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

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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,

  1. Type I: the separation is large enough to allow a separate determination of the intensity and mass ratios [FORMULA] 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, [FORMULA], [FORMULA] and [FORMULA] related to the centre of mass and the two ratios [FORMULA] and B).
  2. 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 [FORMULA] 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 ([FORMULA]) 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 [FORMULA] degrees of one of the angles [FORMULA] (periastron argument) or [FORMULA] (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 [FORMULA] and [FORMULA] instead of [FORMULA] and B. Thus, when the two ratios are combined to form the scale of the photocentric orbit, we get [FORMULA] instead of [FORMULA]. 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 [FORMULA], 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 [FORMULA] or [FORMULA] must be increased by 180 degrees to make the orbit consistent with the Hipparcos observations.

4.2. Discussion

As mentioned above, the quantity ([FORMULA]) 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 [FORMULA], we get, instead of [FORMULA], a quantity [FORMULA], so that the product [FORMULA] 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, [FORMULA] to [FORMULA]:


where K and [FORMULA] are respectively the scale factor (i.e. the biased estimate of [FORMULA]) and its standard error, both given by the processing, and assimilated to [FORMULA] 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 [FORMULA] in each case, with the previous expression. The information on [FORMULA] has been found for only half the systems, giving a median value of the r distribution of only [FORMULA]. The ratio exceeds [FORMULA] for two objects: HIP 87895 ([FORMULA]) and HIP 89937 ([FORMULA]). 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 [FORMULA] to [FORMULA].

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© European Southern Observatory (ESO) 1998

Online publication: January 16, 1998