Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- Part I Idealized homogeneous systems – basic ideas and gentle relaxation
- 1 The average and fluctuating gravitational fields
- 2 Gentle relaxation: timescales
- 3 The dynamics of random impulsive forces
- 4 General properties of Fokker–Planck evolution
- 5 Fokker–Planck description of gravitating systems
- 6 Dynamics with a memory: non-Markovian evolution
- 7 The Boltzmann equation
- 8 Some properties of the Boltzmann equation
- 9 The virial theorem
- 10 The grand description – Liouville's equation and entropy
- 11 Extracting knowledge: the BBGKY hierarchy
- 12 Extracting knowledge: the Fourier development
- 13 Collective effects – grexons
- 14 Collective scattering
- 15 Linear response and dispersion relations
- 16 Damping and decay
- 17 Star-gas interactions
- 18 Problems and extensions
- 19 Bibliography
- Part II Infinite inhomogeneous systems – galaxy clustering
- Part III Finite spherical systems – clusters of galaxies, galactic nuclei, globular clusters
- Part IV Finite flattened systems – galaxies
- Index
16 - Damping and decay
Published online by Cambridge University Press: 05 July 2011
- Frontmatter
- Contents
- Preface
- Introduction
- Part I Idealized homogeneous systems – basic ideas and gentle relaxation
- 1 The average and fluctuating gravitational fields
- 2 Gentle relaxation: timescales
- 3 The dynamics of random impulsive forces
- 4 General properties of Fokker–Planck evolution
- 5 Fokker–Planck description of gravitating systems
- 6 Dynamics with a memory: non-Markovian evolution
- 7 The Boltzmann equation
- 8 Some properties of the Boltzmann equation
- 9 The virial theorem
- 10 The grand description – Liouville's equation and entropy
- 11 Extracting knowledge: the BBGKY hierarchy
- 12 Extracting knowledge: the Fourier development
- 13 Collective effects – grexons
- 14 Collective scattering
- 15 Linear response and dispersion relations
- 16 Damping and decay
- 17 Star-gas interactions
- 18 Problems and extensions
- 19 Bibliography
- Part II Infinite inhomogeneous systems – galaxy clustering
- Part III Finite spherical systems – clusters of galaxies, galactic nuclei, globular clusters
- Part IV Finite flattened systems – galaxies
- Index
Summary
Physical description
If you look for a particular type of response mode in analyzing a mechanical system you might find it. But, if you do not look for it you will never find it. Lack of attention to this truism has often held back progress by promoting the feeling that a system is understood when its Fourier modes have been examined. Thus, it came as a surprise in plasma physics when Landau (1946) discovered that waves in a collisionless plasma, described by the collisionless Boltzmann equation, can damp and decay. At the time it was especially unexpected because damping had been associated with viscosity, and there is no viscosity in such plasmas. Similar behavior occurs in gravitating systems.
The physical reason for collisionless damping arises from the detailed interaction of a wave with the orbits of background stars which are not part of the wave. Thus, this process would not show up in a continuum approximation where the waves could merrily propagate without growth or decay.
To see how this works, consider the idealized triangular (rather than sinusoidal) wave shown in Figure 16. We look at it in a co-moving frame, traveling along with the wave's phase velocity v = ω/k. This ripple has been set up at t = 0 by suddenly imposing a periodic triangular perturbation in the density which gives a similar perturbation to the gravitational potential φ throughout the entire volume.
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- Chapter
- Information
- Gravitational Physics of Stellar and Galactic Systems , pp. 105 - 116Publisher: Cambridge University PressPrint publication year: 1985