Mass estimates for visual binaries with incomplete orbits

TL;DR

This paper develops Bayesian methods to estimate the total mass of visual binaries with incomplete orbits, simplifying the computation by reducing the parameter space and testing the approach on synthetic data.

Contribution

Introduces a Bayesian framework using Thiele-Innes elements to efficiently estimate binary star masses from incomplete orbital data.

Findings

Posterior mean of mass estimator is unbiased with >40% orbit coverage.

Reduces computational complexity from 7-D to 3-D parameter space.

Method validated on synthetic observational data.

Abstract

The problem of estimating the total mass of a visual binary when its orbit is incomplete is treated with Bayesian methods. The posterior mean of a mass estimator is approximated by a triple integral over orbital period, time of periastron and orbital eccentricity. This reduction to 3-D from the 7-D space defined by the conventional Campbell parameters is achieved by adopting the Thiele-Innes elements and exploiting the linearity with respect to the four Thiele-Innes constants. The formalism is tested on synthetic observational data covering a variable fraction of a model binary's orbit. The posterior mean of the mass estimator is numerically found to be unbiased when the data cover > 40% of the orbit.