Non-linear modelling of beat Cepheids: Resonant and non-resonant models

The phenomenon of double-periodic Cepheid pulsation is still poorly understood. Recently we rediscussed the problem of modelling the double-periodic pulsation with non-linear hydrocodes. We showed that the published non-resonant double-mode models are incorrect, because they exclude the negative buoyancy effects. Aims. We continue our efforts to verify whether the Kuhfuss one-equation convection model with negative buoyancy included can reproduce the double-periodic Cepheid pulsation. Methods. Using the direct time integration hydrocode, which implements the Kuhfuss convection model, we search for stable double-periodic Cepheid models. We search for models pulsating in both fundamental and first overtone modes (F+1O), as well as in the two lowest order overtones (1O+2O). In the latter case, we focus on reproducing double-overtone Cepheids of the Large Magellanic Cloud (LMC). Results. We have found full amplitude non-linear beat Cepheid models of both types, F+1O and 1O+2O. In the case of F+1O models, the beat pulsation is most likely caused by the three-mode resonance, 2omega_1=omega_0+omega_2, while in the double-overtone models the underlying mechanism (resonant or non-resonant) cannot be identified beyond doubt. Double-periodic models found in our survey exist, however, only in narrow period ranges and cannot explain the majority of the observed double-periodic objects. Conclusions. With only little doubt left, we conclude that current one dimensional one-equation convection models are incapable of reproducing the majority of the observed beat Cepheids. Among the shortcomings of current pulsation hydrocodes, the simple treatment of convection seems to be the most severe one. Growing evidence for the presence of non-radial modes in Cepheids suggests that the interaction between radial and non-radial modes should also be investigated.Comment: 12 pages, 6 Figures, accepted for publication in Astronomy and Astrophysic

Period doubling and Blazhko modulation in BL Herculis hydrodynamic models

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.Comment: 13 pages, 16 figures, accepted for publication in MNRAS, for associated animation, see http://users.camk.edu.pl/smolec/publications/BLHerM/index.htm