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*Astron. Astrophys. 330, 585-599 (1998)*
## 4. Raw results
### 4.1. Presentation
Significant results have been obtained for 46 systems among the 145
tested. This sample has been divided into 2 categories, called Type I
and Type II solutions, defined as,
**Type I**: the separation is large enough to allow a
separate determination of the intensity and mass ratios
and *B* with an absolute accuracy better
than 0.07. The number of unknowns in the model is seven (The five
usual astrometric parameters *l*, *b*,
, and
related to the centre of mass and the two
ratios and *B*).
**Type II**: binaries with smaller separations; the motion
observed is the photocentric orbit combined to the rectilinear motion
of the centre of mass. We only determine the scale factor
and the astrometric parameters previously
defined (six unknowns).
The solutions are presented in Tables 4 and 5 for 8 Type I and
38 Type II binaries. The full description of the columns is given
below Table 4.
**Table 4.** Astrometric binaries processing. Raw results for eight systems with a solution of first type.
**Table 5.** Astrometric binaries processing. Raw results for 38 stars with solutions of second type. For two stars (HIP 31509 and HIP 107354), results from method B () are also presented, as these stars are 'quasi' Type I objects.
When several orbits are proposed for a system, quite often two of
them differ only by a difference of degrees of
one of the angles (periastron argument) or
(position angle of the ascending node). This is
equivalent to invert the choice of the primary between the two
components. In this case we only kept one representative orbit and
systematically tested the alternate possibility. Formally, this
transformation implies that one gets and
instead of and *B*.
Thus, when the two ratios are combined to form the scale of the
photocentric orbit, we get instead of
. In several instances it was difficult to make
a choice between the two solutions, as their quality were almost
identical, and then we decide to retain the solution based on the
published (not rotated) orbit. When the system was sufficiently well
known to constrain the sign of , the exchange of
the components, if necessary, is indicated in the Tables 4 - 5 by
the minus sign '-' in the third column. In particular this is the case
for Algol AB-C: the sign '-' informs that one of the two angles
or must be increased by
180 degrees to make the orbit consistent with the Hipparcos
observations.
### 4.2. Discussion
As mentioned above, the quantity () represents
the scale factor between the photocentric orbit and the relative
orbit. Practically, if the semi-major axis *a* found in the
literature is wrong by a factor , we get,
instead of , a quantity ,
so that the product is constant. This
phenomenon affects all the Type II solutions, where the hippacentre
and the photocentre are alike. A quantification of this effect can be
achieved from the propagation of the standard error of the semi-major
axis, to :
where *K* and are respectively the
scale factor (i.e. the biased estimate of ) and
its standard error, both given by the processing, and assimilated to
and its standard deviation in the Tables 4
and 5.
A quantification of this effect has been made by taking the set of
the standard deviations of the semi-major axes of the 46 orbits, and
calculating the ratio in each case, with the
previous expression. The information on has
been found for only half the systems, giving a median value of the
*r* distribution of only . The ratio
exceeds for two objects: HIP 87895
() and HIP 89937 ().
However, this study may be biased: the orbits for which the standard
errors are published are probably the best ones. Moreover, most of the
orbits among the 23 were computed very recently from speckle
interferometry, with relative errors on the semi-major axis ranging
from to .
© European Southern Observatory (ESO) 1998
Online publication: January 16, 1998
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