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

Double-mode radial-non-radial RR Lyrae stars. OGLE-IV photometry of two high cadence fields in the Galactic bulge

We analyse the OGLE-IV photometry of the first overtone and double-mode RR Lyrae stars (RRc/RRd) in the two fields towards the Galactic bulge observed with high cadence. In 27 per cent of RRc stars we find additional non-radial mode, with characteristic period ratio, P x /P 1O \in (0.6, 0.64). It strongly corroborates the conclusion arising from the analysis of space photometry of RRc stars, that this form of pulsation must be common. In the Petersen diagram the stars form three sequences. In 20 stars we find two or three close secondary modes simultaneously. The additional modes are clearly non-stationary. Their amplitude and/or phase vary in time. As a result, the patterns observed in the frequency spectra of these stars may be very complex. In some stars the additional modes split into doublets, triplets or appear as a more complex bands of increased power. Subharmonics of additional modes are detected in 20 per cent of stars. They also display a complex structure. Including our previous study of the OGLE-III Galactic bulge data, we have discovered 260 RRc and 2 RRd stars with the additional non-radial mode, which is the largest sample of these stars so far. The additional mode is also detected in two Blazhko RRc stars, which shows that the modulation and additional non-radial mode are not exclusive.Comment: 18 pages, 14 figures, accepted for publication in MNRA