Binary orbits from combined astrometric and spectroscopic data

TL;DR

This paper introduces a Bayesian method for estimating stellar binary parameters using combined astrometric and spectroscopic data, validated through simulations that confirm accurate uncertainty coverage and statistical properties.

Contribution

The paper presents a novel Bayesian approach for binary star parameter estimation from combined data, demonstrating reliable uncertainty coverage and statistical validation.

Findings

Credibility intervals have correct coverage fractions.

Bayesian goodness-of-fit criterion behaves like chi-squared test.

Method validated with 1000 simulation repetitions.

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.