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.
@article{arxiv.1309.2868,
title = {Mass estimates for visual binaries with incomplete orbits},
author = {L. B. Lucy},
journal= {arXiv preprint arXiv:1309.2868},
year = {2015}
}
Comments
12 pages, 13 figures. Revised version accepted by Astronomy and Astrophysics