Determination of Orbital Parameters of Binary Star Systems Using the MCMC Method

We present new spectroscopic orbits for the bright binaries Mizar B, 3 Pup, ν Gem, 2 Lac, and ϕ Aql. Our analysis is based on medium-resolution (R≈ 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 1σ uncertainties on the radial velocity (RV) semi-amplitudes down to 0.02–0.15 km s−1. 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.