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

TL;DR

This paper enhances a statistical moment method for determining the orbits of astrometric binaries, improving accuracy especially with large datasets, and demonstrates its applicability to Cygnus X-1.

Contribution

The paper introduces an improved moment approach that avoids direct Kepler equation use, increasing orbit determination accuracy for low signal-to-noise data with many observations.

Findings

The method achieves less than 10% error in semi-major axis estimation with 10,000 observations.

Numerical tests show the approach outperforms previous methods in accuracy.

Applicability to Cygnus X-1 is demonstrated.

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.