction of the orbit, this is the first time an orbital solution has been evaluated for which the fit converged.

Heintz (1981) published four single-component spectroscopic velocities of HD 76943 (10 UMa—though it is now in the constellation Lynx (Griffin 1999), HR 3579, HIP 44248, and WDS 09006 + 4147); the first was taken a year before the others, which were all on the same night. More recently, Tennessee State University's Automatic Spectroscopic Telescope (AST; Eaton & Williamson 2007) collected 66 blended spectra of 10 UMa spanning 1843 days (23% of the binary orbit). Upon inspection, the single set of absorption lines appeared asymmetric due to the binarity, but remained blended by an amount substantial enough to cause systematic errors in attempts at component velocity determinations. Higher resolution observations at times of maximal velocity separation or individual component spectroscopy behind an Adaptive Optics system may allow better modeling of each component's lines, in which case these measurements could be recovered, but at this time the system remains without useful velocity measurements.

The spectral type is consistently listed as F5V, consistent with the total system mass of 2.44 ± 0.12 M_☉ (Cox 2000) and the S99 component mass values of 1.37 ± 0.08 M_☉ and 1.04 ± 0.06 M_☉.

A few single-component RV measurements of HD 77327 (κ UMa, 12 UMa, HR 3594, HIP 44471, and WDS 09036 + 4709) have been published by Abt et al. (1980) and Heintz (1981). However, these are small in number, span a short time period, and appear to be consistent with constant velocity. As a result, the system is treated as a visual binary only.

HD 77327 is composed of a pair of early (∼A0) dwarf stars. The total mass of 6.30 ± 0.98 M_☉ is not constrained very well, and while the value is a bit high for stars of this type, the large uncertainty indicates there is no cause for alarm.

CORAVEL produced 22 two-component RV measurements of HD 114378 (α Com, 42 Com, HR 4968, HIP 64241, and WDS 13100 + 1732) spanning nearly half (46%) of the binary orbit, making it both a visual binary and double-lined spectroscopic binary (Duquennoy et al. 1991). However, despite the anticipated velocity amplitude of each star being ∼8 km s^-1—several times larger than the ∼1 km s^-1 typical measurement uncertainty— no significant velocity changes appear in the CORAVEL velocities. As a result, the velocities did not agree well with the visual orbit (after orbit fitting, over half have residuals marking them as outliers of >4σ compared to the published measurement uncertainties) and produced a system distance that was much too distant to agree with that of S99 (55.9 ± 1.4 mas) based on Hipparcos astrometry. Thus, these do not appear to be useful in orbit fitting.

Alternatively, Tokovinin & Smekhov (2002) measured nine single-component RVs spanning ∼13% of the binary orbit that were consistent with the visual orbit, though these are clustered at two observing epochs and showing little variation, making spurious orbit fitting likely. Using these velocities and the parallax of 55.9 ± 1.4 mas from S99 yielded a result that is almost certainly spurious; for example, the binary mass ratio was a very low value (0.02). Thus, only the visual orbit is presented at the current time, and additional investigations will need to concentrate on improving the velocity results.

The total mass was found to be 2.45 ± 0.18 M_☉, near the value of 2.54 M_☉ of S99, though this is not surprising given that the parallax values used were identical. The system is a pair of F5 dwarf stars, and this mass range is reasonable for that spectral type.

Most interesting of all, it is likely that this long period (26 years) binary eclipses! This has been anticipated before (Hartkopf et al. 1989; Hoffleit 1996), but previously the orbit was not determined well enough to demonstrate that eclipses are likely. The visual orbit parameters from the present investigation predict a closest approach of 0.32 mas around 2015 January 24 (to within about a week), when the star is observable during early morning hours and lasting about 1.5 days. Mid F dwarfs have physical sizes about 1.3 times larger than the Sun. At a distance of 17.9 pc, this corresponds to diameters of 0.7 mas. Eclipses are likely even if one considers the 1σ upper limits of distance and orbital inclination, for which closest approach increases only to 0.38 mas and the apparent stellar diameters decrease by 2.5%, an amount much smaller than the uncertainty in the stars' physical sizes; see Figure 1. Unfortunately, only one eclipse per orbit is likely for this pair; the eccentric orbit causes the alternative closest separation to be 0.9 mas, and a likely near-miss. α Com, the brightest star in its constellation, with an orbital period of 26 years (nearly as long as Aur) is likely to join Aur as representing long period eclipsing binaries, despite the low probability of such a configuration. Unlike Aur, in which the chance of eclipse is enhanced by the presence of an extended disk around one star, the eclipses in α Com result purely from orbital geometry and the overlapping of the stars themselves.

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HD 129246 (ζ Boo, 30 Boo, HR 5477, HIP 71795, and WDS 1411 + 1344) has an extremely high eccentricity of 0.9977 ± 0.0034. The distance of closest approach is only 0.3 AU. Projected on the sky, the distance of closest approach is 1 mas; in this case, eclipses are unlikely, though the uncertainty on the inclination is large. The next time of closest approach is 2023 August, though at that time the star is not up at night.

Though the system has a very long orbital period of 124 years, nearly two orbits have been observed; the first measurement was from 1796. Despite this time coverage, and as a result of the large eccentricity, the semimajor axis remains poorly determined. As a result, the total mass is found to be very large (122 M_☉) but also very uncertain (±275 M_☉) to the point of being unconstrained.

The AST attempted observations of HD 137391 (μ Boo, 51 Boo, HR 5733, HIP 75411, and WDS 15245 + 3723) several times, but the absorption lines were always too broad and blended for RV measurements. The mass sum of 3.24 ± 0.23 M_☉ is smaller than the value of 3.70 M_☉ from S99 despite using the same distance to the system. The current value of the semimajor axis is smaller than that from S99, explaining the discrepancy.

HD 140159 (ι Ser, 21 Set, HR 5842, HIP 76852, and WDS 15416 + 1940) is a pair of early A dwarfs with mass 3.73 ± 0.53 M_☉, consistent with both the S99 value of 3.79 M_☉ and their spectral types, though slightly on the low side for the latter (Cox 2000).

HD 140436 (γ CrB, 8 Crb, HR 5849, HIP 76952, and WDS 15427 + 2618) is a pair of early A stars. The total mass of 3.73 ± 0.37 M_☉ is slightly lower than the value of 4.23 M_☉ of S99, though still in reasonable agreement. Like HD 140159, this mass is a bit low for their spectral types.

With only 10 PHASES measurements being available, the orbit model of HD 155103 (c Her, HR 6377, HIP 83838, and WDS 17080 + 3556) was not much altered by their addition. The total mass of 3.32 ± 0.39 M_☉ is identical to that from S99. The spectral types are early (A or F), though the spectral class has been reported as either dwarf or giant. The total mass appears to be more consistent with dwarf stars.

HD 187362 (ζ Sge, 8 Sge, HR 7546, HIP 97496, and WDS 19490 + 1909) is a pair of early A dwarfs, though the measured total mass of 2.23 ± 0.35 M_☉ is a bit lower than one would expect for such stars (Cox 2000). This may be due to a remaining error in the parallax: if the original Hipparcos parallax is used instead, the total mass is found to be 4.7 ± 1.2 M_☉, which seems more consistent (Perryman et al. 1997).

Though the binary period of HD 202444 (τ Cyg, 65 Cyg, HR 8130, HIP 104887, and WDS 21148 + 3803) is long and the velocity amplitudes are low, it is possible to use spectroscopy to determine individual velocities for both components. This is because one star is extremely broad lined while the other has very sharp spectral features. Though the spectral lines are always blended, this odd pairing makes a very distinctive line profile that can be fit as the sum of two very different Gaussians. Fekel et al. (2003) published two two-component RVs of the system. The Tennessee State University (TSU) AST recently observed τ Cyg with high cadence to better constrain the mass ratio and search for short period companions to either star. No significant changes were observed in the velocities, and the span of observations was too short to contribute to orbital modeling, so at this time only the system's visual orbit was evaluated.

There is some indication that τ Cyg may have a substellar companion orbiting one of the two stars (see Paper V). There are reasons to doubt the authenticity of this proposed companion, so the visual orbit obtained by modeling the system with only a single Keplerian model has been presented here in addition to the double Keplerian model presented in Paper V. If real, the companion has a long orbital period. This signal could be absorbed into that of the wider binary when only the shorter timespan PHASES data were analyzed to search for tertiary companions, so no compelling evidence for a companion was present when only PHASES measurements were analyzed. However, the continued large value of χ² that results when the combined PHASES and non-PHASES astrometry set described in Section 3 was analyzed prompted a second search for tertiary companions, this time using all the astrometric measurements. The longer timespan non-PHASES astrometry reduced the amount by which the binary orbit parameters could absorb motion of an intermediate period companion (short compared to the binary motion, long compared to the timespan of PHASES measurements) and indicated the presence of a companion with mass corresponding to that of a giant planet.

HD 207652 (13 Peg, HR 8344, HIP 107788, V373 Peg, and WDS 21501 + 1717) is a variable flare star. It has been suggested by Tamazian et al. (1999) that the secondary may be a T Tauri-type variable. However, the variability does not appear to have affected the astrometry measurements; see Figure 2. The total mass is 2.65 ± 0.21 M_☉, in good agreement with the value of 2.67 M_☉ from S99. For the system's early F spectral type, this mass and the overall system luminosity are more consistent with dwarf stars, though the spectral classification is giant or subgiant.

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Five single-component velocity measurements covering 488 days (18% of the binary orbit) of HD 26690 (46 Tau, HR 1309, HIP 19719, and WDS 04136 + 0743) were published by Heintz (1981). An additional 26 unpublished measurements covering 256 days (10% of the binary orbit) have been made by TSU's AST and are presented for the first time in Table 5. A combined fit between the astrometric and velocimetry measurements found typical uncertainties of 1.6 km s^-1 and 0.65 km s^-1 were needed for these data sets, respectively, to make the weighted rms of the velocimetry residuals equal to 1. The revised Hipparcos parallax by S99 of 27.41 ± 0.93 mas was used as a weighted input in orbit fitting, as an observation with associated uncertainty. The combined fit solved for the system distance as a parameter, and both the direct parallax measurement and orbital fit were used to constrain this in an optimal manner. The component masses are 1.38 ± 0.26 M_☉ and 0.82 ± 0.21 M_☉, a mass ratio larger than that from S99, in which masses of 1.15 ± 0.14 M_☉ and 1.10 ± 0.14 M_☉ were found.

Abt & Levy (1976) published 20 spectroscopic measurements covering 1467 days (3.4% of the binary orbit) of HD 81858 (ω Leo, 2 Leo, HR 3754, HIP 46454, and WDS 09285 + 0903). The combined astrometric and velocimetry orbital fit revealed that a measurement uncertainty of 1.0 km s^-1 yielded a weighted rms of 1 for the velocity residuals. The short span of the spectroscopic measurements compared to the orbital period resulted in only loose constraints being placed on the binary mass ratio and individual component masses. The S99 parallax of 27.5 ± 1.1 mas was used as a weighted input in orbit fitting. The masses are only poorly constrained as 1.92 ± 0.96 M_☉ and 0.28 ± 0.92 M_☉; RV measurements covering more of the binary orbit and/or double-line RV measurements are needed to improve these values. The total system mass could be better determined by improved parallax measurements, but additional RV measurements are necessary for improved evaluation of the mass ratio.

A considerable number of RV measurements of HD 137909 ("Peculiar Rosette Stone," β CrB, 3 CrB, HR 5747, HIP 75695, and WDS 15278 + 2906) have been published, spanning nearly a century. These include the following:

• 1.  
  91 measurements by Cannon (1912) (σ ∼ 4.3 km s^-1),
• 2.  
  352 measurements by Neubauer (1944) (σ ∼ 1.2 km s^-1),
• 3.  
  25 measurements by Wolff (1978) (σ ∼ 0.8 km s^-1),
• 4.  
  60 measurements by Oetken & Orwert (1984) (σ ∼ 1.0 km s^-1),
• 5.  
  121 measurements by Kamper et al. (1990) (unit uncertainty σ ∼ 1.2 km s^-1), and
• 6.  
  78 measurements by North et al. (1998) (uncertainties as given in that paper),

where the measurement uncertainties in all but the last case were derived based on that which yields a weighted rms of 1 for the velocity residuals from a combined orbital fit to the astrometric and velocity data. The S99 parallax of 29.31 ± 0.82 mas was used as a weighted input in orbit fitting.

The PHASES and non-PHASES astrometric measurements, velocity measurements, and S99 parallax measurement were combined in a single orbital fit to evaluate the Campbell orbital parameters as well as binary mass ratio and system distance. Alternatively, the orbit semimajor axis and mass ratio were replaced with either the total system mass and mass ratio or the masses of each component; repeating the fit with these substitutions allowed a natural way of evaluating the uncertainties of these degenerate quantities. While the system distance is entirely dependent on the parallax measurement, including this as an input value with its associated uncertainty was necessary to properly evaluate the resulting mass ratio and mass uncertainties at the conclusion of the fitting procedure. The masses are 1.71 ± 0.18 M_☉ and 1.330 ± 0.074 M_☉, values a little smaller than those from North et al. (1998).

At least one substellar companion has already been detected in the HD 137107 (η CrB, 2 CrB, HR 5727, HIP 75312, and WDS 15232 + 3017) system, though it has no impact on the PHASES study. Kirkpatrick et al. (2001) imaged a faint L8 dwarf of mass 0.060 ± 0.15 M_☉ at 194'' southeast of the A–B pair. They concluded that the pair is physically associated with a separation of ∼3600 AU. It is a circumbinary companion to the A–B binary.

CORAVEL produced 31 two-component velocity measurements of HD 137107 A and B, reported first by Duquennoy et al. (1991) and revised by Pourbaix (2000). The TSU AST observed this system 33 times, but unfortunately these observations took place at a time when the lines were blended and thus are not used for orbit fitting. The CORAVEL measurements have been combined with the astrometry to develop a full three-dimensional orbit. The S99 parallax of 53.5 ± 0.9 mas was also used as an additional measurement with associated uncertainty.

The masses are 1.243 ± 0.054 M_☉ and 1.100 ± 0.039 M_☉. As reported in Paper I, the differential magnitude of η CrB was measured in the K band using Keck Adaptive Optics. The differential magnitude is ΔK_p = 0.185 ± 0.001. The apparent K magnitude from Skrutskie et al. (2006) is 3.714 ± 0.216. Combined with the orbit-derived distance of 18.50 ± 0.22 pc (which is consistent with the trigonometric parallax), these correspond to absolute magnitudes of K₁ = 3.04 ± 0.22 and K₂ = 3.23 ± 0.22.

Batten et al. (1985) published 10 single-component velocities and 12 two-component velocity measurements of HD 214850 (HR 8631, HIP 111974, and WDS 22409 + 1433) spanning 1614 days (∼21% of the binary period) and 271 days (∼3.6% of the binary period), respectively. Four more measurements are omitted, as done by the original authors, due to partial blending of the spectral lines. Unit uncertainties of 0.19 km s^-1 for component A and 0.72 km s^-1 for component B were assigned to these measurements, resulting in the weighted rms scatters of each being unity after orbit fitting. The S99 parallax of 29.5 ± 0.8 mas is consistent with the orbital solution and has been included as an input constraint for orbit fitting and is reflected in the orbital parameters and their uncertainties in Table 6. Component masses are measured at the 7% level.