Correlation functions for extended mass galaxy clusters

Abstract

The phenomenon of clustering of galaxies on the basis of correlation functions in an expanding Universe is studied by using equation of state, taking gravitational interaction between galaxies of extended nature into consideration. The partial differential equation for the extended mass structures of a two-point correlation function developed earlier by Iqbal, Ahmad and Khan is studied on the basis of assigned boundary conditions. The solution for the correlation function for extended structures satisfies the basic boundary conditions, which seem to be sufficient for understanding the phenomena, and provides a new insight into the gravitational clustering problem for extended mass structures.Comment: 3 pages, no figure

Thermodynamics and phase transitions in galaxy clustering

“…The two particle correlation function in this context is the probability of finding two particles together within a given volume. The specific form for this correlation function has been defined by (Iqbal et al ). which then yields (for structureless galaxies in the ϵ → 0 limit) (Yang et al 2011; Saslaw & Ahmed ).…”

The peculiar velocity and temperature profile of galaxy clusters

“…In order to understand the simple formalism of peculiar velocity, we make use of quasi equilibrium thermodynamics in which quasi equilibrium evolution takes place through a sequence of quasi equilibrium states whose properties change with time (Saslaw & Hamilton. 1984, Saslaw et al 1990, Ahmad et al 2002, Iqbal et al 2006and Iqbal et al 2012. cluster size R, the average kinetic energy of peculiar motions of N galaxies in a cluster can reasonably be connected with average kinetic temperature T of a cluster (Saslaw.…”

“…The observational studies (Rines & Diaferio 2006), N-body simulations (Wojtak et al 2005;Mamon et al 2004;Cuesta et al 2008) and a combination of both (Mahajan et al 2011) have shown that virialized clusters in gravitating systems are surrounded by infall zones from which most of the galaxies move into the relaxed cluster, as is evident from the earlier result of (Gunn & Gott 1972). In order to understand the simple formalism of a peculiar velocity, we make use of quasi-equilibrium thermodynamics in which quasi-equilibrium evolution takes place through a sequence of quasi-equilibrium states whose properties change with time (Saslaw & Hamilton 1984;Saslaw et al 1990;Ahmad et al 2002;Iqbal et al 2006Iqbal et al , 2012.…”

“…1984, Saslaw & Fang. 1996, Ahmad et al 2002, Iqbal et al 2006, Iqbal et al 2011 and Iqbal et al 2012). The time scale for cluster formation is much larger than the time scale of a galaxy to cross the cluster.…”

“…The auto-correlation functions, rapid computer simulations, theoretical analysis and observational evidence have added considerable knowledge to this field. Earlier studies on the applicability of statistical mechanics and thermodynamics to the cosmological many-body problem have yielded many interesting results and have also generated many related questions (Saslaw & Hamilton 1984;Saslaw & Fang 1996;Ahmad et al 2002;Iqbal et al 2006Iqbal et al , 2011Iqbal et al , 2012. The timescale for cluster formation is much longer than the timescale for a galaxy to cross the cluster.…”