Investigating the Long-term Variability of 4U1705-44; Evidence for an Underlying Nonlinear Double-Welled Oscillator
Abstract
The bright low-mass X-ray binary 4U1705-44 exhibits long-term semi-periodic variability with a timescale of several hundred days. The All-Sky Monitor (ASM) aboard the Rossi X-ray Timing Explorer (RXTE) and the Japanese X-ray All-Sky Monitor (MAXI) aboard the International Space Station together have continuously observed the source from December 1995 through the present. The combined ASM-MAXI data provides a continuous time series over fifty times the length of the timescale of interest. The phase space embedding of the flux versus its first derivative shows a strong resemblance to a double-welled nonlinear oscillator. When comparing our time series against well-known nonlinear oscillators, we find that 4U1705-44 exhibits behavior akin to the Duffing oscillator. Topological analysis can help us identify ‘fingerprints’ in the phase space of a system unique to its equations of motion. If such ‘fingerprints’ are the same between two systems, then their equations of motion must be closely related. We therefore found a range of parameters for which the Duffing oscillator closely follows the time evolution of 4U1705-44 and from this range chose 6 different numerical Duffing time series. We can extract low-period, unstable periodic orbits from both the 4U1705-44 and numerical Duffing time series and compare their topological information in phase space, such as their relative rotation rates. We argue that the associated period-1 orbit in 4U1705-44 has a period between 130 and 170 days. The driving periods of our 6 numerical time series correspond to 140 to 175 days. Assigning a logical sequence name to each orbit, the relative rotation rates can be compiled into a unique ‘intertwining’ matrix. The numerical Duffing time series and the 4U1705-44 intertwining matrices are identical, which provides strong evidence that they share the same underlying template. The implications of this equivalence suggests that we can look to the Duffing equation to describe the X-ray binary’s variability.
- Publication:
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AAS/High Energy Astrophysics Division #15
- Pub Date:
- April 2016
- Bibcode:
- 2016HEAD...1512032P