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Local models of astrophysical discs

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Latter, HN 
Papaloizou, J 

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, emphasizing 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 disc'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.

Description

Keywords

hydrodynamics, accretion, accretion discs, methods: analytical

Journal Title

Monthly Notices of the Royal Astronomical Society

Conference Name

Journal ISSN

0035-8711
1365-2966

Volume Title

472

Publisher

Oxford University Press
Sponsorship
Science and Technology Facilities Council (ST/L000636/1)
Science and Technology Facilities Council (ST/P000673/1)
HNL is partly funded by STFC grant ST/L000636/1.