Determination of Orbital Parameters of Binary Star Systems Using the MCMC Method
Vaidman N.L. Nurmakhametova S.T. Miroshnichenko A.S. Khokhlov S.A. Agishev A.T. Khokhlov A.A. Ashimov Y.K. Yermekbayev B.S.
October 2025Multidisciplinary Digital Publishing Institute (MDPI)
Galaxies
2025#13Issue 5
We present new spectroscopic orbits for the bright binaries Mizar B, 3 Pup, (Formula presented.) Gem, 2 Lac, and (Formula presented.) Aql. Our analysis is based on medium-resolution ((Formula presented.) 12,000) échelle spectra obtained with the 0.81-m telescope and fiber-fed eShel spectrograph of the Three College Observatory (Greensboro, NC, USA) between 2015 and 2024. Orbital elements were inferred with an affine-invariant Markov-chain Monte-Carlo sampler; convergence was verified through the integrated autocorrelation time and the Gelman–Rubin statistic. Errors quote the 16th–84th-percentile credible intervals. Compared with previously published orbital solutions for the studied stars, our method improves the root-mean-square residuals by 25–50% and bring the 1 (Formula presented.) uncertainties on the radial velocity (RV) semi-amplitudes down to 0.02–0.15 km (Formula presented.). These gains translate into markedly tighter mass functions and systemic RVs, providing a robust dynamical baseline for future interferometric and photometric studies. A complete Python analysis pipeline is openly available in a GitHub repository, ensuring full reproducibility. The results demonstrate that a Bayesian RV analysis with well-motivated priors and rigorous convergence checks yields orbital parameters that are both more precise and more reproducible than previous determinations, while offering fully transparent uncertainty budgets.
binary system , MCMC , orbital parameters , radial velocity
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Faculty of Physics and Technology, Al-Farabi Kazakh National University, Al-Farabi Ave., 71, Almaty, 050040, Kazakhstan
Fesenkov Astrophysical Institute, Observatory, 23, Almaty, 050020, Kazakhstan
Department of Physics and Astronomy, University of North Carolina—Greensboro, Greensboro, 27402, NC, United States
Faculty of Physics and Technology
Fesenkov Astrophysical Institute
Department of Physics and Astronomy
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