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 108 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.