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Astron. Astrophys. 364, 665-673 (2000)

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4. Orbital elements and mass measurements

4.1. Orbital adjustment

All orbits were determined with the ORBIT program (Forveille et al. 1999), through a least square adjustment to all available observations: radial velocities or correlation profiles, angular separations, and trigonometric parallaxes. ORBIT supports triple systems, as well as double ones, as long as three-body effects can be neglected. In the present paper this feature was used for two systems, Gl 644 and Gl866. For double and triple-lined systems we directly adjusted the orbit to the cross-correlation profiles (Forveille et al. 1999, for details), rather than use the radial velocities listed in Tables 4 to 10. This significantly improves the accuracy of the orbital parameters, by greatly decreasing the effective number of free parameters of the overall adjustment. This gain is particularly important:

  • for triple systems, whose three correlation peaks blend for many velocity configurations,

  • for large contrast systems, whose weaker component is sometimes only detected with a low signal-to-noise ratio,

  • and for small amplitude pairs, whose peaks remain blended for most of the orbit.

Table 2 lists the orbital elements of the 7 systems for which we obtained a new or significantly improved orbit. Table 3 lists the corresponding orbital parallaxes and masses, whose relative accuracies range between 0.2% and 5%. Fig. 1 and Fig. 2 respectively show the individual radial-velocity curves and visual orbits, which we now briefly discuss.

[FIGURE] Fig. 1. Radial-velocity and visual orbit for the systems with new or improved mass determinations.

[FIGURE] Fig. 2. Radial-velocity and visual orbit for the systems with new or improved mass determinations.


[TABLE]

Table 2. Orbital elements of the newly adjusted orbits. The inclination angles (i) of the two eclipsing binaries, YY Gem and GJ 2069, are fixed to the values derived from analyses of their light curves (from Leung & Schneider 1978and Delfosse et al. 1999a, respectively). Their other orbital elements are derived from the radial-velocity correlation profiles. All orbital elements of the others stars are simultaneously adjusted to the radial-velocity, parallax, and angular separation data. The inner orbits of Gl 644 and Gl 866 have their inclinations i determined by requiring that the total mass of the inner binary, derived from the outer orbit, must match the sum of the two spectroscopic M[FORMULA] obtained from the inner orbit. This leaves an ambiguity between i and [FORMULA], which we have tentatively resolved by assuming the approximat e coplanarity of their two orbits.



[TABLE]

Table 3. Masses and parallaxes derived from the orbits listed in Table 2. Except for the two eclipsing systems, the parallaxes represent an optimally weighted combination of the astrometric and orbital parallaxes. Some of them, such as Gl 644, merely reflect the astrometric parallax. Others, such as Gl 866, are almost completely determined by the orbit.


4.2. Individual objects

4.2.1. Gl 234 (Ross 614)

This well known binary is the longest period system (P = 16.5 years) for which we obtain a significantly improved orbit, thanks to the availability of early measurements that complement the more accurate data we obtained around the 1999 periastron. The system was initially discovered as an astrometric binary (Reuyl, 1936), and intensively studied as such. Probst (1977) is usually considered as the current reference astrometric orbit. Gl 234 was visually resolved on a few occasions (Lippincott & Hershey, 1972), but its 3.5 magnitude contrast made it a difficult target for visual observers. With the benefit of hindsight, the masses of 0.11 and 0.06[FORMULA] derived by Probst (1977) turn out to have been underestimated by a large factor. The system was subsequently resolved in speckle observations by Mc Alister & Hartkopf (1988) and Coppenbarger et al. (1994). Coppenbarger et al. (1994) combined these observations with the astrometric orbit of Probst (1977) to derive masses of MA=0.179[FORMULA]0.047[FORMULA] and MB=0.083[FORMULA]0.023[FORMULA], compatible within 1[FORMULA] with the values listed in Table 3.

Our orbit (Table 2) is adjusted to the visual data from Probst (1977), to the 1D and 2D speckle measurements from Coppenbarger et al. (1994), to our more accurate adaptive optics angular separations obtained, to parallaxes from Probst (1977) and Soderhjelm (1999), and to 14 ELODIE radial velocities of the primary (typical accuracy of 50 m/s). The two masses (Table 3) are determined with accuracies of 5.2% for the primary (0.2027[FORMULA].0106 [FORMULA]), and 3.4% for the secondary (0.1034 [FORMULA].0035).

4.2.2. YY Gem

YY Gem is one of the three known detached M-dwarf eclipsing binaries (Bopp 1974, Leung & Schneider 1978). We have obtained 75 radial-velocity measurements of the two components with ELODIE, with typical standard errors of 2 km/s. Both components of YY Gem have their rotation period synchronized with the short orbital period by tidal interactions. The resulting fast equatorial velocities (v sin i[FORMULA]30 km/s) explains this very degraded velocity accuracy. The noisier measurements of Bopp (1974) ([FORMULA] 10 km/s) are also used in the adjustment and help to constrain the period. The amplitudes, [FORMULA] and [FORMULA], on the other hand are almost completely determined by the ELODIE measurements, and so are therefore the masses, determined with relative accuracies of 0.2%. We are now obtaining infrared lightcurves of this system to improve the determination of the two stellar radii, and will then present a complete reanalysis.

4.2.3. GJ 2069A (CU Cnc)

GJ 2069A is one of the three known detached M-dwarf eclipsing binaries (Delfosse et al. 1999a). We present here an improved orbit, which includes a few radial-velocity measurements obtained after the completion of Delfosse et al. (1999a). More importantly, the new orbit was directly adjusted to the ELODIE cross-correlation profiles, whereas our earlier article adjusted an orbit to radial velocities extracted from these profiles. The resulting masses are now among of the most accurate measured for any star (e.g. Andersen 1991, 1998), with 0.2% accuracies for both components. It is somewhat unfortunate that they are not yet matched with equally precise distance, infrared photometry, metallicity, and radii.

We have recently discovered (Beuzit et al., in prep.) a fainter companion to the GJ 2069Aab pair, at a separation of 0.55" in early 2000 and which we name GJ 2069D. This makes GJ 2069 a quintuple system, since we had earlier found the fainter visual component, GJ 2069B, to be an adaptive optics and spectroscopic binary (Delfosse et al. 1999c). The new companion is 3 magnitudes fainter than GJ 2069Aab in the K band. Its influence on the photometry can therefore safely be neglected at the current precision of the absolute magnitudes, and the extrapolated luminosity contrast in the V band precludes its detection in the integrated visible spectrum. GJ 2069D will also eventually cause a drift in the systemic velocity of GJ 2069Aab. We have attempted to fit this drift in addition to the parameters of the Aab orbit, but we found that this does not decrease the [FORMULA] of the adjusted model. This indeterminacy of the drift parameter indicates that the period of the AD system is significantly longer than the [FORMULA]4 years span of the current radial-velocity data. Its influence does therefore not appreciably bias the measured masses.

4.2.4. Gl 644

At d = 6.5pc, the Gl 644/643 system is the richest stellar system in the immediate solar neighbourhood (d[FORMULA]10pc), with 5 components Gl 644 (M3V), is the brightest visual component and shares a common proper motion with two distant companions, Gl 643 (M3.5V) at 72 arc seconds and vB8 (Gl 644C, M7V) at 220 arc seconds. Gl 644 is itself a 1.7-year binary, identified from astrometric observations by Weiss (1982) and Heintz (1984), and first angularly resolved in speckle observations by Blazit et al. (1987) and Tokovinin & Ismailov (1988). Finally, Pettersen et al. (1984) found that one of the two components of Gl 644 (Gl644B) is itself a short period spectroscopic binary, but could not determine its period.

We have obtained 25 ELODIE radial-velocity measurements of Gl 644, which usually appears as a well separated triple-lined system in those data. This allows us to determine for the first time the elements of the inner orbit, whose period is 2.97 days. Such close orbits are very rapidly circularised by tidal interactions. Here we nonetheless measure a small but highly significant eccentricity of.0209[FORMULA].0008. This most likely results from dynamical interactions between the two orbits (Mazeh & Shaham 1979), as could probably be ascertained through a complete dynamical analysis (which would be beyond the scope of the present paper).

The orbital elements listed in Table 2 were simultaneously determined for the two orbits, using angular separation measuremements from Blazit et al. (1987), Tokovinin & Ismailov (1988), Al-shukri et al. (1996), Balega et al. (1989, 1991, 1994), Hartkopf et al. (1994), our own more accurate adaptive optics measurements (Table 12), the 25 radial-velocity profiles, and the trigonometric parallaxes of both Gl 644 (Soderhjelm 1999) and Gl 643 (ESA 1997). This determines the masses of all three components with relative accuracies of 1.4-1.3%.

This accuracy is obtained even though the orbit is almost seen face-on ([FORMULA]), an adverse orientation for accurate mass measurements from radial velocities. ELODIE generally provides very accurate [FORMULA] for double-lined systems, and the mass errors are then typically dominated by the inclination uncertainty. For nearly edge-on orbits, errors on the inclination do not propagate much to [FORMULA], and we can then obtain accurate masses even for fairly uncertain inclinations. For nearly face-on orbits on the opposite, one needs a very accurate inclination to determine even moderately accurate masses. Gl 644 demonstrates that we can obtain accurate masses even in some rather poorly oriented orbits.

Interferometric measurements would be needed to resolve the very close inner orbit, but its inclination [FORMULA] is nonetheless strongly constrained: [FORMULA], as derived from the outer orbit, must match the sum of the two spectroscopic M[FORMULA] obtained from the inner orbit. This gives [FORMULA]=0.27, and therefore either [FORMULA]=164.2o or [FORMULA]=15.8o. One of those two determinations is very close to the inclination of the outer orbit ([FORMULA]). This probably points to a coplanar system, in keeping with a general tendency of close triple systems (Fekel 1981). To ascertain this, one would need to resolve the inner pair, determining [FORMULA] and obtaining [FORMULA] without the reflexion ambiguity.

4.2.5. Gl 747AB (Kui 90)

Gl 747 was first visually resolved in 1936 by Kuiper. Yet, the orbit of this nearby star (d = 8.5 pc) has apparently never been determined, probably because its separation never exceeds 0.35". It has been resolved in speckle observations once by each of Blazit et al. (1987) and Mc Alister et al. (1987), and three times by Balega et al. (1989). We have complemented these litterature measurements with 15 ELODIE radial-velocity profiles of this double-lined system, and 4 separations obtained with PUE'O. The 5.5-year period orbit listed in Table 2 provides an excellent description of all these measurements, with the (strong) exception of the speckle separation obtained by Mc Alister et al. (1987). We could not identify a likely reason for this discrepancy, except that Gl 747 is significantly fainter than most sources in Mc Alister et al. (1987). It could have been close to their sensitivity limit for the conditions under which it was observed, but is on the other hand a system of two equally bright stars. It should therefore not have been an overly difficult target for speckle observations. We have chosen to ignore this data point, since all other measurements are mutually consistent to within approximately their stated standard errors, and since some of them have been observed within a year of the discrepant point. This orbit determines the masses of the two components (2[FORMULA]0.2[FORMULA]) with an accuracy of [FORMULA]0.4%, and the orbital parallax with a 0.2 mas standard error. The latter is in excellent agreement with the less precise astrometric parallax listed in Van Altena et al. (1995).

4.2.6. Gl 831

Gl 831 was first noticed as a P=1.93-year astrometric binary (Lippincott 1979, Mc Namara et al. 1987), and then resolved by visible speckle observations (Blazit et al. 1987). It appears in ELODIE observations as a double-lined spectroscopic binary, but the contrast between the two peaks of the correlation function is large ([FORMULA]10) and most of the time their separation is not very much larger than their combined width. It is therefore a good illustration of the improvement brought by a direct adjustment of the orbit to the correlation profiles. Using three adaptive optics angular separations, the parallax from Van Altena et al. (1995) and 14 ELODIE correlation profiles we determine both masses with 4% relative accuracy.

Henry et al. (1999) have found tentative evidence for a third component of Gl 831 in their HST FGS observations of this system. This companion would be [FORMULA]3 magnitude fainter in the V band than the primary, and it could be either very close to A or B, or beyond [FORMULA]0.5". We can now firmly exclude the first possibility for a physical member of Gl 831: it would necessarily imply very large velocity variations of the corresponding bright component. A red companion that is only three magnitude fainter in the V band than the primary would be easily detected in our K band adaptive optics images, unless it was always fortuitously within [FORMULA]0.15" of the primary or within 0.1" of Gl 831B, whenever we observed it. As this is rather unlikely, the companion, if real, is most likely bluer than Gl 831. It could then either be a white dwarf member of the system, or an unrelated background object.

4.2.7. Gl 866

We recently (Delfosse et al. 1999b) discussed in detail this system of three very low mass stars (3 [FORMULA] [FORMULA]0.1[FORMULA]), and obtained individual masses with [FORMULA]3% accuracy. Shortly thereafter Woitas et al. (2000) published a large set of new angular separation measurements. Lacking radial-velocity information, they could only obtain the total mass of the system, with [FORMULA]10% accuracy. We analyse here the combination of the two datasets, and obtain a very substantial improvement over either of these previous analyses. All three masses are now determined with [FORMULA]1% accuracy. Gl 866C, the faintest member of the system, is the only star with a dynamically determined mass (0.0930[FORMULA]0.0008[FORMULA]) that is safely lower than 0.1[FORMULA].

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Online publication: January 29, 2001
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