Improving the moment approach for astrometric binaries: possible application to Cygnus X1
Abstract
A moment approach for orbital determinations of astrometric binaries from astrometric observations alone has been recently studied for a low signaltonoise ratio (Iwama et al. 2013, PASJ, 65, 2). Through avoiding a direct use of the timeconsuming 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 value and the standard deviation are also evaluated. For a semimajor 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 approach works better than the previous one for orbital determinations when one has a large number of observed points. The present approach is thus applicable to Cyg X1.
 Publication:

Publications of the Astronomical Society of Japan
 Pub Date:
 October 2014
 DOI:
 10.1093/pasj/psu071
 arXiv:
 arXiv:1407.3913
 Bibcode:
 2014PASJ...66...97Y
 Keywords:

 astrometry;
 binaries: close;
 celestial mechanics;
 methods: analytical;
 Astrophysics  High Energy Astrophysical Phenomena;
 General Relativity and Quantum Cosmology
 EPrint:
 15 pages, 3 figures, 4 table