Fluctuation theory, critical phenomena and gravitational clustering of galaxies

Abstract

We investigate the phenomenon of clustering of galaxies in an expanding universe by applying the fluctuation theory. We evaluate the fluctuation moments for the number of particles as well as the correlated fluctuations for number and energy of particles (galaxies), clustering under their mutual gravitation. The correlated fluctuations \(\langle \Delta N\Delta U\rangle \) show interesting results. The value of \(\langle \Delta N\rangle \) can be both positive and negative, because it is the difference between N and the mean value of N. A negative \(\langle \Delta N\rangle \) corresponds to regions of underdensity and a positive \(\langle \Delta N\rangle \) corresponds to regions of overdensity, as described by the clustering parameter b. The present work is concerned with the region \(b\ge 0\), at which gravitational interaction has already started causing the galaxies to cluster. Thus, for this work, the value of \(\langle \Delta N\rangle \) is positive. Similarly, the energy fluctuations \(\langle \Delta U\rangle \) can also be both positive and negative. For large correlations, the overdense regions typically have negative total energy, and the underdense regions have usually positive total energy. The critical value at which this switch occurs has been calculated analytically. The results obtained by fluctuation theory closely match those obtained earlier by specific heat analysis and Lee-Yang theory. The evaluation has been extended to multicomponent systems, having a variety of masses. It has been found that the gravitational clustering of galaxies is more sensitive to mass ratios and less sensitive to the number densities of galaxies. This means there is little effect of \(\nu \) (number density), but a significant effect of \(\mu \) (mass) of galaxies on the clustering phenomenon. The clustering of galaxies is quicker when the mass of individual galaxies increases. They become nuclei for condensation. As the mass of galaxies increases, the transition from positive to negative energy occurs at a higher stage of clustering than in a single-component system.