Accuracy of binary star separations estimated from interferometric data

Abstract

Errors in binary star separations estimated by model-fitting visibilities obtained from a two-element interferometer are discussed. It is shown that the rms error on any component of a binary star's separation in the sky is linearly proportional to the rms noise in the observed visibilities, and linear proportional to an effective beamwidth for the observation. It varies inversely with the peak-to-peak variation of the visibility of the binary that depends on the ratio of the intensities of the two stars and inversely as the square root of the total number of observed visibilities. It is also shown that, in principle, any visibility data set can be consistent with more than one binary separation and orientation. This leads to alternative solutions for the binary separation vector. The alternative solutions are equally spaced on a straight line in binary separation space. This line, when projected onto the equatorial plane, is parallel to the projection of the physical baseline onto the same plane.