Fractal Measures and Nonlinear Dynamics of Overcontact Binaries

Abstract

Overcontact binary stars are systems of two stars where the component stars are in contact with each other. This implies that they share a common envelope of gas. In this work we seek signatures of nonlinearity and chaos in these stars by using time series analysis techniques. We use three main techniques, namely the correlation dimension,f (α) spectrum and the bicoherence. The former two are calculated from the reconstructed dynamics, while the latter is calculated from the Fourier transforms of the time series of intensity variations(light curves) of these stars. Our dataset consists of data from 463 overcontact binary stars in the Kepler field of view [1]. Our analysis indicates nonlinearity and signatures of chaos in almost all the light curves. We also explore whether the underlying nonlinear properties of the stars are related to their physical properties like fill-out-factor, a measure of the extend of contact between the components of an overcontact binary system . We observe that significant correlations exist between the fill out factor and the nonlinear quantifiers. This correlation is more pronounced in specific subcategories constructed based on the mass ratios and effective temperatures of the binaries. The correlations observed can be indicative of variations in the nonlinear properties of the star as it ages. We believe that this study relating nonlinear and astrophysical properties of binary stars is the first of its kind and is an important starting point for such studies in other astrophysical objects displaying nonlinear dynamical behaviour.

arXiv comment17 pages, 12 figures, submitted to Communications in Nonlinear Science and Numerical Simulation

References in corpus (23)

• Practical implementation of nonlinear time series methods: The TISEAN package
• Kepler Eclipsing Binary Stars. I. Catalog and Principal Characterization of 1879 Eclipsing Binaries in the First Data Release
• Kepler Eclipsing Binary Stars. VII. The Catalog of Eclipsing Binaries Found in the Entire Kepler Data-Set
• Strange Nonchaotic Attractors
• Eclipse Timing Variation Analyses of Eccentric Binaries with Close Tertiaries in the Kepler field
• Strange nonchaotic stars
• Angular momentum and mass evolution of contact binaries
• Kepler photometry of RRc stars: peculiar double-mode pulsations and period doubling
• A non subjective approach to the GP algorithm for analysing noisy time series
• Prediction of a red nova outburst in KIC 9832227
• Chaos and dynamical trends in barred galaxies: bridging the gap between N-body simulations and time-dependent analytical models
• Period-doubling events in the light curve of R Cygni: evidence for chaotic behaviour
• Computing the multifractal spectrum from time series: An algorithmic approach
• Application of chaos indicators in the study of dynamics of S-type extrasolar planets in stellar binaries
• First observations of W Virginis stars with K2: detection of period doubling
• Low-dimensional chaos in RR Lyrae models
• The Correlation Dimension of Young Stars in Dwarf Galaxies
• Recurrence network measures for hypothesis testing using surrogate data: application to black hole light curves
• Chaotic dynamics in the pulsation of DF Cygni, as observed by Kepler
• Effect of data gaps on correlation dimension computed from light curves of variable stars
• Detecting Dynamical States from Noisy Time Series using Bicoherence
• Order and chaos in a galactic model with a strong nuclear bar
• Nonlinearity in Data with Gaps: Application to Ecological and Meteorological Datasets