A simplistic approach to the study of two-point correlation function in galaxy clusters

Abstract

We developed the functional form of the two-point correlation function under the approximation of fixed particle number density ¯n. We solved the quasi-linear partial differential equation (PDE) through the method of characteristics to obtain the parametric solution for the canonical ensemble. We attempted many functional forms and concluded that the functional form should be such that the two-point correlation function should go to zero as the value of system temperature increases or the separation between the galaxies becomes large. Also, we studied the graphical behavior of the developed two-point correlation function for large values of temperature T and spatial separation r. The behavior of the two-point function was also studied from the temperature measurement of clusters in the redshift range of 0.023 − 0.546.

Statistical description of galaxy clusters in Finzi model of gravity

“…We can employ statistical methods to find the statistical distribution of matter at largest possible scales [8]. Recently there has been a lot of progress on the study of the effect of modified gravity laws on the clustering of galaxies using statistical mechanics [9][10][11][12][13][14][15][16][17][18][19][20]. The effect of the modifications incorporated has been anticipated in the strength of the clustering parameter b.…”

Study of the Large Scale Structure Through Modified Gravity Theory Using Statistical Mechanics

“…The statistical method can be emplyed to study the mass distribution on the largest possible scale [9]. In recent past there has been a tremendous effort to study the effect of modified gravity theories on the galaxy clustering through statistical and thermodynamic methods [10][11][12][13][14][15][16][17][18][19][20][21][22]. It has been observed that the modified theories of gravity does affect the clustering process through a change in a parameter that is related to the strength of correlation called clustering parameter, originally defined as the ratio of Kinetic to potential energy, b = K/2W .…”