Hierarchical solutions to the BBGKY hierarchy

Journal Article · Thu Sep 01 04:00:00 EDT 1988 · Astrophys. J.; (United States)

DOI:https://doi.org/10.1086/166629· OSTI ID:6695982

Hamilton, A J.S.

It is thought that the gravitational clustering of galaxies in the universe may approach a scale-invariant, hierarchical form in the small separation, large-clustering regime. Past attempts to solve the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy in this regime have assumed a certain separable hierarchical form for the higher order correlation functions of galaxies in phase space. It is shown here that such separable solutions to the BBGKY equations must satisfy the condition that the clustered component of the solution has cluster-cluster correlations equal to galaxy-galaxy correlations to all orders. The solutions also admit the presence of an arbitrary unclustered component, which plays no dyamical role in the large-clustering regime. These results are a particular property of the specific separable model assumed for the correlation functions in phase space, not an intrinsic property of spatially hierarchical solutions to the BBGKY hierarchy. The observed distribution of galaxies does not satisfy the required conditions. The disagreement between theory and observation may be traced, at least in part, to initial conditions which, if Gaussian, already have cluster correlations greater than galaxy correlations. 26 references.

• Research Organization: Joint Institute for Laboratory Astrophysics, Boulder, CO (USA)
• OSTI ID: 6695982
• Journal Information: Astrophys. J.; (United States), Journal Name: Astrophys. J.; (United States) Vol. 332; ISSN ASJOA
• Country of Publication: United States
• Language: English

Related Subjects

640105* -- Astrophysics & Cosmology-- Galaxies
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BASIC INTERACTIONS
BBGKY EQUATION
CORRELATION FUNCTIONS
COSMOLOGY
DIFFERENTIAL EQUATIONS
DISTRIBUTION
EQUATIONS
FUNCTIONS
GALAXIES
GALAXY CLUSTERS
GRAVITATIONAL INTERACTIONS
INTERACTIONS
SPATIAL DISTRIBUTION