Spatial galaxy distribution function for a three-component system

Abstract

We derive the distribution function and the allied thermodynamic quantities for a system of galaxies with three mass species. A new clustering parameter b 3 that inherently takes into account the masses and the number of galaxies of each kind, emerges directly from the calculations. Our general conclusion is that the inclusion of the third component does not significantly effect the overall features of the distribution function.

Critical phenomena in the cosmological many-body problem

“…The reason that (T c ) mul /(T c ) sin stays nearly constant as N 2 /N 1 increases is that a higher value of N 2 /N 1 corresponds to a system close to a single-component one with the difference that it is now dominated by more massive galaxies. This behaviour is corroborated by the observations in Ahmad et al (2006b) and Malik et al (2009Malik et al ( , 2011, wherein it is inferred that while the dominance of more massive galaxies initiates clustering at an earlier stage, collective phenomena dominate at later stages, leading to a minimal effect on the overall features of the distribution function. This is further supported by the analysis of Itoh, Inagaki & Saslaw (1990), wherein the critical temperature is expressed in terms of the kinetic energy of peculiar motion of N galaxies in a volume V as…”

“…The statistical mechanical description of the cosmological many‐body problem was extended to the simplest multicomponent system (two‐component system) by Ahmad et al (2006b) and Malik et al (2009) for point‐mass and extended structures, respectively. The description has recently been extended to a three‐component system (Malik et al 2011), wherein it has been shown that the inclusion of the third component does not significantly change the overall features of the distribution function. Thus, for convenience, we use the results of Ahmad et al (2006b) for the internal energy where N 1 and N 2 are the numbers of particles of mass m 1 and m 2 , respectively, so that N = N 1 + N 2 is the total number of particles in the whole system.…”

“…An attempt to understand the phase transitions of gravitational galaxy clustering on the basis of statistical mechanics was made by Saslaw & Ahmad (2010). The statistical mechanical description of gravitational galaxy clustering was pioneered by Ahmad, Saslaw & Bhat (2002) and refined from time to time by their co‐workers, adding many new features all the time (Leong & Saslaw 2004; Sivakoff & Saslaw 2005; Ahmad, Saslaw & Malik 2006a; Ahmad, Malik & Masood 2006b; Malik et al 2009; Malik, Nisar & Ahmad 2011; Yang & Saslaw 2011). The new and improved statistical mechanical description of gravitating systems not only provides a more fundamental basis for its thermodynamic predecessor (reviewed in Saslaw 2000), but also provides insights into many new aspects of galaxy clustering.…”

Entropy change and phase transitions in an expanding Universe

“…These symmetry breaking phase transitions play an important role in cosmology. Some studies done on phase transitions like those of Saslaw & Ahmad (2010), Malik et al (2011), andYang &Saslaw (2011) have improved the statis-tical mechanical description of gravitating systems and provide a basic understanding for their thermodynamic properties. In this work, we aim to study the phase transition of gravitational clustering of galaxies on the basis of change in entropy.…”

Modified theory of gravity and clustering of multi-component system of galaxies

“…The techniques of statistical mechanics can also used to analyze the clustering of different types of galaxies. In fact, the clustering of different kind of galaxies has been studied using a multi-component system [32,33,34]. The galaxies in this multi-component system were again assumed to interact through a Newtonian potential.…”