Virial theorem in clusters of galaxies with MOND

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.

accepted to be published in MNRAS

References in corpus (20)

• Concentration, Spin and Shape of Dark Matter Haloes as a Function of the Cosmological Model: WMAP1, WMAP3 and WMAP5 results
• Virial Scaling of Massive Dark Matter Halos: Why Clusters Prefer a High Normalization Cosmology
• The Representative XMM-Newton Cluster Structure Survey (REXCESS) of an X-ray Luminosity Selected Galaxy Cluster Sample
• The relation between velocity dispersion and mass in simulated clusters of galaxies: dependence on the tracer and the baryonic physics
• THINGS about MOND
• Andromeda Dwarfs in Light of MOND
• Galactic rotation curves, the baryon-to-dark-halo-mass relation and space-time scale invariance
• LoCuSS: Hydrostatic Mass Measurements of the High-$L_X$ Cluster Sample -- Cross-calibration of Chandra and XMM-Newton
• MOND rotation curves of very low mass spiral galaxies
• Testing gravity with motion of satellites around galaxies: Newtonian gravity against Modified Newtonian Dynamics
• The velocity distribution of SDSS satellites in MOND
• Biases in galaxy cluster velocity dispersion and mass estimates in the small number of galaxies regime
• Cluster cosmology with the NIKA2 SZ Large Program
• Velocity dispersion and dynamical masses for 388 Galaxy Clusters and groups. Calibrating the $M_{\mathrm{SZ}}$--$M_{\mathrm{dyn}}$ scaling relation for the PSZ2 sample
• A Simple Physical Model for the Gas Distribution in Galaxy Clusters
• Dynamics of Elliptical Galaxies with Planetary Nebulae in Modified Newtonian Dynamics
• X-Ray Studies of the Abell 3158 Galaxy Cluster with eROSITA
• Asymptotic kinematics of Globular Clusters: the emergence of a Tully-Fisher relation
• Low-surface-brightness spheroidal galaxies as Milgromian isothermal spheres
• Exact semianalytical calculation of rotation curves with Bekenstein-Milgrom nonrelativistic MOND

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• On the origin of extreme trans-Neptunian objects within Modified Newtonian Dynamics
• Consistent cosmological structure formation on all scales in relativistic extensions of MOND