Convergence and shear statistics in galaxy clusters as a result of Monte Carlo simulations

In this paper the influence of galaxy cluster halo environment on the deflection properties of its galaxies is investigated. For this purpose circular and elliptical projected cluster haloes obeying Einasto density profiles are modelled in the Λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\varLambda$\end{document}CDM cosmological model. By Monte-Carlo simulations external shear and convergence are calculated for random positions of a test galaxy within its cluster. Throughout the simulations the total virial mass, profile concentration and slope parameters are varied both for cluster and its galaxies. The cluster is composed of smooth matter distribution (intergalactic gas and dark matter) and randomly placed galaxies. As a result of multiple simulation runs robust statistical estimations of external shear and convergence are derived for variable cluster characteristics and its redshift. In addition, the models for external shear and convergence are applied for the galaxy lens seen through the cluster IRC-0218.