Table 1 lists the various samples that have been considered, namely dwarf barium and subgiant CH stars (McClure 1997; North, priv. comm.), mild and strong barium stars (Jorissen et al. 1998), Tc-poor S stars (Jorissen et al. 1998) and CH stars (McClure & Woodsworth 1990). Their spectroscopic orbital parameters have been taken from the reference quoted.

Table 1 also provides various parameters that allow either to assess the quality of the derived orbital solution or to identify the reason why a reliable orbital solution could not be derived for some of the spectroscopic binaries considered. The following parameters potentially control our ability to derive an astrometric orbit from the IAD, with favorable circumstances being mentioned between the parentheses: the parallax (Col. 3; large parallax), the number of available IAD measurements (FAST+NDAC; Col. 4; large number of measurements), the ecliptic latitude (Col. 5; this parameter may play a role since it controls how different the orientations of the reference great circles are; favorable cases have absolute values larger than 47), the orbital period (Col. 6; in the range 1 - 3 yr to ensure a good sampling of the orbit), the orbital eccentricity (Col. 7; low eccentricity).

The following columns characterize the quality of the solution obtained from
the minimization process. Column 11 provides
,
which should be of the order of unity if the internal error (Eq. 2) on the abscissae has been correctly evaluated by the
reduction consortia and if the model provides an adequate representation of
the data. The first risk error associated with rejecting the
null hypothesis that the orbital and Hipparcos 5-parameter solutions are
identical (Eq. 11) is given in Col. 12. Low values of
are
generally associated with Hipparcos solutions of the G, X or O types (as
listed in Col. 9; see the caption to Table 1 for more
details), since the orbital motion is then large enough to have been noticed
already by NDAC or FAST. Columns 13 and 14 compare the
ratio derived from the orbital solution to its expected
value from Eq. (13). In Cols. 11 to 13, the data refer
to the orbital solution obtained by combining NDAC and FAST data.
For dwarf barium stars, the masses used to estimate
according to Eq. (13) are
,
whereas *M*_{1} is derived from the spectroscopic
gravity, with an estimated error of 0.05
(North, priv. comm.).
According to the statistical analysis of the spectroscopic mass
functions performed by Jorissen et al. (1998), *M*_{1} and *M*_{2} pairs (expressed
in )
of (
), (
)
and
(
)
have been
adopted for strong barium stars, mild barium stars and Tc-poor S
stars, respectively. The same analysis performed by
McClure & Woodsworth (1990) for CH stars yielded
and
.

Astrometric orbits were accepted when is smaller than 10 per cent and the expected value falls within the confidence interval. A few cases not fulfilling these criteria were nevertheless accepted after visual inspection of the orbital arc.

Examination of Table 1 reveals that the following criteria need to be fulfilled in order to be able to extract a reliable astrometric orbit from the Hipparcos data: mas, yr, . The success rate is as follows for the various samples: dwarf barium stars (9/13), mild barium stars (3/24), strong barium stars (6/26), Tc-poor S stars (3/10) and CH stars (2/8). The high success rate for dwarf barium stars naturally results from the fact that these dwarf stars are on average closer from the sun than the giant stars.

Table 2 lists the astrometric and orbital parameters for the reliable orbits according to the criteria discussed above. The results from the different processing modes are collected in Table 2, according to the symbol given in Col. 2: H/S refers to the parameters from the Hipparcos catalogue and from the spectroscopic orbit [on that line is the semi-major axis in A.U. estimated from Eq. (13)], F refers to the processing of the IAD from FAST only, N to the IAD from NDAC only, A from the processing of the combined FAST/NDAC data set, O to the orbital parameters from the DMSA/O, and T to the parameters resulting from the TD.

Most of the retained orbits are indeed characterized by values of the order of unity, as expected. The first-risk errors are not always close to 0, but if the derived value for the semi-major axis is in good agreement with its expected value, that agreement has been considered as sufficient for retaining the orbit. The only cases where the reverse situation occurs (small but discrepant ) are the dwarf barium star HIP 60299, the mild barium star HIP 36042 and the CH star HIP 53763. Although the orbit of the latter is not well defined, it has been kept in our final list to illustrate the large uncertainty on resulting from an orbital period close to 1 yr (Sect. 4).

The F, N and A solutions for the retained orbits are also generally in good
agreement, the only exceptions being the dwarf Ba stars HIP 62409 and
HIP 116233, and the mild Ba star HIP 117607.
However, the model parameters
of these systems are highly correlated, and the
different measurement errors in the different data sets thus drive the
solution in different directions.
This statement may be expressed in a quantitative way using the
concept of *efficiency*
introduced by Eichhorn (1989) and
Pourbaix & Eichhorn (1999).
It is defined as

where are the eigenvalues of the covariance matrix of the estimated parameters,

In Table 2, the uncertainty on
has been computed
by combining the upper and lower limits on *a*_{0} and ,
thus neglecting any possible
correlation between these two quantities
(which is generally small - except for
the three systems listed above - as derived from the efficiency being close to
unity).

The orbital solutions derived in the present paper are too many to display the astrometric orbit for all cases. A few representative cases among the different subsets of Table 1 (orbital periods shorter or longer than the duration of the Hipparcos mission, small or large parallaxes...) have instead been selected and are presented in Fig. 1.

Figure 1:
The orbital arc on the plane tangent to the line of sight for some
representative orbits among those listed in
Table 2. The segments connect the computed
position on the orbit to the great circle (not represented,
perpendicular to the segment) corresponding to the
observed position (Hipparcos measurements are one-dimensional).
HIP 50805 is the only system for which the DMSA/O provides an orbital
solution from scratch; HIP 53763 has a small parallax (about 2 mas),
not very well determined since the orbital period is close to 1 yr;
only the NDAC solution is acceptable for
HIP 62409; the orbit of HIP 103546 is at limit of what can be
extracted from the IAD; HIP 105881 is an example of an incomplete, albeit well
determined, orbital arc;
HIP 116233 is one case where the NDAC and FAST solutions are
rather different |

For HIP 17296 (Tc-poor S), 31205 (strong Ba) and 56731 (strong Ba), orbital solutions are provided in the DMSA/O and were derived using spectroscopic elements from the literature. HIP 50805 (dwarf Ba) is the only case in our sample where an orbit could be derived from scratch by the Hipparcos consortia. For all these systems, the astrometric orbits derived by the methods described in Sect. 2 are in excellent agreement with the DMSA/O elements, thus providing an independent check of the validity of our procedures. Further checks are presented in Sect. 3.2.

The large number (23) of systems for which orbital solutions could be extracted from the Hipparcos data (as compared to only 4 of those already present in the DMSA/O) illustrates the great potential that still resides in the Hipparcos IAD or TD.

3.2 Check of the astrometric orbit

Several checks are possible to evaluate the accuracy of the astrometric elements derived in the present paper. First, it is possible to compare the astrometric and spectroscopic values of , the argument of periastron. In most cases, the two determinations agree within 2 (Fig. 2). However, even when the orbital period is shorter than the Hipparcos mission, the derived from the IAD is seldom as precise as the spectroscopic one.

Figure 2:
Comparison of the astrometric (ordinate) and spectroscopic (abscissa)
determinations of the argument of periastron |

In a few cases, the spectroscopic orbit is assumed to be circular. In
that case, the time *T* of passage at periastron becomes meaningless,
and is replaced by the time of the nodal
passage (or, equivalently, the time of maximum radial velocity). This
is equivalent to setting
equal to 0. Non-zero values for
would correspond to
other conventions for the origin epoch.
Among our systems with acceptable orbits, two
have circular orbits: HIP 53763 (CH star) and HIP 52271 (strong barium star).
For these systems, our fit leads to values of
significantly different
()
from 0, indicating that at the reference epoch, the star
is in fact far from the node where it was expected to be.

It is also possible to compare the astrometric value of *K*_{1} (using in
Eq. (12) the value of *a*, *i* and
from the astrometry
and *e* and *P* from the spectroscopy) with the spectroscopic value.
Figure 3 shows that, even if
is well defined, the
inclinations are generally not very accurately determined, thus leading to
uncertain values of *K*_{1}.
This unfortunate property of *i* is well illustrated
in Figs. 4 and 5.
One example where the accuracy of the astrometric value of *i* must be
questioned is the dwarf barium star HIP 105969: despite the fact that
the astrometric
ratio perfectly agrees with its estimate based on the
masses, the astrometric prediction of the semi-amplitude of the
radial-velocity variations differs by almost of factor of 2 as
compared to the actual spectroscopic value
(Table 2). The only way to resolve that discrepancy is
to assume that the orbital inclination is largely in error.

The semi-major axis
as derived from its astrophysical
estimate (Eq. 13) is compared to its astrometric value in
Fig. 6, and the two values are often consistent with each
other. Although the value of *a*_{0} is likely to be affected by a positive
bias (i.e., a positive *a*_{0} value is derived even when the data consist
of pure noise, as clearly apparent from the astrometric
values
listed in Table 1), this bias does not markedly affects
the retained solutions displayed in Fig. 6, except for
solutions with mas, which all have
.
Solutions
for larger
values are almost equally distributed around unity.

Figure 3:
Comparison of the semi-amplitude of the radial velocity curve derived from
the astrometry (using Eq. 12) and the spectroscopic value.
The three panels show the results derived from FAST, NDAC and FAST+NDAC (from
top to bottom respectively) |

Figure 5:
Correlation between the uncertainties on the inclination i and
the semi-major axis a_{0}. The symbols have the same meaning as in
Fig. 4 |

Figure 6:
Comparison of the semi-major axis
derived from the astrometry
and from Eq. (13). The upper panel displays the
results from the FAST data, the middle panel the results from the NDAC data,
and the lower panel the results from FAST and NDAC combined. The error bars
assume that M_{1}, M_{2} and P are error-free |

For the sake of completeness, we checked the astrophysical consistency of the orbit derived for the 22 systems for which TD are available. All systems but the five already accepted were rejected. In essence, this confirms that the astrometric content of the TD is basically equivalent to the IAD and that nothing new can come out from TD if IAD do not yield a reliable solution.

Figure 8:
Same as Fig. 7 for the
proper-motion modulus |

Figure 9:
Comparison of the Hipparcos parallax with that
derived when account is made of the orbital motion (present work), as a
function of the orbital period. As in Fig. 7, results
from FAST, NDAC and FAST+NDAC are presented in the upper, middle and lower
panels, respectively. Error bars include only the uncertainty on
the parallaxes derived from the
present work, and are computed according to Eq. (9) |

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