Introduction

1. Period evolution of Very Long Period Variables: The Miras L. SABIN , A. A. ZIJLSTRA University of Manchester, School of Physics  Astronomy P.O. Box 88, Manchester M60 1QD, United Kingdom Email: laurence.sabin@manchester.ac.uk aaz@iapetus.phy.umist.ac.uk Introduction The study of the period changes in variable stars may reveal the action (or not) of physical processes such as thermal pulses, magnetism, convection . . . etc via the observation of stable or unstable behavior. Furthermore, the pulsation period affects the mass loss which is characteristic of the AGB stars: it aids the formation of dust via the phenomenon of levitation of the atmosphere. Period variability may therefore lead to mass loss change. We study stars with periods greater than 450 days as their long-period evolution is more likely to permit us to see perturbations in their behavior. We present here the results for the Mira-type stars. Conclusion We observed different behaviors in the period evolution of this category of long pulsating Mira-type stars: sudden, continuous, meandering and “large” meandering changes. These instabilities are mostly thought to be related to thermal pulses or Helium flashes: we may see here their consequences on the pulsation at different time. Indeed in some stars like R Cen (Hawkins et al, 2001), RU Aur and RU Her (Lebzelter and Hron 2003), Technetium 99 has been found. This element denotes the presence of a 3DUP and then thermal pulses. But the doubt subsists for example on the origin of the very small variations in the meandering stars. So, we mustn’t forget the hypothesis on the implication of other processes as convection, magnetism, rotation ...etc. It seems also that there is no obvious link between the type of period change and the chemical composition of the stars. The pulsation is supposed to play a role in the dust formation and also in the mass loss which characterize AGB stars, leading to the presence of the circumstellar shells. The modeling of this piston motion is therefore necessary by taking into account not only its long term behavior but also its mode. The Sample The number of objects corresponding to our criterion is not high: we counted about 50 stars (mostly O-rich stars). In order to obtain information on the period evolution, the study of the light curves of these stars is necessary. All the data come from the AAVSO database which provides information for several years. The use of the wavelet analysis (developed by Foster- 1996) allows the visualization of periodic variations. Unfortunately only 23 stars remained due to the bad quality of the light curves . • II. V Del-type shows a continuous change of period in the sense of a rapid decrease. This mira with an observed period of 533.51d , presents a drop of 22 days over 88 years. We can also notice that this change is not straight but presents fluctuations. The period evolution Following the example of Templeton, Mattei and Willson(2005) we used a linear fitting to define the change (by dlnP/dt: the slope over the mean period). A significant period change is considered by the authors at 2 (1σ dlnP/dt error: 0.0002, in days) and most of the stars they studied lay in this interval (the large majority of them having a period less than 450 days). The values found for the stars of our sample are much greater than this level; the Miras seem significantly unstable. • III. V Cam-type is representative of the majority of the stars of our sample. It shows series of changes that is close to a sinusoidal trend. There is no obvious sign of drop or increase in the long run. Zijlstra  Bedding called them “meandering stars”. Future work The next step in this study is to know how the pulsation acts on the mass loss and the link with the rings seen around some AGB stars and Planetary Nebulae. We will therefore use a hydrodynamical code to reproduce the outflows and include the physics representing the pulsation. The introduction of thermal pulses will allow us to see the effects not only on the stars’ pulsation but also on the dispersal of the matter. Once done, the use of the code DUSTY will give us the dust distribution for the given model. The same operation will be done for the Semi regulars. • IV. RU Tau-type is among the few stars that could be put in the previous group but it presents a few number of oscillations in comparison with V Cam for example. The sinusoid that describes it is “quasi regular”: is it the sign that no drastic events occur in the star? • Evolution trends : THE CLASSIFICATION OF THE LPVs • The observation of the graphics relative to the variations shows four different trends ( three of them also defined by Zijlstra  Bedding, 2002) . They are characterized by the behavior of four example stars. If only one process is involved, then we may relate to the different phases in its evolution. • R Cen-type which presents a double maximum in its light curve, underwent a suddenchange: from 1919 to 1935 the period decreases from 550 to 543 days and after a brief episode of increase to 553 days until 1949, we see a spectacular drop to 512 days by 2001 (- 41d). This fall may be due to the occurrence of a thermal pulse. References Hawkins et al., 2001,ASP, 113:501-506 Lebzelter T. and Hron J., 2003, AA 411,533-542. Templeton M.R. Mattei ,J.A., Willson L.A. 2005, AJ, 130:776-788 Zijlstra A.A and Bedding T.R, 2002,JAAVSO,31,2 We acknowledge the AAVSO for the data as well as all the observers who provide them.