Local models of astrophysical discs

Abstract

Local models of gaseous accretion discs have been successfully employed for decades to describe an assortment of small-scale phenomena, from instabilities and turbulence, to dust dynamics and planet formation. For the most part, they have been derived in a physically motivated but essentially ad hoc fashion, with some of the mathematical assumptions never made explicit nor checked for consistency. This approach is susceptible to error, and it is easy to derive local models that support spurious instabilities or fail to conserve key quantities. In this paper we present rigorous derivations, based on an asympototic ordering, and formulate a hierarchy of local models (incompressible, Boussinesq, and compressible), making clear which is best suited for a particular flow or phenomenon while spelling out explicitly the assumptions and approximations of each. We also discuss the merits of the anelastic approximation, emphasising that anelastic systems struggle to conserve energy unless strong restrictions are imposed on the flow. The problems encountered by the anelastic approximation are exacerbated by the disk's differential rotation, but also attend non-rotating systems such as stellar interiors. We conclude with a defence of local models and their continued utility in astrophysical research.

arXiv commentMNRAS, accepted

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Cited by in corpus (28)

• The initial conditions for planet formation: Turbulence driven by hydrodynamical instabilities in disks around young stars
• Vortices and the saturation of the vertical shear instability in protoplanetary disks
• Gravitoturbulent dynamos in astrophysical discs
• Local simulations of MRI turbulence with meshless methods
• The vertical shear instability in poorly ionised, magnetized protoplanetary discs
• Dust Settling Instability in Protoplanetary Discs
• Wavelike nature of the vertical shear instability in global protoplanetary disks
• The saturation of the VSI in protoplanetary disks via parametric instability
• Dust dynamics and vertical settling in gravitoturbulent protoplanetary discs
• MRI turbulence in accretion discs at large magnetic Prandtl numbers
• Electric heating and angular momentum transport in laminar models of protoplanetary disks
• Axisymmetric simulations of the convective overstability in protoplanetary discs
• Hydrodynamic convection in accretion discs
• Spiral density waves and vertical circulation in protoplanetary discs
• Instabilities in dusty non-isothermal proto-planetary discs
• Turbulence in particle laden midplane layers of planet forming disks
• Dissipative structures in magnetorotational turbulence
• MRI turbulence in vertically stratified accretion discs at large magnetic Prandtl numbers
• Magnetohydrodynamic convection in accretion discs
• MHD in a cylindrical shearing box II: Intermittent Bursts and Substructures in MRI Turbulence
• Resonant drag instabilities for polydisperse dust. II. The streaming and settling instabilities
• The stress-pressure lag in MRI turbulence and its implications for thermal instability in accretion discs
• Developing a Non-Newtonian Fluid Model for Dust, for Application to Astrophysical Flows
• A Local Model for the Spherical Collapse/Expansion Problem
• Nonlinear Evolution of the Unstratified Polydisperse Dust Settling Instability
• Dust Growth in ALMA Rings: II. Dusty Rossby Wave Instability
• Nonlinear analysis of gravitational instability in a 3D gaseous disc
• Streaming instabilities in accreting protoplanetary disks: A parameter study