Period doubling and Blazhko modulation in BL Herculis hydrodynamic models

TL;DR

This paper presents hydrodynamic models of BL Herculis stars exhibiting amplitude and phase modulation, supporting the hypothesis that a half-integer resonance mechanism explains the Blazhko effect observed in RR Lyrae stars.

Contribution

The study demonstrates, through hydrodynamic simulations, that the same resonance mechanism causing period doubling can also produce modulation patterns similar to the Blazhko effect.

Findings

Models show both periodic and quasi-periodic modulation.

Quasi-periodic modulation may result from dynamics near an unstable saddle point.

The mechanism is applicable despite the models being more luminous than typical RR Lyrae stars.

Abstract

We present the hydrodynamic BL Herculis-type models which display a long-term modulation of pulsation amplitudes and phases. The modulation is either strictly periodic or it is quasi-periodic, with the modulation period and modulation pattern varying from one cycle to the other. Such behaviour has not been observed in any BL Her variable so far, however, it is a common property of their lower luminosity siblings - RR Lyrae variables showing the Blazhko effect. These models provide a support for the recent mechanism proposed by Buchler & Kollath to explain this still mysterious phenomenon. In their model, a half-integer resonance that causes the period doubling effect, discovered recently in the Blazhko RR Lyrae stars, is responsible for the modulation of the pulsation as well. Although our models are more luminous than is appropriate for RR Lyrae stars, they clearly demonstrate, through direct hydrodynamic computation, that the mechanism can indeed be operational. Of great importance are models which show quasi-periodic modulation - a phenomenon observed in Blazhko RR Lyrae stars. Our models coupled with the analysis of the amplitude equations show that such behaviour may be caused by the dynamical evolution occurring in the close proximity of the unstable single periodic saddle point.