In binary stellar systems, the masses of their individual components can be directly calculated from the orbital parameters through Kepler's laws using astrometric and spectroscopic observations.
Mass is the most critical parameter that determines the structure and evolution of stars.
This novel analysis provides a better understanding of the effect of the different sources of information on the shape and uncertainty in the orbit and radial velocity curve. Our sample-based methodology allows us also to study the impact of different posterior distributions in the corresponding observations space.
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As a proof of concept, the proposed methodology is applied to 12 single-line spectroscopic binaries with astrometric data that lacked a joint astrometric–spectroscopic solution, for which we provide full orbital elements. Our results show that the system's mass ratio can be estimated with an uncertainty smaller than 10% using our approach. Our methodology is tested by analyzing the posterior distributions of well-studied double-line spectroscopic binaries treated as single-line binaries by omitting the radial velocity data of the secondary object. This scheme allows us to directly incorporate prior information about the system-in the form of a trigonometric parallax, and an estimation of the mass of the primary component from its spectral type-to constrain the range of solutions, and to estimate orbital parameters that cannot be usually determined (e.g., the individual component masses), due to the lack of observations or imprecise measurements. Our approach is designed to provide a precise and efficient estimation of the joint posterior distribution of the orbital parameters in the presence of partial and heterogeneous observations. We present a Bayesian inference methodology for the estimation of orbital parameters on single-line spectroscopic binaries with astrometric data, based on the No-U-Turn sampler Markov chain Monte Carlo algorithm.