Binary orbits from combined astrometric and spectroscopic data

Abstract

An efficient Bayesian technique for estimation problems in fundamental stellar astronomy is tested on simulated data for a binary observed both astrometrically and spectroscopically. Posterior distributions are computed for the components' masses and for the binary's parallax. One thousand independent repetitions of the simulation demonstrate that the 1- and 2-$\sigma$ credibility intervals for these fundamental quantities have close to the correct coverage fractions. In addition, the simulations allow the investigation of the statistical properties of a Bayesian goodness-of-fit criterion and of the corresponding p-value. The criterion has closely similar properties to the traditional chi^{2} test for minimum-chi^{2} solutions.

9 pages, 3 figures. Typos corrected. Appendix C.1 added. Generalisation for correlated measurement errors

References in corpus (6)

• EXOFAST: A fast exoplanetary fitting suite in IDL
• State of the Field: Extreme Precision Radial Velocities
• Efficient fitting of multiplanet Keplerian models to radial velocity and astrometry data
• Frequentist tests for Bayesian models
• Frequentist confidence intervals for orbits
• A study of non-Keplerian velocities in observations of spectroscopic binary stars

Cited by in corpus (4)

• Weighing the Darkness: Astrometric Mass Measurement of Hidden Stellar Companions using Gaia
• Bayes-based orbital elements estimation in triple hierarchical stellar systems
• Bayesian model checking: A comparison of tests
• Bayesian inference in single-line spectroscopic binaries with a visual orbit