Computing Visual Binary Orbits via MCMC Methods

Determining precise orbits for visual binary stars is fundamental for deriving stellar masses and testing evolutionary models, yet it remains challenging due to sparse, noisy astrometric data and the nonlinearity of orbital motion. This paper introduces a robust, integrated Bayesian framework for visual binary orbit determination and ephemeris prediction using a Markov Chain Monte Carlo (MCMC) methodology. Our pipeline employs a multi-stage approach: we first perform global exploration of apparent ellipse coefficients via simulated annealing, refine them with MCMC sampling, and then derive the Campbell orbital elements. A key feature is the explicit, high-precision solution of Kepler's equation within the statistical sampler, enabling consistent anomaly determination. We rigorously validate the framework on artificial orbits, demonstrating its accuracy and stability. Applied to four historical visual binaries (ADS 6554, ADS 1709, ADS 10188, and ADS 281), the method produces orbital elements in strong agreement with established literature while providing refined, probabilistic estimates of their uncertainties. Furthermore, we generate updated future ephemerides (through 2030) essential for planning high-resolution follow-up observations.