Mathematics – Logic
Scientific paper
Dec 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992daec.conf..263b&link_type=abstract
In Distribution of Matter in the Universe, 2nd DAEC mtg, ed. G.A. Mamon and D. Gerbal (Meudon: Obs. de Paris) p. 263-268
Mathematics
Logic
Scientific paper
We present theoretical results on the correlation of condensed objects starting from general assumptions on the matter correlations. We assume that the matter correlation functions have the so-called "hierarchical" form given by a tree development in powers of the two-body correlation functions. We were able to calculate the two and three-body correlation functions of condensed objects which appear to have the same topological dependences (tree-developments), with a strength depending only on their scaling parameter X proportional to M/R^{3-gamma} where M is the mass of the object, R its size, and gamma is the power-law index of the 2-body correlation function. This permits to describe matter, galaxy and cluster correlation properties in the same frame, in good accordance with the observations. Quantitative results concerning the value of the observed bias and its luminosity dependence are obtained: For a galaxy 2-d catalogue we determine an observed value b=1.5 - 3 independent of the catalogue depth, whereas the particular model prediction is b approx 3; and Q_3, that measures the strength of the 3-body correlation function, is found to be about 0.8 to 1.
Bernardeau Francis
Schaeffer Richard
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