Abstract
Astrophysical objects have many kinds of configurations due to subtle balances among such various forces as gravitational, pressure, rotational, and magnetic ones. Related to this, many kinds of restoring force work on fluid motions when the fluid is perturbed from equilibrium states, which leads to various kinds of wave motions (oscillations) and instabilities. In this chapter, we explore wave motions resulting from various restoring forces except for magnetic and radiation fields, including shock waves. Wave motions resulting from magnetic fields are described in Chap. 13, while those from radiation are given in Chap. 23.
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- 1.
The condition of convective instability is often expressed as ∇ad < ∇. This is the case where N 2 < 0. Convection is discussed in Chap. 5.
- 2.
The waves resulting from metric variation in general relativity are called gravitational waves.
- 3.
The presence of the evanescent region is due to idealization of isothermal atmosphere. In general cases of non-isothermal atmosphere, there is no clear separation of frequency domains.
- 4.
The meaning of subscript 1 to Γ is different from that to other quantities.
- 5.
In the case considered in Sect. 4.1.2, the change to the convection mode does not occur since the medium was assumed to be isothermal.
- 6.
In this subsection ζ is used to denote vorticity. It should not be confused with the displacement vector.
- 7.
Except for Keplerian disks with no temperature (\(\varOmega ^2_{\bot }=\varOmega ^2_{\mathrm {K}}=\kappa ^2\)), \(\varOmega _\bot ^2>\kappa ^2\) holds in general relativistic disks and tidally deformed disks.
- 8.
In general, v z has n − 1 node(s) in the vertical direction, when h 1 has n node(s) in the vertical direction.
- 9.
Equation (4.94) has the different sign from their expression since we adopt the opposite sign of k.
- 10.
For gravitational instability, see Sect. 6.4.
- 11.
In stellar disks the value corresponding to c s is slightly different from c s, and thus the expression for Q-value is different from that given here.
- 12.
- 13.
The subscript n is neglected hereafter, since the flow has no transverse component.
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Kato, S., Fukue, J. (2020). Wave Phenomena in Astrophysical Objects. In: Fundamentals of Astrophysical Fluid Dynamics. Astronomy and Astrophysics Library. Springer, Singapore. https://doi.org/10.1007/978-981-15-4174-2_4
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