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Eigenstates of quasi-Keplerian self-gravitating particle discs

Melton, Walker and Batygin, Konstantin (2021) Eigenstates of quasi-Keplerian self-gravitating particle discs. Monthly Notices of the Royal Astronomical Society, 502 (3). pp. 3955-3963. ISSN 0035-8711. doi:10.1093/mnras/stab344.

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Although quasi-Keplerian discs are among the most common astrophysical structures, computation of secular angular momentum transport within them routinely presents a considerable practical challenge. In this work, we investigate the secular small-inclination dynamics of a razor-thin particle disc as the continuum limit of a discrete Lagrange–Laplace secular perturbative theory and explore the analogy between the ensuing secular evolution – including non-local couplings of self-gravitating discs – and quantum mechanics. We find the ‘quantum’ Hamiltonian that describes the time evolution of the system and demonstrate the existence of a conserved inner product. The lowest-frequency normal modes are numerically approximated by performing a Wick rotation on the equations of motion. These modes are used to quantify the accuracy of a much simpler local-coupling model, revealing that it predicts the shape of the normal modes to a high degree of accuracy, especially in narrow annuli, even though it fails to predict their eigenfrequencies.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Melton, Walker0000-0003-2723-7633
Batygin, Konstantin0000-0002-7094-7908
Additional Information:© 2021 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( Accepted 2021 January 31. Received 2021 January 11; in original form 2020 March 27. WM is grateful to the Caltech Summer Undergraduate Research Fellowship program, during which this work was initiated. KB is grateful to the David and Lucile Packard Foundation and the Alfred P. Sloan Foundation for their generous support. Additionally, we would like to thank the anonymous referees for providing useful insights that have led to an improvement of the manuscript. DATA AVAILABILITY. The data underlying this article will be shared on reasonable request to the corresponding author.
Funding AgencyGrant Number
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:methods: analytical, protoplanetary discs, Galaxy: nucleus
Issue or Number:3
Record Number:CaltechAUTHORS:20210526-160617950
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Official Citation:Walker Melton, Konstantin Batygin, Eigenstates of quasi-Keplerian self-gravitating particle discs, Monthly Notices of the Royal Astronomical Society, Volume 502, Issue 3, April 2021, Pages 3955–3963,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109265
Deposited By: George Porter
Deposited On:27 May 2021 15:18
Last Modified:16 Nov 2021 19:35

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