Abstract
Corotation resonance is one of important processes which excite or dampen disk oscillations. Especially, in the case of non-axisymmetric p-mode oscillations, this is one of important excitation processes. The corotation instability had been recognized in fields outside the accretion disk dynamics (i.e., fluid dynamics, oceanography, meteorology, and galactic dynamics), before its importance in tori was found by Papaloizou and Pringle (Mon Not R Astron Soc 208:721, 1984) (see Chap. 2). This work by Paparoizou and Pringle stimulated many subsequent studies on corotation instability in tori and disks. In this chapter, we will describe the essence of corotation instability in geometrically thin disks by presenting Drury’s work (Mon Not R Astron Soc 217:821, 1985).
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- 1.
This paper seems to have errors.
- 2.
If vertically integrated disks are considered, instead of H-constant disks, the condition of presence of corotation singularity is
$$\displaystyle{\biggr [ \frac{d} {dr}\biggr (\frac{\kappa ^{2}/2\varOmega } {\varSigma _{0}} \biggr )\biggr ]_{\mathrm{c}}\not =0,}$$where Σ 0 is the surface density in the unperturbed disks.
- 3.
Equation (3.62), for example, shows that the energy flux is given by \(\rho _{0}h_{1}\boldsymbol{u}\).
- 4.
Equation (10.22) shows that \(\mathcal{R}_{\mathrm{i}} \gg 1/4\) in the case where n ≥ 1, because r 2∕H 2 ≫ 1.
- 5.
We consider the point of \(\tilde{\omega } = 0\) on the complex r-plane. The point is written as (r c, ε) on the plane. Then, because \(\tilde{\omega } =\omega -m\varOmega =\omega _{\mathrm{c}} - m\varOmega _{\mathrm{c}} + i\omega _{\mathrm{\ i}} - m(d\varOmega /dr)i\epsilon = 0\), we have ε ∼ ω i(md Ω∕dr)−1 > 0 for ω i < 0.
- 6.
As mentioned before, we can study overreflection at the corotation point by examining local behavior at corotation point.
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Kato, S. (2016). Corotation Instability. In: Oscillations of Disks. Astrophysics and Space Science Library, vol 437. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56208-5_10
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