Strange attractors of long-period variable stars in a one-zone model of stellar pulsation

Abstract

We explore a one-zone model of stellar pulsation that exhibits period-doubling routes to chaos for variations in two different control parameters. One of these parameters is associated with the strength of the κ-mechanism and the other with the strength of non-adiabaticity. Through the use of first return maps, we are able to visualize these period-doubling cascades to chaos. We then compare the strange attractors formed in the velocity return maps for parameter values corresponding to some long-period variable (LPV) stars. We find a "y"-shaped structure in the chaotic regime associated with the non-adiabaticity. This "y"-shaped structure had previously only been associated with the κ-mechanism derived chaotic regime. This leads to the insight that LPVs with these "y"-shaped attractors may have chaotic oscillations deriving from variations in either of these two processes, instead of just the κ-mechanism.