Low-dimensional chaos in RR Lyrae models

Abstract

The recent precise photometric observations and successes of the modelling efforts transformed our picture of the pulsation of RR Lyrae stars. The discovery of additional frequencies and the period doubling phenomenon revealed that a significant interaction may occur between pulsational modes. The signs of irregularities were detected both in observed light curves and hydrodynamic calculations. In this paper we present the analysis of four peculiar hydrodynamic model solutions. All four solutions were found to be chaotic. The fractal (Lyapunov) dimensions of their attractors were calculated to be ~2.2. We also investigated possible resonances between the fundamental mode and the first overtone in the dynamical neighbourhood of these models. The most important is the 6:8 resonance that was also detected in the Kepler observations of RR Lyrae itself. These results reveal that the investigation of chaotic models is important in discovering and understanding resonances in RR Lyrae stars.

7 pages, 8 figures, accepted for publication in MNRAS

References in corpus (2)

• Automated Nonlinear Stellar Pulsation Calculations: Applications to RR Lyrae stars. The Slope of the Fundamental Blue Edge and the First RRd Model Survey
• Period doubling and Blazhko modulation in BL Herculis hydrodynamic models

Cited by in corpus (14)

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• Revisiting CoRoT RR Lyrae stars: detection of period doubling and temporal variation of additional frequencies
• V473 Lyrae, a unique second-overtone Cepheid with two modulation cycles
• Periodicities of the RV Tau-type pulsating star DF Cygni: a combination of Kepler data with ground-based observations
• Chaos in hydrodynamic BL Herculis models
• Revisiting the Kepler non-Blazhko RR Lyrae sample: Cycle-to-cyle variations and additional modes
• Chaotic dynamics in the pulsation of DF Cygni, as observed by Kepler
• Nonlinear dynamical analysis of the Blazhko effect with the Kepler space telescope: the case of V783 Cyg
• The additional-mode garden of RR Lyrae stars
• The space photometry revolution and our understanding of RR Lyrae stars
• Blazhko effect in Cepheids and RR Lyrae stars
• Fractal Measures and Nonlinear Dynamics of Overcontact Binaries
• Order and chaos in hydrodynamic BL Her models