Exploring Dynamical Chaos in Stellar Evolution Models

Stellar evolution models predict the evolution of the physical properties of stars using a complicated set of nonlinear differential, algebraic, and tabular equations. Such complicated, strongly nonlinear equations can be capable of dynamical chaos – extreme sensitivity to very small changes in initial conditions. Modules for Experiments in Stellar Astrophysics (MESA) is an open stellar evolution model (SEM) that is widely used by stellar astrophysicists to study star development. We present evidence of dynamically chaotic behavior in MESA when applying rotation to the development of main-sequence sun-like stars. We induce a perturbation on the order of $10^{-11$} in the hydrogen mass fraction of the core of the star after 1 Gyr into the star’s main sequence evolution and then track differences in the perturbed and unperturbed models’ temperature, density, and composition profiles, which constitute the system’s phase space. We use this phase space separation to estimate the largest Lyapunov exponent for the system. Notable discoveries include the necessity of rotation for the star to exhibit chaotic dynamics and a strong positive correlation between the temporal resolution of the SEM and the Lyapunov exponent of the system. When analyzing an ensemble of 49 stars each with a random perturbation to the core hydrogen fraction, we find that there can be differences in the effective temperature of the stars as high as 50 K after the SEMs reach 8 Gyr. This indicates a potential intrinsic upper limit on the accuracy of SEMs.