A Method of Estimating the Orbit of a Binary-Star System from Extracted Reflected Signals

Received signals from a binary-star system include signals reflected by the companion star. The time delay of reflected signals is related to the position and velocity of the companion star, so that the reflected signals after being extracted can be used to estimate the orbit of the binary-star system. In principle reflected signals can be extracted from the Auto-Correlation Function (ACF) of a received-signal sequence. However, a straightforward extraction is out of reach because of the relative motion within a binary-star system. In this paper we propose a method based on mapping the received signals in the time domain to those in a time-delay domain. Reflected signals can be extracted by calculating cross-correlation functions between raw received signals and signals in the time-delay domain after the mapping. We search for the peak value of cross-correlation coefficients within the space of parameters describing the binary-system orbit. The peak value is related to the values of the orbital elements. This allows finding the orbital-parameter values of a binary-star system. We have successfully tested the method through MATLAB simulations. Our simulations are for an X-ray binary system with an edge-on orbital plane, X-ray binary systems are usually rather luminous, which makes our method more easily applicable. There are 4 parameters needed to describe the elliptical-orbit motion of an X-ray binary system. These are the semi-axis, the eccentricity, the area swept per unit time by the line section from the centroid to the companion, and the initial polar angle of the companion. We finally discuss the influence of the reflection coefficient on the effectiveness of the method. We expect that our method is more effective for X-ray binary systems whose accretion processes are via Roche-lobe overflows than for other cases. This is based on some simple estimates and a case study of the X-ray binary system GRS1915+105.