Dynamical Chaos in Stellar Evolution Models

Stellar evolution models are a ubiquitous tool in astrophysics for understanding stars individually and in groups, with applications from exoplanet characterization to galaxy formation. These models solve a system of highly nonlinear intergo-differential equations and have a very high dimensional effective phase space, thus they have the potential to exhibit dynamical chaos. Using the open source MESA (Modules for Experiments in Stellar Evolution) code to conduct our simulations, we simulate a variety of stars around one solar mass with differing values of initial surface rotational velocity. Each model is compared against an otherwise identical model whose initial conditions differ by one part in $10^8$. We compute the distance between the two nearly-identical models in a phase space of density, temperature, and hydrogen fraction as functions of radius, which allows us to compute the maximum Lyapunov exponent. This determines the rate of exponential divergence or convergence of trajectories through phase space. We present initial results that demonstrate that a solar-like stellar evolution model yields dynamical chaos with a Lyapunov time of about $10^8$ years.