We study the thermodynamics of galaxy clusters in a modified Newtonian potential motivated by a general solution to Newton’s ‘sphere-point’ equivalence theorem. We obtain the N particle partition function by evaluating the configurational integral while accounting for the extended nature of galaxies (via the inclusion of the softening parameter ϵ into the potential energy function). This softening parameter takes care of the Galaxy-halos whose effect on structuring the shape of the galactic disc has been found recently. The spatial distribution of the particles (galaxies) is also studied in this framework. A comparison of the new clustering parameter b
+ to the original clustering parameters is presented in order to visualize the effect of the modified gravity. We also discuss the possibility of system symmetry breaking via the behavior of the specific heat as a function of temperature.
We exploit a new theory of gravity proposed by Finzi, which gives stronger interaction at large scales, to study the thermodynamic description of galaxy clusters. We employ a statistical model to deduce various thermodynamics equations of state. In addition, we analyze the behavior of clustering parameter in comparison to its standard (Newtonian) counterpart. The general distribution function and its behavior with varying strength of clustering parameter are also studied. The possibility of phase transition is also investigated and observed that a phase transition is possible though hierarchically.
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.
We exploit a new theory of gravity proposed by Finzi, which gives stronger interaction at large
scales, to study the thermodynamic description of galaxy clusters. We employ a statistical model
to deduce various thermodynamics equations of state. In addition, we analyze the behavior
of clustering parameter in comparison to its standard (Newtonian) counterpart. The general
distribution function and its behavior with varying strength of clustering parameter are also
studied. The possibility of phase transition is investigated and it is observed that a phase
transition is possible though hierarchically. We also analyze the model by comparing the results
with data available through SDSS-III, and obtain the parameters involved.
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