DISTRIBUTION FUNCTION OF GALAXIES FOR TWO-COMPONENT SYSTEMS

We extend the statistical mechanical theory of cosmological many-body problem to a system consisting of two kinds of galaxies with different masses. The general partition function for such a two-component system, in the grand canonical ensemble, is developed. From this partition function various thermodynamical quantities and distribution functions are evaluated. A quantity b_m, called the clustering parameter for the two-component system, which inherently takes into account the ratio of the number of particles (galaxies) of each kind and their masses, emerges directly from the calculations. Various clustering phenomena can be explained on the basis of this parameter. We find these results in agreement with the available N-body simulation results as well as the observational distribution function determined from the 2MASS survey. Besides, our distribution function, for the two-component system, makes these comparisons more objective and easily comprehensible.