Mass estimates for visual binaries with incomplete orbits

摘要

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, orbital eccentricity and time of periastron. This reduction to 3D from the 7D 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.