The Pomeau-Manneville intermittent transition to chaos in hydrodynamic pulsation models

Abstract

Hydrodynamic simulations of nonlinear pulsation for less-massive cool supergiants have been performed by several authors. Outburst of large amplitude oscillations at times is one of common features of these models. To find out routes of the transition from the limit cycles to the irregular pulsations. We performed hydrodynamic simulation for a series of models of luminosity log(L/L ⊙)=3.505, andT e =5300 K with the range of the mass 1.4M ⊙≤M≤1.5M ⊙. With decreasing the mass, we confirm a transition from limit cycles to irregular oscillations. The nature of the transition is finally specified by examining the dissipation of pulsational kinetic energies in limit cycle models, when pulsations start with larger amplitudes than their limiting pulsations. We find that the rates of dissipation are so small that they might be marginally stable. Furthermore, the oscillation starting with even larger amplitudes gets the kinetic energies until it reaches a limit where the oscillation induces strong shock waves and dissipates its kinetic energy. Thus, we conclude that the model which has the stable limit cycle near the transition has another unstable fixed point above the limit cycle. The transition, therefore, is induced by disappearance of these two fixed points, as the mass, the control parameter in our case, is varied, and is found exactly in aggreement with the intermittency proposed by Pomeau and Manneville as a route to chaos in dissipative systems.