http://arxiv.org/abs/1803.01258
An understanding of the long-term evolution of self-gravitating disks ranks among the classic outstanding problems of astrophysics. In this work, we show that the secular inclination dynamics of a geometrically thin quasi-Keplerian disk, with a surface density profile that scales as the inverse square-root of the orbital radius, are described by the time-dependent Schr\”odinger equation. Within the context of this formalism, nodal bending waves correspond to the eigenmodes of a quasiparticle’s wavefunction, confined in an infinite square well with boundaries given by the radial extent of the disk. We further show that external secular perturbations upon self-gravitating disks exhibit a mathematical similarity to quantum scattering theory. Employing this framework, we derive an analytic criterion for the gravitational rigidity of a nearly-Keplerian disk under external perturbations. Applications of the theory to circumstellar disks and Galactic nuclei are discussed.
K. Konstantin Batygin
Tue, 6 Mar 2018
32/70
Comments: 15 pages, 7 figures, published in Monthly Notices of the Royal Astronomical Society, 475, 5070
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