5 Masses

The test presented in Sect. 2.1.5 (Eq. 13) to evaluate the astrophysical relevance of the orbital solution on the basis of $a_0/\varpi$ is in essence based on an a priori knowledge of the masses, since Eq. (13) may in fact be rewritten as

$$Q =\frac{M_2^3}{(M_1 + M_2)^2} =\frac{(a_0/\varpi)^3}{P^2}.$$

The orbital solutions that appear to be statistically significant on the basis of the F-test in almost all cases turned out to have a semi-major axis $a_0/\varpi$ consistent with its expected value based on the estimated masses, the dwarf barium star HIP 60299 being however a notable exception. This agreement is well illustrated in Fig. 6.

Therefore, the present analysis does not add much to our previous knowledge of the masses, especially since the astrometric orbit only allows to eliminate i from the mass function but does not give access to the individual masses.

It was originally hoped that the present astrometric results might be used to test the hypothesis which played a central role in the statistical analysis of the mass functions of CPRS (Jorissen et al. 1998), namely that their Q distributions are quite peaked, because they host a white dwarf companion. However, the error bar on $a_0/\varpi$ (and hence on Q) is too large, even for the best determined barium-dwarf orbits (Table 2), to be able to draw a meaningful Q-distribution from the astrometric orbits.