Local and global dynamics of eccentric astrophysical discs

Abstract

We formulate a local dynamical model of an eccentric disc in which the dominant motion consists of elliptical Keplerian orbits. The model is a generalization of the well known shearing sheet, and is suitable for both analytical and computational studies of the local dynamics of eccentric discs. It is spatially homogeneous in the horizontal dimensions but has a time-dependent geometry that oscillates at the orbital frequency. We show how certain averages of the stress tensor in the local model determine the large-scale evolution of the shape and mass distribution of the disc. The simplest solutions of the local model are laminar flows consisting of a (generally nonlinear) vertical oscillation of the disc. Eccentric discs lack vertical hydrostatic equilibrium because of the variation of the vertical gravitational acceleration around the eccentric orbit, and in some cases because of the divergence of the orbital velocity field associated with an eccentricity gradient. We discuss the properties of the laminar solutions, showing that they can exhibit extreme compressional behaviour for eccentricities greater than about $0.5$, especially in discs that behave isothermally. We also derive the linear evolutionary equations for an eccentric disc that follow from the laminar flows in the absence of a shear viscosity. In a companion paper we show that these solutions are linearly unstable and we determine the associated growth rates and unstable modes.

17 pages, 6 figures, to be published in MNRAS

References in corpus (4)

• Planetesimal and gas dynamics in binaries
• The dynamics of eccentric accretion discs in superhump systems
• Comprehensive simulations of superhumps
• Viscous overstability and eccentricity evolution in three-dimensional gaseous discs

Cited by in corpus (17)

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• The Physics of Accretion Discs, Winds And Jets in Tidal Disruption Events
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• Hamiltonian hydrodynamics of eccentric discs
• HFQPOs and discoseismic mode excitation in eccentric, relativistic discs. II. Magnetohydrodynamic simulations
• Nonlinear resonant torus oscillations as a model of Keplerian disc warp dynamics
• Dynamical structure of highly eccentric discs with applications to tidal disruption events
• Eccentric debris disc morphologies I: exploring the origin of apocentre and pericentre glows in face-on debris discs
• Importance of magnetic fields in highly eccentric discs with applications to tidal disruption events
• Order-disorder phase transition in black-hole star clusters -- III. A mono-energetic cluster
• Evolution of $\alpha$ Centauri B's protoplanetary disc
• Focusing of nonlinear eccentric waves in astrophysical discs
• Parametric instability in warped astrophysical discs: growth, saturation and feedback
• Focusing of nonlinear eccentric waves in astrophysical discs. II. Excitation and damping of tightly-wound waves
• Developing a Non-Newtonian Fluid Model for Dust, for Application to Astrophysical Flows
• Linear and nonlinear eccentric mode evolution in unstratified MHD discs