Schrödinger Evolution of Self-Gravitating Disks

Abstract

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 Schrödinger 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.

15 pages, 7 figures, published in Monthly Notices of the Royal Astronomical Society, 475, 5070

References in corpus (15)

• HST/ACS Multiband Coronagraphic Imaging of the Debris Disk around Beta Pictoris
• The Kozai-Lidov Mechanism in Hydrodynamical Disks
• Reduced gas accretion on super-Earths and ice giants
• Chaos in the Test Particle Eccentric Kozai-Lidov Mechanism
• Cross Sections for Planetary Systems Interacting with Passing Stars and Binaries
• Chaotic Disintegration of the Inner Solar System
• Early Excitation of Spin-Orbit Misalignments in Close-in Planetary Systems
• The gravitational interaction between planets on inclined orbits and protoplanetary disks as the origin of primordial spin--orbit misalignments
• Circumstellar Debris Disks: Diagnosing the Unseen Perturber
• Lidov-Kozai Mechanism in Hydrodynamical Disks: Linear Stability Analysis
• HD 106906: A Case Study for External Perturbations of a Debris Disk
• Alignment of Protostars and Circumstellar Disks During the Embedded Phase
• Stellar Dynamics around a Massive Black Hole III: Resonant Relaxation of Axisymmetric Discs
• Nonlinear hydrodynamical evolution of eccentric Keplerian discs in two dimensions: validation of secular theory
• Accurate calculation of the complex eigenvalues of the Schrödinger equation with an exponential potential

Cited by in corpus (5)

• Constraining the Circumbinary Disk Tilt in the KH 15D system
• Self-gravity of debris discs can strongly change the outcomes of interactions with inclined planets
• Eigenstates of Quasi-Keplerian Self-Gravitating Particle Discs
• Exponential distance relation (aka Titius-Bode rule) in extra solar planetary systems
• Emergent Quantum Dynamics of Vortex Line under Linear Local Induction Approximation