Visual observations of long period variable stars over 20 years were provided by the American Association of Variable Stars Observers, and were analysed as part of the preparation of the HIPPARCOS mission.
A set of frequencies is extracted from the light curve by using Fourier transform, preliminary Van Cittert deconvolution and comparison of the results obtained through different kinds of spectral windows. The same procedure is applied to the residual obtained after nonlinear fit of the main frequency. After final comparison of both sets, a nonlinear fit of the common frequencies gives the ‘clean’ power spectrum.
Different equilibrium stellar model (i) give theoretical linear nonadiabatic pulsation modes (vj) with their growth rates (ηj)i) (Tuchman 1978). The metallicity is taken between 0.005 and 0.02; the mixing length is λ = 1±0.2; the upper bound is r = 0.7. Assuming two peaks of the power spectrum to be the fundamental (vo) and first overtone (v1) modes, one looks for the corresponding models. The best one is selected by checking the other theoretical overtones they give. So are obtained the mass, the luminosity, the effective temperature and the effective radius of each star.