## 4. Nonlinear effects## 4.1. Existence of a limit cycleFor most of the models we started the simulation with small
amplitude, which grew until the pulsation settled into a limit cycle
oscillation. Some of the models, however, did not have limit cycles in
nonlinear regime. For the most luminous models in Fig. 1 the
amplitude at the photosphere became so large that it was not possible
to continue the simulation. There are similar cases in the
less-massive supergiant stars and most of them show chaotic pulsations
as steady states of nonlinear pulsation. Although we cannot confirm a
steady state of nonlinear pulsation of the present models, we suspect
these stars do not have limit cycles. Thus, we expect that observed
counterparts of these stars, namely those with ## 4.2. Nonlinear periodsIt is well known that the differences among periods in linear adiabatic, linear nonadiabatic and limit cycle pulsation calculations are quite small in short period Cepheids. For longer period Cepheids, however, the differences become significant. There is a strong coupling between acoustic waves and thermal waves, and this makes the nonadiabatic periods quite longer than adiabatic ones in luminous cepheids (Aikawa 1985). We show in Fig. 3 that the pulsation periods at limit cycles are even longer than the linear nondiabatic ones, and the relative difference between linear nonadiabatic () and nonlinear () periods, increases remarkably for small changes of the luminosity
Carson & Stothers (1984) tried to explain the observed
flattening of the It is possible to conclude from Fig. 3 that the lengthening is
typical of low metallicity galaxies, because, on the one hand, it
should not be possible to find very long © European Southern Observatory (ESO) 2000 Online publication: December 11, 2000 |