Transport of Magnetic Helicity in Accretion Disks

Abstract

<p>Astrophysical disks are found in many areas of astrophysics, from the protoplanetary disks in which planets are thought to be born, to the accretion disks around white dwarfs, merging stars, and black holes. The key to understanding these disks, is to understand how material overcomes the rotational support and acretes. 'Whatever mechanism is responsible must necessarily explain the transport of angular momentum outward.</p> <p>The current mechanism used to explain this is the magnetorotational instability (MRI). Its ability to transport angular momentum as well as drive a magnetic dynamo, will be discussed in this thesis. The linear equations of motion for a locally Cartesian patch will be solved numerically to get the time evolution of the magnetic and velocity fields. From these solutions, quadratic quantities in the perturbation variables will be calculated, namely the angular momentum and magnetic helicity. The time evolution of these quantities can tell us about the MRI's ability to both transport angular momentum and drive a dynamo through magnetic helicity.</p> <p>By solving the equations of motion in a locally Cartesian patch of a shearing disk, I have calculated the flux of angular momentum and magnetic helicity. The time evolution of these quantities shows that the ability to transport magnetic helicity is very similar the ability to transport angular momentum. This relation is true for a parameter space which corresponds to the asymptotic limit for the MRI.</p>