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Hydrodynamical models of pulsating stars of BL Herculis type

In a paper "Chaos in Hydrodynamic BL Herculis models", Smolec i Moskalik (2014), accepted for publication in MNRAS, authors analyse a sequence of hydrodynamic, type II Cepheid models of BL Herculis type. The models show a wealth of dynamical behaviours characteristic for deterministic chaos and present in other, well known chaotic systems, like logistic map or Lorenz equations. Most of the chaotic phenomena are detected for the first time in hydrodynamic models of pulsating stars.

The bifurcation diagram (see Figure), that shows a possible values of maximum radii versus the models' effective temperature, reveals a rich internal structure. The chaotic bands are reached through a period doubling cascades both from the cool and the hot side of the computation domain. Within chaotic bands several windows with periodic behavior are detected, including e.g. cycle-3, cycle-7 or cycle-9 pulsation (in cycle-k pulsation variability repeats after k pulsation cycles). At the edges of these windows intermittent behaviour (sporadic switching between chaotic and almost periodic behaviour) was detected.

So far only period doubling effect was detected in BL Her stars (Smolec et al. 2012). Chaotic dynamics is present in more luminous cousins of BL Her stars, in RV Tau stars and in semi-regular pulsators. Models of Smolec & Moskalik may help to understand these poorly studied stars and motivate the search for new phenomena, like intermittency or cycle-k pulsation, in the observations of these stars.

Figure: Bifurcation diagram for the computed hydrodynamic models. It reveals a striking similarity to bifurcation diagram of the simplest chaotic system, i.e. logistic map.