Studying evolution of magnetic fields in disk galaxies

Hi there! This website is a project report I made for my final semester course Plasma Physics and Magneto-hydrodynamics, instructed by Dr. Luke Chamandy. An understanding of Maxwell’s equations and basic Electromagnetic theory is required to make sense of the theory, but feel free to contact me regarding any questions!

Abstract

Galaxies contain ionised plasma which interacts and evolves with the galactic magnetic field. Studying the evolution of the mean galactic magnetic field would therefore help us understand the global evolution of the galaxy itself. Galaxy disk rotation($\omega$ effect) and interstellar medium turbulence($\alpha$ effect) influence the growth or decay of the mean fields. Depending on the extent of these effects, it is possible to observe mean fields that are oscillatory in nature, which could affect the galaxy’s properties periodically. In this project, I work on the $R_{\alpha}, R_{\omega}$ parameters which characterise the $\alpha$ and $\omega$ effects, to understand which points in the $R_\omega - R_\alpha$ parameter space correspond to oscillatory solutions of the mean field dynamo equations. I use a Runge-Kutta solver with finite difference method to solve the dynamo equations along the galaxy height, at a constant radius. Then I use fourier transforms to detect the oscillatory solutions among eigenfunctions of the dynamo equations. I find that as $R_\alpha$ increases, the range of values of $R_\omega$ for which the solutions are oscillatory becomes broader. Therefore, as the $\alpha$ effect becomes significant, galaxy mean fields show oscillatory behaviour for various $\omega$ effect strengths. I also show that, in general, the mean fields oscillate at higher frequencies when both $\alpha$ and $\omega$ effects are significant. These results could help us predict and understand the oscillatory behaviour of mean fields for galaxies with observational constrains on $R_\alpha$ and $R_{\omega}$ parameters.

Throughout the course of this project, I had to reach some checkpoints by completing some tasks. I have listed my work here for completeness. I go over them generally in the main content, by the details of the specific tasks are in the following pages.

The first task of this project is to solve the diffusion equation, which we get by neglecting the $\nabla \times(\bar{V} \times \bar{B})$ and $\alpha$ terms.

Task 1

In the second task I solve the $\alpha\Omega$ dynamo equations.