4 Conclusions and summary

Our conclusions based on the results presented in this paper can be summarized as follows.

1. We have re-analysed the light curve of the carbon Mira star Y Per complemented with the most recent observations. Its variation has been transformed from a monoperiodic oscillation to a bimodal one since 1987, which periods suggest first and third overtone pulsation. The suddennes of this switch is interpreted as a consequence of a strong coupling between pulsation and convection. We conclude that the unphysical classification scheme of LPVs (Mira and semiregulars) could be misleading when speculating on different evolutionary states of these variables. A simple distinction between monoperiodic and multiply periodic red variables may be more straightforward in some cases. Another important consequence of first plus third overtone assumption is that Y Per, a typical carbon Mira before 1987, has pulsated in the first overtone mode. That would imply short period Miras to pulsate in the first overtone, but no firm conclusion can be drawn on this issue based on only one star.

2. We report two stars (RX UMa and RY Leo) with significant amplitude modulation with no changes of the mean brightness. We have interpreted this behaviour as beating of two closely separated periods, most likely high-order radial or radial plus non-radial oscillation. Similar frequency doublet is reported for V CVn, confirming earlier results of Loeser et al. (1986). Unfortunately, there is no thorough theoretic study on the non-radial oscillations of red giants so far, thus we could only speculate on this explanation comparing semiregulars with other well-documented types of variables with similar close frequencies (i.e. $\delta$ Scuti and ZZ Ceti stars). However, the relatively large fraction of such SRVs in our sample of 93 stars implies that this phenomenon may be quite common in these stars.

3. We have also found another type of amplitude modulation resembling RR Lyrae variables with Blazhko effects in RY UMa and possibly in RS Aur. Again, since this aspect has no firm theoretic background yet, we assumed similar physical mechanism being responsible for similar light variations. Our qualitative model involving highly distorted stellar shape describes very well the observed modulation, though the initial physical assumptions may be considered quite unlikely. However, there are indications for oblate stellar shapes from high-resolution observations in several Mira stars and also there are empirical pieces of evidence for complex circumstellar structures around semiregular variables, though mainly observed in the infrared (Bergman et al. 2000; Kerschbaum & Oloffson 1999; Knapp et al. 1998). Further observation with high spatial and spectral resolution are highly recommended in order to clarify the situation.

4. Two bright semiregular stars, W Cyg and AF Cyg, are used to illustrate the repetitive excitation and damping of main modes of pulsation. The characteristic time scale is roughly 2000-3000 days. We have shown that only weak evidence is present for correlated or anticorrelated amplitude changes of different modes implying the possibility of independent excitation mechanisms. Theoretical pulsation models including the coupling between convection and pulsation were used to identify W Cyg and AF Cyg to be first+third and second+fourth overtone pulsators, respectively.

Acknowledgements

We sincerely thank variable star observers of AFOEV, VSOLJ, HAA/VSS and AAVSO whose dedicated observations over many decades made this study possible. Comments and suggestions by B. Skiff are acknowledged. This research was supported by the "Bolyai János" Research Scholarship of LLK from the Hungarian Academy of Sciences, Hungarian OTKA Grants #F022249, #T022259, #T032258 and Szeged Observatory Foundation. The NASA ADS Abstract Service was used to access data and references.