Virial theorem in clusters of galaxies with MOND

TL;DR

This paper investigates the virial theorem in galaxy clusters under MOND, showing that with proper pressure corrections and realistic baryonic profiles, MOND can match observed cluster dynamics without dark matter.

Contribution

It demonstrates that MOND can reproduce galaxy cluster dynamics similar to Newtonian gravity with dark matter when pressure corrections and accurate baryonic profiles are applied.

Findings

Solutions exist for MOND in galaxy clusters that align with observations.

Pressure corrections and realistic baryonic profiles are crucial for MOND's success.

Previous discrepancies are due to inadequate assumptions and parameters.

Abstract

A specific modification of Newtonian dynamics known as MOND has been shown to reproduce the dynamics of most astrophysical systems at different scales without invoking non-baryonic dark matter (DM). There is, however, a long-standing unsolved problem when MOND is applied to rich clusters of galaxies in the form of a deficit (by a factor around two) of predicted dynamical mass derived from the virial theorem with respect to observations. In this article we approach the virial theorem using the velocity dispersion of cluster members along the line of sight rather than using the cluster temperature from X-ray data and hydrostatic equilibrium. Analytical calculations of the virial theorem in clusters for Newtonian gravity+DM and MOND are developed, applying pressure (surface) corrections for non-closed systems. Recent calibrations of DM profiles, baryonic ratio and baryonic ($\beta $ model or others) profiles are used, while allowing free parameters to range within the observational constraints. It is shown that solutions exist for MOND in clusters that give similar results to Newton+DM -- particularly in the case of an isothermal $\beta $ model for $\beta =0.55-0.70$ and core radii $r_c$ between 0.1 and 0.3 times $r_{500}$ (in agreement with the known data). The disagreements found in previous studies seem to be due to the lack of pressure corrections (based on inappropriate hydrostatic equilibrium assumptions) and/or inappropriate parameters for the baryonic matter profiles.