Detection of chaos in RR Lyrae models

TL;DR

This paper demonstrates the presence of chaotic dynamics in RR Lyrae star models using global flow reconstruction, revealing a fractal attractor dimension of about 2.2, and discusses implications for analyzing Kepler data.

Contribution

It introduces a method to detect chaos in RR Lyrae models through radius variation analysis, highlighting the potential for chaos detection in observational data.

Findings

Chaotic behavior can be identified in RR Lyrae models via radius variations.

The fractal (Lyapunov) dimension of the attractor is approximately 2.2.

Luminosity variations are less suitable for chaos analysis than radius variations.

Abstract

The period doubling phenomenon was recently discovered in RR Lyrae stars with the Kepler space telescope and has been theoretically explained by hydrodynamic calculations. However, peculiar solutions of the Florida-Budapest turbulent convective hydrodynamic code suggest that bifurcation cascade may evolve to chaos in these dynamical systems. We show that chaotic behaviour may be recovered from the radius variations of the model using the global flow reconstruction method. The fractal (Lyapunov) dimension of the underlying dynamical attractor is calculated to be ~2.2. Compared to the radius, the luminosity variations proved to be less suitable for such investigations due to their complexity. That suggest that even the continuous Kepler data would require transformation before conducting a similar analysis.