Long-term Dynamics of Astrophysical Disks

Abstract

context: The long-term evolution of a self-gravitating astrophysical disk can be modeled using secular perturbation theory. Recently, Batygin published a paper where he claims that such a disk with a special density can be described by a Schrödinger equation by using this method. aims: In this thesis, we will study the secular perturbation theory applied to an astrophysical disk with the same density as Batygin, using the Laplace-Lagrange equations. We will take the continuum limit of those equations, and try to find a wave equation like Batygin. methods: We first apply the Laplace-Lagrange equations to a disk with a large number of planets. Then we take the continuum limit of an infinite number of planets. We then compare the numeric results of the discrete disk to the analytic results of the continuum limit. results: The eigenmodes of the system are well approximated by damped sinusoids. Mode number n changes sign n times. The eigenvalues are linear in the mode number. conclusions: The eigenmodes do not satisfy a wave equation.