Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- Part I Idealized homogeneous systems – basic ideas and gentle relaxation
- Part II Infinite inhomogeneous systems – galaxy clustering
- 20 How does matter fill the Universe?
- 21 Gravitational instability of the infinite expanding gas
- 22 Gravitational graininess initiates clustering
- 23 Growth of the two-galaxy correlation function
- 24 The energy and early scope of clustering
- 25 Later evolution of cosmic correlation energies
- 26 N-body simulations
- 27 Evolving spatial distributions
- 28 Evolving velocity distributions
- 29 Short review of basic thermodynamics
- 30 Gravity and thermodynamics
- 31 Gravithermodynamic instability
- 32 Thermodynamics and galaxy clustering; ξ(r)∝r-2
- 33 Efficiency of gravitational clustering
- 34 Non-linear theory of high order correlations
- 35 Problems and extensions
- 36 Bibliography
- Part III Finite spherical systems – clusters of galaxies, galactic nuclei, globular clusters
- Part IV Finite flattened systems – galaxies
- Index
33 - Efficiency of gravitational clustering
Published online by Cambridge University Press: 05 July 2011
- Frontmatter
- Contents
- Preface
- Introduction
- Part I Idealized homogeneous systems – basic ideas and gentle relaxation
- Part II Infinite inhomogeneous systems – galaxy clustering
- 20 How does matter fill the Universe?
- 21 Gravitational instability of the infinite expanding gas
- 22 Gravitational graininess initiates clustering
- 23 Growth of the two-galaxy correlation function
- 24 The energy and early scope of clustering
- 25 Later evolution of cosmic correlation energies
- 26 N-body simulations
- 27 Evolving spatial distributions
- 28 Evolving velocity distributions
- 29 Short review of basic thermodynamics
- 30 Gravity and thermodynamics
- 31 Gravithermodynamic instability
- 32 Thermodynamics and galaxy clustering; ξ(r)∝r-2
- 33 Efficiency of gravitational clustering
- 34 Non-linear theory of high order correlations
- 35 Problems and extensions
- 36 Bibliography
- Part III Finite spherical systems – clusters of galaxies, galactic nuclei, globular clusters
- Part IV Finite flattened systems – galaxies
- Index
Summary
Some non-linear descriptions, such as the cosmic virial theorem, can be derived directly from first principles, but so far this has not been done for clustering efficiency. Here the technique is to construct a model, simple enough to solve analytically, which retains the essential physics of the problem.
Let us suppose there is a hierarchy of clustering on different well-defined levels. Consider the interaction of two adjacent levels of this hierarchy. For example, these levels could represent the clustering of globular clusters (or subgalaxies if these are formed from many globular clusters) to form galaxies. They could also represent the clustering of galaxies to form clusters of galaxies. Objects at the lower level are presumed to be tightly bound; we shall call them particles and represent them by point masses. Objects at the higher level are more loosely bound; they are the clusters.
Our analysis starts in a region which has already undergone its phase transition. The density of a cluster is large compared to the average background density. Not all the particles are in clusters. We shall consider the fate of an arbitrary vagrant particle moving through a field of clusters, and ask: ‘What is the probability that vagrant particles will be captured by clusters?’ This probability is a measure of the clustering efficiency.
The vagrant particle may be one which has been ejected from a forming cluster, or it may never have been bound.
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- Information
- Gravitational Physics of Stellar and Galactic Systems , pp. 238 - 244Publisher: Cambridge University PressPrint publication year: 1985