Period Doubling with Hysteresis in BL HerType Models
Abstract
We have performed recently a survey of the nonlinear hydrodynamical models of the BL Hertype variables (Buchler & Moskalik 1992). Within this project we have studied several sequences of models, i.e., families in which only T_{eff} has been varied from model to model, while all other stellar parameters have been kept constant. The fundamental mode pulsations of each model have been converged to strict periodicity with the relaxation code (Stellingwerf 1974). Such approach speeds up to the calculations and simultaneously yields information about the stability properties of the resulting limit cycles. In all studied sequences except one, we have found a narrow range of T_{eff} (typically 100150K), in which regular solution becomes unstable towards a priod doubling bifurcation. The instability has its origin in a halfinteger resonance, namely the 3:2 coupling between the fundamental mode and the first overtone. This is the same resonance, which also causes period doubling in the models of classical Cepheids. The bifurcation leads to stable periodtwo oscillations, characterized by an RV Taulike, albeit strictly periodic behavior of all variables. In other words, the pulsation light curves and velocity curves will exhibit two alternating minima (as well as maxima) of different values. We show the bifurcation for one of our sequences, by plotting minimum pulsational velocities V_{min} versus T_{eff}.
 Publication:

Astrophysics and Space Science
 Pub Date:
 December 1993
 DOI:
 10.1007/BF00657913
 Bibcode:
 1993Ap&SS.210..301M
 Keywords:

 Hydrodynamics;
 Hysteresis;
 Period Doubling;
 Stellar Models;
 Stellar Oscillations;
 Variable Stars;
 Light Curve;
 Radial Velocity;
 Stellar Evolution;
 Stellar Luminosity;
 Astrophysics