Low-dimensional chaos in RR Lyrae models

TL;DR

This paper demonstrates that certain hydrodynamic models of RR Lyrae stars exhibit low-dimensional chaos, revealing complex pulsational behaviors and resonances that enhance understanding of observed irregularities.

Contribution

It presents the first analysis of chaotic hydrodynamic models of RR Lyrae stars, linking chaos with observed resonances and irregularities in stellar pulsations.

Findings

Hydrodynamic models of RR Lyrae stars can be chaotic with fractal dimensions ~2.2.

A 6:8 resonance between pulsation modes was identified, matching Kepler observations.

Chaotic models help explain irregularities and mode interactions in RR Lyrae stars.

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.