The Chaotic Long-term X-ray Variability of 4U 1705-44.

The low-mass X-ray binary 4U1705-44 exhibits dramatic long-term X-ray time variability with a timescale of several hundred days. The All-Sky Monitor () aboard the () and the Japanese () aboard the International Space Station together have continuously observed the source from December 1995 through May 2014. The combined data provide a continuous time series over fifty times the length of the timescale of interest. Topological analysis can help us identify fingerprints in the phase-space of a system unique to its equations of motion. The Birman-Williams theorem postulates that if such fingerprints are the same between two systems, then their equations of motion must be closely related. The phase-space embedding of the source light curve shows a strong resemblance to the double-welled nonlinear Duffing oscillator. We explore a range of parameters for which the Duffing oscillator closely mirrors the time evolution of 4U1705-44. We extract low period, unstable periodic orbits from the 4U1705-44 and Duffing time series and compare their topological information. The Duffing and 4U1705-44 topological properties are identical, providing strong evidence that they share the same underlying template. This suggests that we can look to the Duffing equation to help guide the development of a physical model to describe the long-term X-ray variability of this and other similarly behaved X-ray binary systems.