Searching for Chaos in the Mira Variable Star U Cygni (Poster abstract)

Volume 37 number 2 (2009)

Amanda Tougas

Matthew M. Beaky

Abstract

(Abstract only) Mira variable stars are pulsating red giant stars whose light curves often exhibit seemingly random variations in amplitude and period from cycle to cycle. One possibility is that the long-term variations in Mira variable light curves are due to a simple linear combination of two or more pulsation modes. For some pulsating red giant stars, however, a multi-periodic solution has been shown to be insufficient, and a nonlinear analysis is required for complete description of the light curve behavior. The application of chaos theory to the light curves of pulsating variable stars remains relatively unexplored, however. In this project we investigated U Cygni, a pulsating Mira-type variable star with a period of approximately 463 days. Over 100 years of U Cyg visual photometric data were obtained from the American Association of Variable Star Observers. A Fourier analysis was conducted on the data and an O–C diagram was created to explore the limitations of standard linear time series analysis. Next, a nonlinear analysis using the TISEAN software package was conducted to search for chaotic behavior in the light curve of U Cyg. From the nonlinear analysis, we obtained phase space projections, determined the maximum Lyapunov exponent, and created a synthetic light curve to represent the U Cyg data. The results provide evidence for the presence of chaotic behavior in the light curve of U Cyg.