3 Main features of the processing

The practical implementation of the processing is described in Paper I, Sect. 4.2 and will not be repeated here. The important points are simply summarized below.

The general astrometric processing of the observations carried out by Hipparcos produced for each of the $118\,300$ program stars, the five astrometric parameters representing the position, the parallax and the proper motion. When the program star was single, the previous quantities were associated with the centre of light of the star, that is to say its astrometric direction. In the case of a double star with or without detectable orbital motion, each one-dimensional observation along the scan direction was linked to a point specific to the Hipparcos detection system which was closely related to the photocentre of the pair, but not always identical. The term Hippacentre was coined to convey this idea. For very close pairs, the Hippacentre and the photocentre could not be distinguished by Hipparcos.

For orbital astrometric binaries, the absolute motion of the photocentre F referred to the barycentre G, is related to the relative orbit $\boldmath\rho$ by,

$$\vec{GF} = \left(\beta - B\right)\,\hbox{$\boldmath\rho$}$$ (1)

where $\beta={I_2 \over{ I_1+ I_2}}$ and $B={ M_2 \over{ M_1+M_2}}$ are the relative intensity and mass of the secondary component. A more general expression is given in Paper I.

  

Table 5: Spectral types and Johnson-Morgan's colour indices of the components of 13 binaries. The last column indicates the type of transformation^* to be made in order to get the Cousin's (V-I) index (see Sect. 5.2 and Fig. 4 in Paper II)

^* Not all the listed systems need this transformation; it depends on the origin of $\Delta m$ (see Tables 7-8).

The processing consists of extending the standard Hipparcos astrometric treatment by adding to the usual five astrometric unknowns (l, b, $\pi$, $\mu_l$ and $\mu_b$) related to the centre of mass, the two unknowns $\beta$and B or simply the combination $\beta-B$ for the closest pairs. The full process goes by successive iterations, starting with reference values $\rm \beta_r$ and $B\rm _r$ of the intensity and mass fractions, until a satisfactory convergence is reached. When several orbits were competing, each of them was tested individually. In each case the reversed orbit was also systematically checked (exchange of the components on the celestial sphere), allowing us to detect an eventual 180 degrees error in the ascending node's position $\Omega$ or in the argument of periastron $\omega$.

In addition to the position and proper motion, the output includes the parallaxes, which can be slightly different from the Hipparcos published values, because our model accounts for the photocentric displacement. In general the effect is very small and within the error bar. The results of this processing are presented in Table 6.

  

Table 6: Astrometric binaries processing: raw results for 22 systems. See the orbit's reference in Tables 3-4

orient.: The orientation is that of the published orbit (+) or has been reversed after examination of the residuals (-).
$N\rm _i$, $N\rm _p$: Number of iterations and number of unknowns in the model.
$\beta-B$, B: the two "physical" solutions of the reduction followed by the corresponding standard errors.
$(\beta - B)\rm _r$, $B\rm _r$: reference values used to start the algorithm (see Table 9).