Improving the Moment Approach for Astrometric Binaries: Possible Application to Cygnus X-1

Abstract

A moment approach for orbit determinations of astrometric binaries from astrometric observations alone has been recently studied for a low signal-to-noise ratio (Iwama et al. 2013, PASJ, 65, 2). With avoiding a direct use of the time-consuming Kepler equation, temporal information is taken into account to increase the accuracy of statistical moments. As numerical tests, 100 realizations are done and the mean and the standard deviation are also evaluated. For a semi-major axis, the difference between the mean of the recovered values and the true value decreases to less than a tenth in the case of $10000$ observed points. Therefore, the present moment approach works better than the previous one for the orbit determinations when one has a number of the observed points. The present approach is thus applicable to Cyg X-1.

arXiv comment15 pages, 3 figures, 4 table; accepted by PASJ

References in corpus (5)

• The gamma-ray binary LS 5039: mass and orbit constraints from MOST observations
• Inversion formula for determining parameters of an astrometric binary
• Simplified solution to determination of a binary orbit
• Note on Inversion Formula to Determine Binary Elements by Astrometry
• Moment Approach for Determining the Orbital Elements of an Astrometric Binary with Low Signal-to-noise Ratio

Cited by in corpus (1)

• Uncovering the identities of compact objects in high-mass X-ray binaries and gamma-ray binaries by astrometric measurements