Book contents
- Frontmatter
- Contents
- Preface
- 1 A selective overview
- I Stellar convection and oscillations
- II Stellar rotation and magnetic fields
- III Physics and structure of stellar interiors
- IV Helio- and asteroseismology
- V Large-scale numerical experiments
- VI Dynamics
- 25 A magic electromagnetic field
- 26 Continuum equations for stellar dynamics
- 27 Formation of planetary systems
26 - Continuum equations for stellar dynamics
Published online by Cambridge University Press: 11 November 2009
- Frontmatter
- Contents
- Preface
- 1 A selective overview
- I Stellar convection and oscillations
- II Stellar rotation and magnetic fields
- III Physics and structure of stellar interiors
- IV Helio- and asteroseismology
- V Large-scale numerical experiments
- VI Dynamics
- 25 A magic electromagnetic field
- 26 Continuum equations for stellar dynamics
- 27 Formation of planetary systems
Summary
The description of a stellar system as a continuous fluid represents a convenient first approximation to stellar dynamics, and its derivation from the kinetic theory is standard. The challenge lies in providing adequate closure approximations for the higher-order moments of the phase-space density function that appear in the fluid dynamical equations. Such closure approximations may be found using representations of the phase-space density as embodied in the kinetic theory. In the classic approach of Chapman and Enskog, one is led to the Navier–Stokes equations, which are known to be inaccurate when the mean free paths of particles are long, as they are in many stellar systems. To improve on the fluid description, we derive here a modified closure relation using a Fokker–Planck collision operator. To illustrate the nature of our approximation, we apply it to the study of gravitational instability. The instability proceeds in a qualitative manner as given by the Navier–Stokes equations but, in our description, the damped modes are considerably closer to marginality, especially at small scales.
A kinetic equation
If we have a system of N stars, with N very large, and wish to study its large-scale dynamics, we have to choose the level of detail we can profitably treat. Even if we could know the positions and velocities of all N stars for all times, we would be mainly interested in the global properties that are implied by this information.
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- Information
- Stellar Astrophysical Fluid Dynamics , pp. 377 - 392Publisher: Cambridge University PressPrint publication year: 2003
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