Chaos in hydrodynamic BL Herculis models

Abstract

We present non-linear, convective, BL Her-type hydrodynamic models that show complex variability characteristic for deterministic chaos. The bifurcation diagram reveals a rich structure, with many phenomena detected for the first time in hydrodynamic models of pulsating stars. The phenomena include not only period doubling cascades en route to chaos (detected in earlier studies) but also periodic windows within chaotic band, type-I and type-III intermittent behaviour, interior crisis bifurcation and others. Such phenomena are known in many textbook chaotic systems, from the simplest discrete logistic map, to more complex systems like Lorenz equations. We discuss the physical relevance of our models. Although except of period doubling such phenomena were not detected in any BL Her star, chaotic variability was claimed in several higher luminosity siblings of BL Her stars - RV Tau variables, and also in longer-period, luminous irregular pulsators. Our models may help to understand these poorly studied stars. Particularly interesting are periodic windows which are intrinsic property of chaotic systems and are not necessarily caused by resonances between pulsation modes, as sometimes claimed in the literature.

arXiv comment17 pages, 21 figures, accepted for publication in MNRAS. Two animations available as ancillary files

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• Luminosities and infrared excess in Type II and anomalous Cepheids in the Large and Small Magellanic Clouds
• A theoretical framework of BL Her stars. I. Effect of metallicity and convection parameters on period-luminosity and period-radius relations
• Diversity of dynamical phenomena in type II Cepheids of the OGLE collection
• 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
• A theoretical framework for BL Her stars III. A case study: Robust light curve optimisation in the LMC
• Type II and anomalous Cepheids in the Kepler K2 mission
• The light curve model fitting of LMC Cepheids: MESA-RSP versus Stellingwerf's code predictions