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
23 - Growth of the two-galaxy correlation function
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
Two are better than one; because they have a good reward for their labour.
EcclesiastesIf we look out from any point in an isotropic, homogeneous Universe it must appear to expand in the same way. This expansion, mentioned in Section 21, has the form H(t)x with H = Ṙ/R when the coordinate system is chosen to coincide with a point of zero systematic motion.
To see this pretend to be a ‘fundamental observer’ at point O, moving with the average flow. Looking out at time t to an arbitrary point P along the position vector x = OP, you see the velocity v(x, t) of P relative to you. Another fundamental observer is moving with the flow at O′ and his velocity relative to you is v(s, t) where s = OO′. (The reader may find it helpful to draw a diagram.) He measures the velocity of the same point P, located at x′ = x - s in his coordinate system, and finds it to be v′(x′, t) = v′(x - s, t) = v(x, t) - v(s, t). Now, since the Universe is homogeneous and isotropic, v′ must be the same function of x′ and t that v is of x and t. Therefore, v(x - s, t) = v(x, t) - v(s, t). By inspection the solution of this functional equation is that the velocity is a linear function of position, so it has the form v = f(t)x = Ẉ.
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- Chapter
- Information
- Gravitational Physics of Stellar and Galactic Systems , pp. 163 - 170Publisher: Cambridge University PressPrint publication year: 1985