Abstract
A twisted disc forms around a rotating black hole each time when the disc outskirts are not aligned with the black hole’s equatorial plane. We derive equations describing the evolution of the shape of twisted discs and perturbations of density and velocity necessarily arising in such a disc. This is done under the following simplifying assumptions: a small aspect ratio of the disc, a slow rotation of the black hole, and a small tilt angle of the disc rings with respect to the black hole equatorial plane. Nevertheless, the GR effects are considered accurately. Additionally, an analysis of particular regimes of non-stationary twist dynamics (the wave and diffusion regimes) is presented both in the framework of the Newtonian dynamics and taking into account Einstein’s relativistic precession. At the end of the chapter, a calculation of the shape of a stationary relativistic twisted accretion disc for different values of free parameters of the model is done.
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Notes
- 1.
For the sake of making the description as rigorous as possible, it is important also to add that the coincidence of azimuthal location of maxima of (∇p)r and ρ 1 occurs only when the effect of viscosity on the gas elements of the ring is neglected.
- 2.
Here and hereafter, r denotes the twisted radial coordinate.
- 3.
To shorten the equations, we omit the term with the second viscosity ζ: as it can be shown using the analysis given below, this term does not contribute to the final equations in the leading order in the small parameters of the problem.
- 4.
As we discussed above, the smallness of t d∕t ev is necessary to ensure that the accretion flow outside the equatorial plane of the black hole can be considered a ‘disc’. In turn, this is jointly ensured by the smallness of both δ and t d∕t LT ≪ 1 (see Sect. 4.1.1).
- 5.
a = 0 also in the expression for \(T^{\varphi \xi }_\nu \).
- 6.
Retaining the term ω 2 in (4.92) and considering the inviscid Newtonian limit for the set of Eqs. (4.92)–(4.93), we may obtain a cubic equation with respect to ω, and check that it always has three real roots, one always being of the order of ∼ Ω, even for kh ≪ 1, which violates the restriction of slow evolution of the twist imposed in our model.
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Zhuravlev, V. (2018). Relativistic Twisted Accretion Disc. In: Shakura, N. (eds) Accretion Flows in Astrophysics . Astrophysics and Space Science Library, vol 454. Springer, Cham. https://doi.org/10.1007/978-3-319-93009-1_4
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