Generalized theory of clustering of extended galaxies with core halos

Abstract

We discuss the clustering of core halo-galaxies of radius predicted by gravitational lensing. We appeal to a blend of recent (1) mathematical results and (2) statistical mechanics techniques. The exact configurational integrals of extended galaxies is evaluated together with the pertinent partition functions, the corresponding thermodynamics, and the distribution function. We are motivated by data regarding observational deflections and measured Einstein radius in gravitational microlensing and macrolensing. The halo size comparable with that of the Einstein radius or the Schwarzschild one, is taken as the lower limit of the configurational integral. The work may provide new insight with regards to gravitational lensing. Giant arcs produced by gravitational lensing, as observed from clusters of galaxies, seem to require the inclusion of substantial quadruple and higher multipole moments in the cluster potential. This opens a possibility of ”modified gravities”, in clustering studies that compare data associated to gravitational lensing.