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

TL;DR

This paper presents a new analytical approach to modeling the two-point correlation function in galaxy clusters, considering temperature effects and spatial separation, with solutions derived via PDE methods.

Contribution

It introduces a parametric solution for the two-point correlation function using PDEs and explores its behavior under varying temperature and separation conditions.

Findings

Correlation function decreases with increasing temperature.

Correlation diminishes as galaxy separation increases.

Graphical analysis supports theoretical predictions.

Abstract

We developed the functional form of the two-point correlation function under the approximation of fixed particle number density n(bar). 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 to 0.546.