Orbits for eighteen 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

TL;DR

This paper introduces a Bayesian orbit-fitting method using Markov Chain Monte Carlo for visual and spectroscopic binaries, providing precise orbital parameters and component masses, and enhancing the efficiency of orbital analysis.

Contribution

The paper develops a new MCMC-based Bayesian algorithm for orbit determination, enabling robust uncertainty estimation and dimensionality reduction in binary star analysis.

Findings

Orbital elements for 18 binaries, including 5 new orbits.

Precise component masses with ~0.1 MSun uncertainty for spectroscopic binaries.

Self-consistent orbital parallax consistent with trigonometric measurements.

Abstract

We present orbital elements and mass sums for eighteen visual binary stars of spectral types B to K (five of which are new orbits) with periods ranging from 20 to more than 500 yr. For two double-line spectroscopic binaries with no previous orbits, the individual component masses, using combined astrometric and radial velocity data, have a formal uncertainty of ~0.1 MSun. Adopting published photometry, and trigonometric parallaxes, plus our own measurements, we place these objects on an H-R diagram, and discuss their evolutionary status. These objects are part of a survey to characterize the binary population of stars in the Southern Hemisphere, using the SOAR 4m telescope+HRCAM at CTIO. Orbital elements are computed using a newly developed Markov Chain Monte Carlo algorithm that delivers maximum likelihood estimates of the parameters, as well as posterior probability density functions that allow us to evaluate the uncertainty of our derived parameters in a robust way. For spectroscopic binaries, using our approach, it is possible to derive a self-consistent parallax for the system from the combined astrometric plus radial velocity data ("orbital parallax"), which compares well with the trigonometric parallaxes. We also present a mathematical formalism that allows a dimensionality reduction of the feature space from seven to three search parameters (or from ten to seven dimensions - including parallax - in the case of spectroscopic binaries with astrometric data), which makes it possible to explore a smaller number of parameters in each case, improving the computational efficiency of our Markov Chain Monte Carlo code.