1 Introduction

The possibilities to derive stellar masses by a direct method (non model dependent) are not very numerous, and in nearly all cases involve the gravitational attractions in a system formed by two or more stars, (a notable exception to this rule is the binary pulsar PSR 1913+16, where the individual masses are determined unambiguously from the relativistic periastron shift and the gravitational redshift of the pulsar signal). When the components are close enough to exhibit a fast relative motion and if the two stars are of comparable brightness, spectroscopic measurements may yield the radial velocity of each component with respect to the centre of mass, and thus the mass ratio of the components. The difficulty in this case is to obtain the total mass from Kepler's third law, since only a function of the semi-major axis and inclination of the relative orbit can be reached by this method. Moreover, the number of objects (double-lined spectroscopic binaries) is not very large. The alternative method, using photographic plates, rests upon the astrometric analysis of the motion of the components (when the separation is larger than 1$.\!\!^{\prime\prime}$5) or of the photocentre, with respect to nearby stars. When the scale of the relative orbit is known, the previous analysis yields the proper motion, parallax and mass ratio of the system. Whatever the method, its combination with other techniques like speckle interferometry (orbital elements) or visual CCD observations (magnitude difference) is often needed to make the full analysis and derive the individual masses.

The method used in this study has been extensively described in the first paper of the present series (Martin et al. 1997), and is nothing else than a modern version of the astrometric method, with the reservation that in some cases the Hipparcos signal is tied to a point which is not the photocentre (we called it "Hippacentre"). Unlike the situation prevailing with standard astrometric binaries, this fortunate circumstance allows the direct determination of the mass fraction (the independent knowledge of the magnitude difference $\Delta m$ is no longer needed).

This third paper is a continuation of the work presented in Martin & Mignard (1998). This has been possible essentially through the access to new or previously overlooked orbital data. One of our purposes is to present all the available results, and not only the best ones (it could have been limited to the 10 best results, in good agreement with ground-based determinations), since the anomalous results may question the validity of the orbital elements, or simply reveal the true limitation of the Hipparcos sampling. As for Algol in the previous paper, an emphasis is made on a specific system, namely 12 Persei, which has been simultaneously studied by McAlister and his colleagues from a set of ground-based data (this paper, Sect. 5.2). A mass-luminosity relation is also derived from the set of reliable results, including those presented in the previous paper.

For the sake of clarity and conciseness, we will refer in the following to the first two papers of this series as "Paper I" (Martin et al. 1997) and "Paper II" (Martin & Mignard 1998).