Mass ratio of single-line spectroscopic binaries with visual orbits using Bayesian inference and suitable priors

Abstract

We present orbital elements for twenty-two single-line binaries, nine of them studied for the first time, determined from a joint spectroscopic and astrometric solution. The astrometry is based on interferometric measurements obtained with the HRCam Speckle camera on the SOAR 4.1m telescope at Cerro Pachon, Chile, supplemented with historical data. The spectroscopic observations were secured using Echelle spectrographs (FEROS, FIDEOS and HARPS) at La Silla, Chile. A comparison of our orbital elements and systemic velocities with previous studies, including Gaia radial velocities, show the robustness of our estimations. By adopting suitable priors of the trigonometric parallax and spectral type of the primary component, and using a Bayesian inference methodology developed by our group, we were able to estimate mass ratios for these binaries. Combining the present results with a previous study of other single-line from our team we present a pseudo mass-to-luminosity relationship based on twenty three systems (45 stars) in the mass range 0.6 <= M_Sun <= 2.5. We find a reasonable correspondence with a fiducial mass-to-luminosity relationship. We conclude that our methodology does allow to derive tentative mass ratios for this type of binaries.