On Hierarchical Solutions to the BBGKY Hierarchy
Abstract
It is thought that the gravitational clustering of galaxies in the universe may approach a scaleinvariant, hierarchical form in the small separation, largeclustering regime. Past attempts to solve the BBGKY hierarchy in this regime have assumed a certain separable hierarchical form for the higher order correlation functions of galaxies in phase space. I show here that such separable solutions to the BBGKY equations must satisfy the condition that the clustered component of the solution has clustercluster correlations equal to galaxygalaxy correlations to all orders. The solutions also admit the presence of an arbitrary unclustered component, which plays no dynamical role in the largeclustering 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.
 Publication:

The Astrophysical Journal
 Pub Date:
 September 1988
 DOI:
 10.1086/166629
 Bibcode:
 1988ApJ...332...67H
 Keywords:

 Bbgky Hierarchy;
 Cosmology;
 Galactic Clusters;
 Correlation;
 Random Walk;
 Spatial Distribution;
 Astrophysics;
 GALAXIES: CLUSTERING