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Published April 21, 2018 | Published + Submitted
Journal Article Open

Schrödinger evolution of self-gravitating discs


An understanding of the long-term evolution of self-gravitating discs ranks among the classic outstanding problems of astrophysics. In this work, we show that the secular inclination dynamics of a geometrically thin quasi-Keplerian disc, with a surface density profile that scales as the inverse square-root of the orbital radius, are described by the time-dependent Schrödinger equation. Within the context of this formalism, nodal bending waves correspond to the eigenmodes of a quasi-particle's wavefunction, confined in an infinite square well with boundaries given by the radial extent of the disc. We further show that external secular perturbations upon self-gravitating discs exhibit a mathematical similarity to quantum scattering theory. Employing this framework, we derive an analytic criterion for the gravitational rigidity of a nearly-Keplerian disc under external perturbations. Applications of the theory to circumstellar discs and Galactic nuclei are discussed.

Additional Information

© 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society. Received: 26 June 2017. Revision Received: 30 December 2017. Accepted: 04 January 2018. I am grateful to G. Laughlin, F. Adams, D. Stevenson, A. Morbidelli, C. Spalding, S. Michalakis, A. Kitaev, S. Tremaine, and J. Touma for illuminating discussions. Additionally, I would like to thank the anonymous referee for providing a thorough and insightful report that has led to a considerable improvement of the manuscript, as well as the David and Lucile Packard Foundation for their generous support.

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Published - sty162.pdf

Submitted - 1803.01258.pdf


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