Finding Dynamical Chaos in Stellar Models

Stellar structure and evolution models are foundational to much of astrophysics by providing a big range in evolution calculations for astrophysics research. Since modern stellar evolution models can approach a precise stellar model followed by a series of equations that describe the chemical composition, fluid dynamics, thermodynamics, and other properties of stars that are calculated by astrophysics. These equations are highly complex, and it is in our goal to show if these equations and stellar model simulations are chaotic.

Using MESA we have modeled the main sequence evolution of a solar-like model, and then again with a small perturbation on the order of one part in 10^8 on the central hydrogen fraction to examine the divergence of the two models, and also the perturbation in rotation in the same order of magnitude.

We find that these models are indeed chaotic when rotating, showing an exponential divergence on very short time-scales and a maximum phase space separation of approximately 0.01 in our time scale run from 3 to 7 Gyr when we fit data to the Lyapunov exponent. Calculations of ensembles of these models show that increment in resolution does not increase the accuracy in the exponential growth region, which leads to being more dependent on the time factor on each model due to evolution time process for each model.

This suggests an intrinsic limit to the precision of stellar structure and evolution models due to dynamical chaos showed in the program and the accuracy in the program for the stars simulations.