Properties of Cepheids and long-period variables

Some recent theoretical results concerning Cepheids and long-period variables are presented and compared with observations. Nonlinear pulsation calculations for select bump Cepheids are shown capable of yielding very accurate fundamental properties of these stars. The implications of the derived parameters are discussed. For the long-period variables, recent observational and theoretical results pertaining to the long-standing problem of the mode of pulsation are presented. The conflicting results point to some fundamental problem with current interpretations.

A Nonlinear Pulsation Model for V652 Her

When compared with observation, stellar pulsation model predictions provide a test of stellar envelope opacities. Of specific interest, is the radially pulsating extreme helium star V652 Her for which luminosity and radial velocity observations are published. Nonlinear pulsation models of V652 Her, calculated using Opacity Project (OP) opacities, predict luminosity and radial velocity variations in close agreement with observation.

The Importance of Radiative Transfer in Stellar Pulsation Models

With the advent of new astrophysical opacities it seems appropriate to discuss the need for a full radiative transfer (RT) theory instead of the usual equilibrium diffusion theory used in most nonlinear pulsation codes. Early studies on the importance of RT in the calculation of light curves for Cepheid models showed little effect over diffusion theory. The new opacities though may help to explain the “bump” mass discrepancy problem. For RR Lyrae models the use of RT theory causes some effects both in the color differences (U-B) as well as in the light curves. New opacities help to explain the period ratios for double mode RR Lyrae and beat Cepheids. A new area of research is in the modeling of stars with high luminosity to mass ratios that show tendencies for doubling and transitions to chaos, such as W Virginis and RV Tauri stars. For these stars it has been shown that RT is necessary in calculating their light curves and that the understanding of the shock dynamics depends on the transfer of lines in the pulsating RT dependent atmospheres (Fokin 1991).

Bifurcation in Hydrodynamic Models of Stellar Pulsation

Phenomena of bifurcation in hydrodynamic stellar models of radial pulsation are reviewed. By changing control parameters of models, we can see qualitatively different pulsation behaviors in hydrodynamic models with transitions due to various types of bifurcation.In weakly dissipative models (classical Cepheids). the bifurcation is induced by modal resonances. Two types of the modal resonances found in models are discussed: The higher-harmonic resonances of the second overtone mode in the fundamental mode pulsator and of the fourth overtone mode in the first overtone pulsator are relevant to observations. The subharmonic resonance between the fundamental and first overtone modes is confirmed in classical Cepheid models.In strongly dissipative models (less-massive supergiant stars), the bifurcation of nonlinear pulsation is induced by the hydrodynamics of ionization zones as well as modal resonances. The sequence of the bifurcation sometimes leads to chaotic behaviors in nonlinear pulsation. The transition routes from regular to the chaotic pulsations found in models are discussed with respect to the theory of chaos in simple dynamical systems: The cascade of period-doubling bifurcation is confirmed to cause chaotic pulsation in W Virginis models. For models of higher luminosity, the tangent bifurcation is found to lead intermittent chaos.Finally, hydrodynamic models for chaotic pulsation with small amplitudes observed in the post-AGB stars are briefly discussed.

New Opacities and First Overtone Mode Cepheids

Some results of linear adiabatic and nonlinear pulsation models of first overtone mode Cepheids are discussed. New and augmented opacities and a nonstandard mass-luminosity relation have been taken into account. The models indicate the possible importance of the resonance P1/P4 = 2 near P1 = 3 days. The resonance could explain the observed characteristics of the light curve shape of first overtone mode Cepheids.