Abstract
This chapter reviews theoretical work on the stellar dynamics of galaxy disks.All the known collective global instabilities are identified and their mechanismsdescribed in terms of local wave mechanics. A detailed discussion of warps andother bending waves is also given. The structure of bars in galaxies, and theireffect on galaxy evolution, is now reasonably well understood, but there is still noconvincing explanation for their origin and frequency. Spiral patterns havelong presented a special challenge, and ideas and recent developments arereviewed. Other topics include scattering of disk stars and the survival of thindisks.
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Notes
- 1.
- 2.
Goldreich and Lynden-Bell (1965a) derived the vertically integrated equations for “2D pressure” in a gas disk.
- 3.
The reduction factor used assumes a Gaussian distribution of radial velocities.
- 4.
Additional Bernstein-type waves exist near integer values of s > 1, but such solutions seem to be of little dynamical importance.
- 5.
Mestel (1963) solved the far greater challenge of a disk of finite radius that has an exactly flat rotation curve.
- 6.
The “sling amplification” mechanism proposed by Shu et al. (1990) applies only to gaseous accretion disks, since it relies on sound waves propagating outside the OLR.
- 7.
Korchagin et al. (2005) calculated essentially gas-dynamical modes for models of specific galaxies, and argued that the shapes of one, or more, of the lower-order modes could be matched to the observed spiral pattern. However, it is unclear that rapidly growing, linear modes can be seen for long at finite amplitude before nonlinear effects will change their appearance, and it seems even less likely that two modes with different growth rates should have similar large amplitudes at the time a galaxy is observed.
- 8.
Cuzzi et al. (2010) found evidence for similar behavior within Saturn’s A ring.
- 9.
The resonance condition (18.5) for a pure cos(mθ) potential variation also implies frequency commensurabilities at multiples of m. The small denominators that characterize the principal resonances (BT08, Sect. 3.3.3) arise at these “ultraharmonic resonances” only for noncircular orbits. A new family of orbits appears at the 4:1 resonance that closes after four radial oscillations (see Sect. 9.3 and Sellwood and Wilkinson 1993).
- 10.
- 11.
This behavior is inconsistent with the non-linear mode coupling ideas discussed in Sect. 7.4.
- 12.
- 13.
A razor-thin disk is not destabilized by orbital motions with no velocity spread.
- 14.
Shocks may be avoided when pressure is significant (Englmaier and Gerhard 1997).
- 15.
The opposite happens in shocks outside CR, where the gas gains angular momentum from the bar.
- 16.
The ratio σ R ∕ σ ϕ ≈ 2Ω ∕ κ (BT08, Eq. 8.117) is forced by epicyclic motions of disk stars.
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Acknowledgements
The author is indebted to James Binney, Victor Debattista, Agris Kalnajs, Juntai Shen, Alar Toomre, and Scott Tremaine for numerous valuable comments on a draft of this chapter.
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Sellwood, J. (2013). Dynamics of Disks and Warps. In: Oswalt, T.D., Gilmore, G. (eds) Planets, Stars and Stellar Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5612-0_18
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