On the equations of warped disc dynamics

• Verfasst von: Dullemond, Cornelis [VerfasserIn]
• Verfasst von: Kimmig, Carolin [VerfasserIn]
• Verfasst von: Zanazzi, John J. [VerfasserIn]
• Titel: On the equations of warped disc dynamics
• Verf.angabe: C.P. Dullemond, C.N. Kimmig and J.J. Zanazzi
• Jahr: 2022
• Umfang: 23 S.
• Fussnoten: Advance access publication 2021 October 2 ; Gesehen am 21.04.2021
• Titel Quelle: Enthalten in: Royal Astronomical SocietyMonthly notices of the Royal Astronomical Society
• Ort Quelle: Oxford : Oxford Univ. Press, 1827
• Jahr Quelle: 2022
• Band/Heft Quelle: 511(2022), 2, Seite 2925-2947
• ISSN Quelle: 1365-2966
• DOI: doi:10.1093/mnras/stab2791
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1799496236

Abstract

The 1D evolution equations for warped discs come in two flavours: For very viscous discs, the internal torque vector $\boldsymbol {G}$ is uniquely determined by the local conditions in the disc, and warps tend to damp out rapidly if they are not continuously driven. For very inviscid discs, on the other hand, $\boldsymbol {G}$ becomes a dynamic quantity, and a warp will propagate through the disc as a wave. The equations governing both regimes are usually treated separately. A unified set of equations was postulated recently by Martin et al., but not yet derived from the underlying physics. The standard method for deriving these equations is based on a perturbation series expansion, which is a powerful, but somewhat abstract technique. A more straightforward method is to employ the warped shearing box framework of Ogilvie & Latter, which so far has not yet been used to derive the equations for the wave-like regime. The goal of this paper is to analyse the warped disc equations in both regimes using the warped shearing box framework, to derive a unified set of equations, valid for small warps, and to discuss how our results can be interpreted in terms of the affine tilted-slab approach of Ogilvie.