Virial theorem in clusters of galaxies with MOND

ABSTRACT A specific modification of Newtonian dynamics known as MOND has been shown to reproduce the most astrophysical systems at different scales without invoking non-baryonic dark matter (DM). There is, however, a long-standing unsolved problem when is applied rich clusters galaxies in form deficit (by factor around two) predicted dynamical mass derived from virial theorem with respect observations. In this article, we approach using velocity dispersion cluster members along line sight rather than temperature X-ray data and hydrostatic equilibrium. Analytical calculations for gravity + DM are developed, applying pressure (surface) corrections non-closed systems. Recent calibrations profiles, baryonic ratio, (β model or others) profiles used, while allowing free parameters range within observational constraints. It that solutions exist give similar results Newton – particularly case an isothermal β = 0.55–0.70 core radii rc between 0.1 0.3 times r500 (in agreement data). The disagreements found previous studies seem be due lack (based on inappropriate equilibrium assumptions) and/or profiles.