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.

MNRAS, accepted

References in corpus (5)

• On the vertical-shear instability in astrophysical discs
• Energy Conservation and Gravity Waves in Sound-proof Treatments of Stellar Interiors: Part I Anelastic Approximations
• On the viability of the shearing box approximation for numerical studies of MHD turbulence in accretion disks
• Local and global dynamics of eccentric astrophysical discs
• Universal small-scale structure in turbulence driven by magnetorotational instability

Cited by in corpus (6)

• Local simulations of MRI turbulence with meshless methods
• The vertical shear instability in poorly ionised, magnetized protoplanetary discs
• The saturation of the VSI in protoplanetary disks via parametric instability
• Axisymmetric simulations of the convective overstability in protoplanetary discs
• Instabilities in dusty non-isothermal proto-planetary discs
• Magnetohydrodynamic convection in accretion discs