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Computing visual binary orbits via MCMC methods
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DOI：10.1007/s10686-026-10066-8.png)
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Abstract
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Determining precise orbits for visual binary stars is fundamental for deriving stellar masses and testing stellar 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 ephemerides 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 numerical solution of Kepler’s equation within the statistical sampler at every iteration, ensuring strict self-consistent Keplerian dynamics throughout the chain and achieving Newton-Raphson-level precision with absolute errors of ~ 10⁻¹¹. The framework is validated against ADS 9982 (WDS J16160 + 0721, STF 2026 AB), a Grade 3 short-arc system whose observed arc covers only ~ 40° of its full revolution, precisely the regime where classical conic-section fitting methods fail. Our derived orbital elements are in close agreement with the Sixth Catalog solution across all seven elements, with a period of P = 408.765 year and eccentricity e = 0.8135, demonstrating that the MCMC framework succeeds where the classical Kowalsky method produces a non-elliptic conic fit. Applied subsequently to four historical visual binaries with well-covered orbits, ADS 6554, ADS 1709, ADS 10,188, and ADS 281, the method produces orbital elements in strong quantitative agreement with established literature while providing refined, probabilistic estimates of their uncertainties. Updated ephemerides through 2030 are generated for all four systems, providing statistically rigorous, credible predictive intervals directly applicable to observational planning with current high-resolution facilities.
Keywords:
Visual binaries
MCMC method
Kepler’s equation
Orbital elements
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2.2
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112
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ShareSaveOrbits for 18 Visual Binaries and Two Double-line Spectroscopic Binaries Observed with HRCAM on the CTIO SOAR 4m Telescope, Using a New Bayesian Orbit Code Based on Markov Chain Monte Carlo.png)
ASTRONOMICAL JOURNAL
OAAI
ASTRONOMICAL JOURNALIF5.1
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