Colour-dependent accurate modelling of dynamical parallaxes and masses of visual binaries

Abstract

Context. Two fundamental characteristics of binary systems are the masses of their components and their distance to the Earth. In this way, the dynamical parallax is an accurate and very helpful tool. Nevertheless, there has been some concern with regard to the use of a unique linear mass–luminosity relation (MLR) for the entire main sequence (MS). Aims. This article describes the accurate computation of both dynamical parallaxes and individual masses of visual binaries. The main aim is to formulate a model which would be suitable for binary systems attending to the exact locations of the components on the MS in the HR diagram. Methods. An analytical model was developed which allows calculation of dynamical parallaxes and individual masses using a non-linear MLR valid for the entire MS. This up-to-date MLR is given by a polynomial of degree 20. In contrast to previous approaches, this model can be applied even in the case of components with unequal masses, that is, with an arbitrarily large difference of magnitudes between them. On the other hand, considering the fundamental equation of the theory that forms the basis of the model, we propose to estimate uncertainties in parallax and masses using Monte Carlo simulations. Results. The model was validated by means of numerical tests using a synthetic sample comprising 103 systems. The results are much more accurate than those for previous models reported in the literature for deriving dynamical parallaxes and masses. Furthermore, we present dynamical parallaxes and individual masses for the 19 double-lined spectro-interferometric systems with definitive visual orbits and compare the former with the orbital parallaxes as well as with those measured by HIPPARCOS and Gaia. It is worth mentioning that the latter can only be a reliable source when the orbital motion is taken into account. Thus, at present, many Gaia DR2 parallaxes of binaries are biased. Conclusions. Our model, composed of an exact analytical theory, along with a non-linear MLR, guarantees high accuracy even in cases where the components are of unequal mass.