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Astron. Astrophys. 330, 585-599 (1998)

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6. Comments on individual systems

6.1. Remarkable pairs

[FORMULA] HIP 171 (85 Peg): the orbit of this visual and spectroscopic binary is very well known (flagged 'definitive' by Worley), even if its determination is not recent. The large semi-major axis (see Table. 2) is a very favourable instance for a direct determination of the mass ratio B based on the Hipparcos data. One of the peculiarities of this 'anomalous' system is that the mass of the secondary appears often larger than that of the primary, while the primary is much brighter ([FORMULA]  mag). This is why the companion 85 peg B is suspected to be an unresolved binary star (Heintz, 1993). At least six distinct determinations of the individual masses of 85 Peg have been made between 1949 and 1992 (Fernandes, 1996), half of them giving the secondary more massive than the primary, but not significantly (according to the error bars). Feierman, 1971, has shown that for close pairs with [FORMULA], the [FORMULA] ratio was overestimated, which implies an overestimation of the mass ratio B, and thus of [FORMULA], but his study is restricted to measurements made on photographic plates. There is no special reason to suspect such an effect with the present material. Moreover, the masses derived from the present study do not really allow to conclude: they do not significantly differ from one another ([FORMULA] means that the standard errors of the masses are slightly underestimated, see Sect. 5.1).

[FORMULA] HIP 2762 (13 Cet): this double-lined binary belongs to a set of 23 short period nearby G stars for which Duquennoy et al., 1991, have monitored the radial velocities. Mazeh et al., 1992, have used these results to determine the mass ratio distribution. The large standard errors of the masses are probably realistic and follow from the relative smallness of the parallax : the parallax derived by S"oderhjelm S., 1997, is larger than ours by only one mas and the semi-major axis smaller by six mas and this leads to a total mass 0.4 solar mass below the value derived here.

[FORMULA] HIP 7580 (Kui 7): the old orbital solution given by Baize, 1985, and Heintz, 1988, yielded, with a distance of 42 pc, too small masses for a pair of late F/early G dwarfs (0.3 and 0.6 [FORMULA] respectively). The new orbital elements taken from Hartkopf et al., 1996, result, with the old distance estimate, in a much reasonable value of 2.8 [FORMULA] for the total mass. With the Hipparcos parallax, we obtain an intermediate value ([FORMULA]), and a secondary component slightly more massive than the primary.

[FORMULA] HIP 12390 ([FORMULA] Cet): A well known spectroscopic double-lined binary. The orbit is based uniquely on speckle data, which covers more than 4 revolutions. The new parallax estimate given by Hipparcos yields a total mass appreciably larger than before, while the mass ratio is slightly smaller (see Table 9).

[FORMULA] HIP 14328 ([FORMULA] Per): As [FORMULA] Cygni (HIP 96683), this spectroscopic binary contains highly evolved stars. The orbit is one of the most inclined ([FORMULA] degrees) of this set. It is almost the more massive object of our study (after HIP 43671 = Fin 316). The masses and the parallax are in excellent agreement with the previous estimates (McAlister et al., 1982). The remark made for [FORMULA] Per also holds true in the present case: the small value of the parallax results in a high relative error, and affects the quality of the sum of the masses.

[FORMULA] HIP 19719 (46 Tau): Single lined spectroscopic and speckle binary. Thanks to speckle interferometry (Hartkopf et al., 1996), the orbit of this close binary is now very well known. Although the components are nearly equally bright, one of the stars seems clearly more massive than the other (the 'primary/secondary' status remains uncertain inside this object). At the moment, no comparison can be made because of the lack of other mass determination.

[FORMULA] HIP 24608 (Capella): Famous double-lined spectroscopic binary, the brightest object of our sample ([FORMULA]). The masses derived here are slightly smaller than the commonly adopted values (Hummel et al., 1994a), due to the Hipparcos new estimate of the parallax. The extremely short period and the exceptional brightness of this pair could have resulted in better estimates than those presented in this paper had the orbit been larger.

[FORMULA] HIP 44248 (10 Uma, Kui 37): As for 85 Peg (HIP 171), its large a and small P favour the direct estimate of the fractional mass B. The proposed solution is highly reliable.

[FORMULA] HIP 45170 (81 Cnc, Fin 347 Aa): Visual, interferometric and spectroscopic solar-type binary, one of the shortest-period visual pairs (2.7 years, perfectly adapted to the Hipparcos time span). We have used the extremely precise orbit of Mason et al., 1996, yielding parallax and mass estimates in excellent agreement with his own determination. The present work tends to confirm the 'over-massive' status of this pair of G8-V stars.

[FORMULA] HIP 75695 ([FORMULA] CrB): Cool Ap astrometric and spectroscopic binary star, and a famous magnetic variable. The new parallax estimate, four times more accurate than the previous one (Kamper et al., 1990), leads to a reduction of the error of the total mass by a factor six. Accurate estimates ([FORMULA]) of the individual masses are proposed for the first time.

[FORMULA] HIP 80346 (Gliese 623): Low mass short-period spectroscopic binary, one of the nearest pairs of our sample. The mass of the secondary component is expected to be near the substellar limit (Marcy et al., 1989). The authors mentioned a serious discrepancy between the dynamical mass estimates (0.51 and 0.11 [FORMULA]) and those deduced photometrically (0.34 and 0.084 [FORMULA]), a priori justified by a large underestimate of the parallax (134 mas). With the new parallax estimate derived from the Hipparcos data ([FORMULA] mas), this assumption is no longer valid. If the published orbital elements are correct (Henry et al., 1993), the real masses could be even slightly larger than the dynamical estimates. Nevertheless, the discussion is not completely settled, as the errors of the masses are still quite large (essentially due to the bad quality of the semi-major axis value).

[FORMULA] HIP 84140 (Kui 79): This pair of dM3 red dwarfs is the nearest star of our sample ([FORMULA] pc). Despite a good configuration for direct determination of the fractional mass (small period, large separation), Method B yields better estimates of the masses than those derived from Method A. In term of quality, these estimates are the best among the Type I stars (see Table 7). Masses of [FORMULA] for each component are proposed by Henry et al., 1993, assuming a semi-major axis a =0:0071 and a parallax of nearly 160 mas. The new revised values, [FORMULA] mas (this study) and [FORMULA] 0:0076 (Hartkopf et al., 1996), yield larger masses: 0.40 and 0.34 [FORMULA] with the same quality ([FORMULA]).

[FORMULA] HIP 86032 ([FORMULA] Oph): Classical astrometric binary with a large magnitude difference. One of the most recently published photocentric orbits is that of Augensen et al., 1992, which is of no use in the frame of the present work. Augensen et al. provides also an estimate of the masses: [FORMULA] and [FORMULA], which differ strongly from the estimates of Kamper et al., 1989 : respectively 4.9 and 1.2 [FORMULA]. The present solution (4.0 and 0.7 [FORMULA]) tends to confirm the previous one, with the reserve that the precisions are not very good.

[FORMULA] HIP 89937 ([FORMULA] Dra): Nearby speckle and double-lined spectroscopic binary with solar-type primary component. This object is one of the few systems older than the Sun (about 8 billion years) whose parameters have been accurately determined, providing a benchmark for evolutionary theory. The masses presented in this study are in satisfactory agreement (especially for the primary) with the old estimates of McAlister (1980): [FORMULA] and [FORMULA], but not with the results taken from the more recent work of Tomkin et al., 1987 ([FORMULA] and [FORMULA]), whose main purpose was precisely to update the mass estimates of McAlister, qualified as "surprisingly low for a system with an F7 V primary". This discrepancy holds however only for the mass of the primary.

[FORMULA] HIP 96683 ([FORMULA] Cyg): Famous double-lined spectroscopic binary, formed by two 'normal' giants with comparable magnitudes and spectral types. The very small orbit ([FORMULA] mas) is based on observations carried out with the Mark III Interferometer. The mass ratio proposed here is fully reliable, but the total mass is very sensitive to the value adopted for the parallax. For example, adopting [FORMULA]  mas instead of [FORMULA]  mas yields a total mass of 4.3 [FORMULA] instead of 3.35 [FORMULA]. The individual masses are indeed probably larger than those announced here, according to the numerous works on that system. The knowledge of the orbit size must be improved.

[FORMULA] HIP 104858 ([FORMULA] Equ): Spectroscopic binary with solar type primary. As for HIP 171, the errors of the orbital elements are ignored, so that the mass estimates of Table 7 should be affected by a larger error. Compared to previous determinations, the mass of the primary seems somewhat overestimated. A more reliable orbit is awaited for confirmation.

[FORMULA] HIP 112158 ([FORMULA] Peg): Spectroscopic and interferometric binary containing a G2II-III giant, one of the smallest orbit in our sample. Although no information could be found on the masses, the mass estimates presented in Table 8 are consistent with the position of the components in the HR diagram.

6.2. The case of Algol

Because of its photometric peculiarities, the eclipsing system Algol AB-C (HIP 14576) deserves a special treatment. Due to its small separation, the contact eclipsing binary A-B is equivalent, for Hipparcos, to a variable single star. Associated to the C dwarf, this triple system thus shows up as an astrometric binary with a variable component. Between March 1990 and February 1993, the Algol system has been observed 81 times on the modulating grid of the Hipparcos instrument (each observation is a [FORMULA] transit across the whole grid), corresponding to 24 different epochs (two consecutive epochs being separated by about six weeks). The resulting photometric curve of Fig. 7 has been built from this material and the information on the phase (S&0uml;derhjelm S., 1980),


where t is the observation time in JD. The curve reveals five 'atypical' observations located during the eclipse, with discrepant magnitudes from the rest of the distribution. The lowest magnitude transit is exactly located during the deepest eclipse phase, which lasts about 20 minutes. In order to get a photometrically homogeneous set of observations, consistent with the input value of the magnitude difference outside the eclipses (see Table 9), these few observations have been excluded from the analysis. Owing to the precisions involved, it was not necessary to eliminate the few observations located at [FORMULA] (secondary minimum of the curve). The quantity [FORMULA] derived for Algol is one of the most precise determinations. The stability of the solution is excellent. It is not sensitive to the choice of the input values for [FORMULA] and B, and does not depend too much on the weighing of the observations. This result is in good agreement with the previous determination of Pan et al., 1993, which provides also a very reliable orbit.

[FIGURE] Fig. 7. Light curve of Algol AB-C (HIP 14576), derived from the Hipparcos observations. The deepest minimum ([FORMULA]) corresponds to the occultation of the bright B type component by the K0 IV red subgiant. The symmetrical situation ([FORMULA]) produces a minimum at [FORMULA]  mag.

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Online publication: January 16, 1998