5 Comments on individual systems

5.1 General cases

$\bullet$ HIP 7918 (Gl 67): A close astrometric binary comprised of a solar-type star and a cool low-mass companion 1000 times fainter. In this sample of 70 candidates, this is the only system with a direct determination of the fractional mass (a consequence of its large separation, see Paper I). The companion was resolved for the first time by Henry et al. (1992), using infrared speckle imaging techniques. With the same orbital elements, Kepler's third law and the Hipparcos parallax yield a total mass about 30% smaller than Henry's value. The most surprising discrepancy lies with the fractional mass B of the companion, significantly smaller in this study. The combination of both effects yields a secondary's mass about half the value derived by Henry, although affected by a large relative error. Our result may be not very reliable, as suggested by the large correlations found between the unknowns.

$\bullet$ HIP 8903 ($\beta$ Ari): Famous double-lined spectroscopic binary with an unusually large orbital eccentricity. The new Hipparcos parallax value, slightly larger than the one determined by Pan et al. (1990), leads to smaller individual masses, but still consistent with Pan's estimates of $2.34\pm 0.10$ and $1.34\pm 0.07\ M_{\odot}$.

$\bullet$ HIP 12153 (31 Ari): This object was first detected as double by lunar occultation (Africano et al. 1978), then studied with speckle interferometry and spectroscopy. A preliminary orbit has been computed very recently from speckle data (Mason 1997a), in good agreement with the Hipparcos observations. It provides an accurate estimate of $\beta-B$. The true value of the parallax remains puzzling however. Balega's dynamical value of 21 mas (Balega & Balega 1988) is not consistent with Hipparcos (28.15 mas), still too small to yield realistic masses for this system (see the position of HIP 12153 in the mass-luminosity diagram, Fig. 2). If the latter value is confirmed, a revision of both the orbital period and the size of the relative orbit will be needed. The value of $\Delta m$ taken here is the average of two estimates (Africano et al. 1978), one in the red (0.3), the other in the blue (0.1).

$\bullet$ HIP 20087 (51 Tau): Single-lined spectroscopic binary, whose probable large magnitude difference is not yet accurately known. Considering the dynamical parallax, Baize (1989) suggested a total mass of 3.4 $M_\odot$ and accounted for the large mass of the secondary (about 1.6 $M_\odot$) by assuming that the star is an evolved subgiant. The new parallax and mass fraction estimates confirm the mass of the primary (about 1.8 $M_\odot$)but yield a companion's mass more typical of a main sequence dwarf with a G0 spectral type ($\approx 1\ M_\odot$).

$\bullet$ HIP 33451 (I 65): Visual/speckle binary mostly observed by visual techniques during the last century. The orbit is flagged "definitive" in the catalog of Worley & Heintz (1983). Unfortunately we did not find any information concerning the masses of the components. Our masses and absolute magnitudes agree nicely with the empirical mass-luminosity relation.

$\bullet$ HIP 45571 (128 Car): First detected as double in 1960, this system is in fact triple, the C component with a magnitude 12.2 lies at 18'' from the close AB binary. At this distance from the central pair, the attenuation effect caused by the Hipparcos dissector tube makes the C component nearly invisible, and thus too faint to disturb the signal of AB. The magnitude difference derived from Hipparcos is very poor ($1.37\pm 0.87$) and we have used the value given by Worley. This pair is one of the 6 stars of this sample with a standard deviation of $\beta-B$smaller than 0.01. The two masses are found nearly equal which suggests either a pair of two G7 giant stars, or a pair of A0 dwarfs. This is not compatible with the absolute magnitudes, however (see the mass luminosity relation, Fig. 2). The orbital elements are indeed still preliminary and need to be confirmed.

$\bullet$ HIP 55016 (73 Leo): Speckle and spectroscopic binary, the very first star to have a photoelectric velocity published (see Griffin 1990). As it is mentioned by Mason (1997b), the exact determination of spectral types and $\Delta m$ are now no clearer than they were in 1990, so the mass fraction proposed in this paper is not very reliable (we have taken $\Delta m \approx 2.9$, which is probably too large). Unfortunately the high relative error of the parallax does not improve the situation and yields an inaccurate total mass. This system will probably remain problematic for another few years, since a recent attempt to study it with adaptive optics has failed.

$\bullet$ HIP 60129 (McA 37): $\eta$ Virginis is a triple system formed by a close spectroscopic pair (undetectable by Hipparcos) and a more distant speckle companion. Again, the large relative errors of the parallax and semi-major axis prevent a good determination of the total mass. The even worst quality of the individual masses is caused by the uncertain value of $\Delta m$, as derived by speckle interferometry (Hartkopf et al. 1992). The masses and the mass ratio listed as references in Table 9 are based on arbitrary assumptions and must be considered with caution. Due to its long orbital period, $\eta$Vir clearly deserves further investigations, both with adaptive optics ($\Delta m$) and speckle (orbital elements).

$\bullet$ HIP 68682 (HR 5273): Astrometric-spectroscopic binary, recently studied by Kamper (1987). This is one of the 3 best results of the present research (mass uncertainties at about 5%), but some restrictions must be mentioned. The secondary component is actually unseen and the $\Delta m$ proposed by Kamper and used in this study is uncertain. This is not a serious problem however, since the value of the fractional intensity $\beta$ is anyway close to zero and the calculation of the fractional mass B is not very sensitive to a possible error of $\Delta m$. More important is the consequence of the semi-major axis of the relative orbit, estimated at about 0$.\!\!^{\prime\prime}$33 by Kamper, a value based on uncertain assumptions (see the two last paragraphs of the previously mentioned paper). The adoption of a different value would of course change the estimate of B and of the total mass M. Taking $a=0\hbox{$.\!\!^{\prime\prime}$}33$ yields a mass ratio perfectly consistent with Kamper's value, but our mass estimates are slightly larger, a consequence of the Hipparcos parallax. The periastron argument $\omega$should be rotated by 180 degrees.

$\bullet$ HIP 71094 (A 570): Variable speckle binary, one of the best results regarding $\beta-B$despite the long period. The fairly small parallax is consistent with the dynamical estimate of $15\pm 5$ mas (Heintz 1991). The lack of individual spectral types for this system makes the validation of the masses difficult. The location of the two components in the mass-luminosity diagram is reasonable.

$\bullet$ HIP 71729 (McA 40): Single-lined spectroscopic and speckle triple system formed by a very short-period ($\approx\!100$ days) pair and a more distant speckle companion. The closest companion was unresolved by Hipparcos and the primary is in fact composite. The new parallax yields a total mass about 30% larger than the previous estimate by Barlow & Scarfe (1991). The mass ratio also differs, so that the total mass of the primary component (Aa+Ab) is conserved, while the secondary mass appears to be much larger, with fairly large underestimated relative errors. We are not very confident in these new results. The magnitude difference and the spectral types also need more checks.

$\bullet$ HIP 76852 (21 Ser): Astrometric/speckle binary. No mass estimates have been found in the literature, but the spectral types B9V and A1V are not compatible with the masses derived here (they suggest masses close to $3\ M_\odot$ instead of $2\ M_\odot$). The new parallax compares quite well with previous estimates and is probably not suspect. Thus, either the orbital elements (there is still a doubt regarding the period) or the spectral types may be wrong. A couple of A4V stars would fit better.

$\bullet$ HIP 81126 ($\sigma$ Her): Speckle binary star containing an object suspected to be a $\beta$Pictoris-like star, due to its large colour excess in the infrared. The mass excess mentioned by Baize (1989), based on a dynamical parallax close to 10 mas (Balega & Balega 1988) is not confirmed here, due to the new parallax estimate. The value of $\Delta m$ is still not very clear, since Balega proposed $1.6\pm 0.3$ instead of 3.5, as previously assumed.

$\bullet$ HIP 82817 (Kui 75): Famous UV emitting flare star and visual/speckle binary. This is the only system in the present sample for which the new parallax produced by the specific processing for short-period binaries is significantly different (about 12% smaller) from the catalogue's value (ESA 1997). This new estimate ($155.42\ \pm\ 1.85$ mas) agrees well with the most recent ground-based trigonometric determination: $152\, \pm\, 4$ (Jenkins 1963) and is much more accurate than the Hipparcos value. The latter determination was in fact quite uncertain because no orbital model was used in the data reduction, and there is little doubt that the new value is closer to reality. This situation is very akin to that of Algol.

$\bullet$ HIP 83895 ($\zeta$ Dra): The most recent paper concerning this object (Olevic et al. 1997) supports a significant change in the orbital elements previously computed by Zulevic (1992). The new elements are still considered as preliminary, however, and indeed do not improve the results already obtained with the former orbit. Unfortunately, masses and parallax of the pair were not calculated because of the lack of magnitudes and spectra, as mentioned by Olevic (1997). It is thus difficult to assess the quality of the present results, based on Zulevic's orbit (1992) and differential photometry (1993). The total mass derived here ($\approx 10\ M_\odot$) suggests a pair of giants.

$\bullet$ HIP 84949 (McA 47, HR 6469): Speckle/spectroscopic triple system consisting of a close eclipsing pair containing a F2V star, orbitting a more distant G5IV variable component. This very interesting system was the subject of three papers published at the same time (Wasson et al.; Van Hamme et al.; Scarfe et al. 1994) in the same journal. We have used the more recent orbital elements proposed by Scarfe et al. (1994) together with $\Delta m = 0$ as suggested by Baize (1991), although this must be used with care because of the photometric peculiarities of the system. The evolved G5 star is referred to as the primary and has a period of variability of about 83 days in V, while the secondary is taken as the brighter star of the close eclipsing pair, whose period is 2.23 days (Van Hamme 1994). The duplicity of the second component could not be seen by Hipparcos, and the double variability phenomenon (eclipse + spotted variable) entails reasonably small change of the magnitude (<0.09 mag), so the set of Hipparcos observations may be considered as photometrically homogeneous, at least for the purpose of this study. We obtain a mass of $1.15\ M_\odot$ for the evolved primary and a total mass of $2.63\ M_\odot$ for the eclipsing pair, with formal errors of 20% and 14% respectively. While the mass of the secondary is perfectly consistent with Scarfe's determination, it is not true for the primary ($1.86\pm 0.09\ M_\odot$). This can be traced to small discrepancies in the estimates of the parallax and the fractional mass. Combining Scarfe's fractional mass B=0.587 with our $\beta-B$ yields an estimate of $\beta$ and thus of the approximative magnitude difference between the evolved primary and the close eclipsing pair, $\Delta m\approx 0.54$ (in the Hipparcos band), half a magnitude larger than Baize's. This assumption leads to individual masses of $1.56\, \pm\, 0.31\ M_\odot$ and $2.21\, \pm\, 0.31\ M_\odot$. The composite secondary has been excluded from the mass-luminosity diagram (Sect. 6.2) and thus does not contribute to the fit.

$\bullet$ HIP 85141 (Rst 3972): Visual/speckle binary formed by two G0 giant stars. For many years the orbital period was assumed to be close to 30 years, until Hartkopf et al. (1996) set forth a half-period alternative, which fits better the recent measurements. We used these orbital elements in Paper II to derive masses of $1.51\ M_\odot$and $2.94\ M_\odot$ with formal errors at the level of 30%. These elements are now superseded by the new orbit computed by Heintz (1997), in better agreement with the whole set of obervations. We find this time two identical masses of about $1.8\ M_\odot$, with errors at the same level. Values of $\beta-B$ and $\Delta m$ agree well with the fact that both components have indentical spectral types, but the total mass is slightly too small for two G0III stars. If we consider the smallest possible parallax allowed by the error bar ($\approx\!14.3$ mas), we find a total mass of 4.6 $M_\odot$, closer to the expected value.

$\bullet$ HIP 86722 (Gl 692.1): Single-lined spectroscopic and speckle binary, recently studied by Duquennoy using the CORAVEL and RVM radial-velocity spectrometers and near IR speckle data (Duquennoy et al. 1996). All the values derived here (masses and absolute magnitudes) agree perfectly with Duquennoy's assumptions, except for the mass of the primary component, which we found to be 20% larger. These new results are the most accurate to date and must replace any previous determination.

$\bullet$ HIP 95995 (McA 56): This K star of the solar neighbourhood is a speckle-spectroscopic binary containing a low mass companion, mainly noticed for its high proper motion. Very precise total mass and $\beta-B$ have been determined in this study, but the quality of $\Delta m$ is still too poor and causes the estimates of the individual masses to be rather uncertain. Better differential photometry is needed.

$\bullet$ HIP 96302 (9 Cyg): Single-lined spectroscopic binary presenting one of the smallest separations of this set. As with all the most distant stars, the masses are not very reliable. The $\Delta m$ estimate of Baize (1989) does not agree with the value (which we have adopted) found in the Worley catalogue. Moreover, the period is not accurately known.

  

Table 9: Reference values of component's masses and physical ratios

¹ The three first characters of the author's name followed by the two last digits of the publication's year.

$\bullet$ HIP 98001 (Ho 581): Visual binary star containing a spectroscopic system (the A component is associated with a low mass spectroscopic companion, see Griffin 1997). The parallax and total mass derived here are compatible with the determination of Heintz (1990), but the very large mass fraction (B=0.656) is not confirmed here. We find a $B=0.459\pm 0.052$, yielding a primary component slightly more massive than the secondary. The positions of both stars in the empirical mass-luminosity diagram look satisfactory.

5.2 A special attention for 12 Per (HIP 12623)

The system was identified by McAlister (1976) as a likely candidate for resolution by speckle interferometry, and, indeed, the two components had been resolved by C.R. Lynds in an unpublished, exploratory speckle program at the Kitt Peak 4-meter telescope in 1973. Routine speckle measurements of the system were begun in 1975, and McAlister (1976) published an orbital solution based upon five speckle measurements and the spectroscopic elements of Colacevich (1941). Some 40 speckle measures are now available for analysis. We have calculated new orbital elements for this system, presented in Table 11. They do not differ strongly from the previous estimations, see for example McAlister (1978) although the formal errors are significantly reduced. The $\Delta m$estimate of 0.30 is originally from Colacevich (1935), and no better value has been proposed since then. A confirmation would be especially helpful for a mass determination free of bias. We have studied this system in two different ways:

1.

The specific processing from Hipparcos data and a ground-based orbit (like all the other stars of this paper),

2.

A combination of available spectroscopic and speckle interferometric data for a three-dimensional orbit solution.

Because of the quantity and quality of available data, the second method yields better results. The available radial velocity data span 97 orbital revolutions of 12 Persei while the speckle measurements cover 25 orbits. The relevant data for 12 Persei have been analyzed thanks to the reduction softwares routinely used for CHARA binary star orbit studies, namely a least-squares "grid search" algorithm for the speckle observations and a program developed by Tokovinin for combining radial velocities and speckle astrometry.

In a first step, the orbital elements for 12 Per given in Table 11 were determined from the entire dataset composed of speckle measurements from the CHARA Catalogue of Speckle Interferometric Measurements of Binary Stars (maintained by W.I. Hartkopf and available on-line) and of the radial velocities of Colacevich (1935, 1941) and Duquennoy & Mayor (1991). The orbital period from this solution was then fixed and the remaining orbital elements were determined by combining the speckle data with the Duquennoy and Mayor spectroscopic data, leaving out the old measurements of Colacevich. Independent orbits from these two datasets show excellent agreement between common elements.

The combination of the two data types also permits the determination of an orbital parallax of 42.6 $\pm$ 1.0 mas which is in excellent agreement with the Hipparcos parallax of 41.9 $\pm$ 1.6 mas corrected for the orbital motion of the binary.

While we adopt the masses derived from the combined speckle/spectroscopic analysis, we note that masses can also be derived by applying the Hipparcos parallax to the ground-based orbit, i.e. option number 1 above. Table 10 shows the different values obtained by each method.

  

Table 10: Comparison of parameters for 12 Persei

The discrepancy observed for the individual masses probably arises from the fact that the value of $\Delta m$ used to retrieve the fractional mass B in the first method is uncertain. Assuming the values B=0.478 (ground-based) and $\beta-B=-0.121$ (Hipparcos) are correct, we find $\Delta m=0.64\ \pm\ 0.10$, which is not unrealistic. With the Hipparcos parallax, this would produce the following masses: $M_1=1.31\ \pm\ 0.16$ and $M_2=1.20\ \pm\ 0.13$. An accurate determination of $\Delta m$ would result in truly definitive masses for this system, and we note that ground-based, long-baseline optical interferometers offer this potential.

  

Table 11: New speckle orbital elements of 12 Per

5.3 The 6 revised systems

The results presented in Table 8 for 6 revised systems of Paper II are simply an update of the individual masses and their errors, coming from a more reliable $\Delta m$ estimate. Thus, the parallaxes and total masses are unchanged. The modifications are briefly discussed below.

$\bullet$ HIP 2237 (B 1909): The slight increase of $\Delta m$ makes the mass of the secondary closer to the primary's one.

$\bullet$ HIP 2762 (Kui 7): $\Delta m$ is unchanged but known with a better precision, resulting in more accurate estimates of the masses.

$\bullet$ HIP 44248 (10 Uma): $\Delta m$ is 10% larger and 4 times more accurate. The mass difference between the components is then slightly larger.

$\bullet$ HIP 84140 (Kui 79): A $\Delta m$ about 2 times smaller reduces the mass difference in a significant way. The almost identical small masses obtained are therefore more acceptable for this pair of quasi-similar red dwarfs.

$\bullet$ HIP 93574 (Fin 357): The magnitude difference is significantly larger than the previous estimate, and allows the primary component to recover his logical status of more massive star of the pair. Its mass is actually 14% larger than the secondary's mass (instead of 22% smaller before).

$\bullet$ HIP 107354 ($\kappa$ Peg): The components are this time found to be almost of equal brightness, a fact which increases the mass difference, already fairly large, between the two stars. The respective status of both components is thus not clear, and we should probably exchange them in order to have the primary more massive than the secondary. The spectral types are still needed to check the solution.

  

Table 12: Absolute magnitudes for 52 (17+35) systems with relative errors on individual masses less than 25%