Mass Discrepancy In Clusters Research Articles

The virial theorem in Eddington-Born-Infeld gravity

We consider the possibility that the Eddington-Born-Infeld (EBI) modified gravity provides an alternative explanation for the mass discrepancy in clusters of galaxies. For this purpose we derive the modified Einstein field equations, finding an additional “geometrical mass” term which provides an effective contribution to the gravitational binding energy. Using some approximations and assumptions for weak gravitational fields, and taking into account the collisionless relativistic Boltzmann equation, we derive a generalized version of the virial theorem in the framework of EBI gravity. We show that the “geometrical mass” term may account for the well known virial mass discrepancy in clusters of galaxies. We also derive the velocity dispersion relation for galaxies in the clusters, which could provide an efficient method for testing EBI gravity from astrophysical observations.

Ultra-diffuse cluster galaxies as key to the MOND cluster conundrum

MOND reduces greatly the mass discrepancy in clusters of galaxies, but does leave a consistent global discrepancy of about a factor of two. It has been proposed, within the minimalist and purist MOND, that clusters harbor some indigenous, yet-undetected, cluster baryonic (dark) matter (CBDM). Its total amount has to be comparable with that of the observed hot gas. Following an initial discovery by van Dokkum & al. (2015a), Koda & al. (2015) have recently identified more than a thousand ultra-diffuse galaxy-like objects (UDGs) in the Coma cluster. Robustness of the UDGs to tidal disruption seems to require, within Newtonian dynamics, that they are much more massive than their observed stellar component. Here, I propound that a considerable fraction of the CBDM is internal to UDGs, which endows them with robustness. The rest of the CBDM objects formed in now-disrupted kin of the UDGs, and is dispersed in the intracluster medium. While the discovery of cluster UDGs is not in itself a resolution of the MOND cluster conundrum, it lends greater qualitative plausibility to CBDM as its resolution, for reasons I discuss. Alternatively, if the UDGs are only now falling into Coma, their large size and very low surface brightness could result from the adiabatic inflation due to the MOND external-field effect, as described in Brada & Milgrom (2000). I also consider briefly solutions to the conundrum that invoke more elaborate extensions of purist MOND, e.g., that in clusters, the MOND constant takes up larger-than-canonical values of the MOND constant.

Virial mass in warped DGP-inspired $\mathcal{L}(R)$ gravity

A version of the virial theorem is derived in a brane-world scenario in the framework of a warped DGP model where the action on the brane is an arbitrary function of the Ricci scalar, \(\mathcal{L}(R)\). The extra terms in the modified Einstein equations generate an equivalent mass term (geometrical mass), which give an effective contribution to the gravitational energy and offer viable explanation to account for the virial mass discrepancy in clusters of galaxies. We also obtain the radial velocity dispersion of galaxy clusters and show that it is compatible with the radial velocity dispersion profile of such clusters. Finally, we compare the result of the model with \(\mathcal{L}(R)\) gravity theories.

Generalized virial theorem in warped DGP brane-world

We generalize the virial theorem to the warped DGP brane world scenario and consider its implications on the virail mass. In this theory the four dimensional scalar curvature term is included in the bulk action and the resulting four dimensional effective Einstein equation is augmented with extra terms which can be interpreted as geometrical mass, contributing to the gravitational energy. Estimating the geometrical mass using the observational data, we show that these geometric terms may account for the virial mass discrepancy in clusters of galaxies. Finally, we obtain the radial velocity dispersion of galaxy clusters and show that it is compatible with the radial velocity dispersion profle of such clusters.

The generalized virial theorem inf(R) gravity

We generalize the virial theorem inf(R) modified gravity using the collisionless Boltzmann equation. We find supplementarygeometric terms in the modified Einstein equation providing an effective contribution tothe gravitational energy. The total virial mass is proportional to the effective massassociated with the new geometrical term, which may account for the well-known virialtheorem mass discrepancy in clusters of galaxies. The model predicts that thegeometric mass and its effects extend beyond the virial radius of the clusters.We also consider the behavior of the galaxy cluster velocity dispersion inf(R) models. The metric inside the galactic cluster, as well as the Lagrangian of the modifiedgravity model, are obtained in terms of quantities directly related to the physical propertiesof the clusters, and which can be determined from astrophysical observations. Thus, thef(R) virial theorem can be an efficient tool in observationally testing the viability of this class ofgeneralized gravity models.

Gravitational lenses and unconventional gravity theories

We study gravitational lensing by clusters of galaxies in the context of the generic class of unconventional gravity theories of the scalar--tensor type. For positive energy scalar fields with any dynamics, the bending of light by a weakly gravitating system (galaxy or cluster) is always smaller than the bending predicted by general relativity for the mass of visible and hitherto undetected matter (but excluding the scalar field energy). The same conclusion obtains within general relativity if a nonnegligible part of the mass in clusters is in coherent scalar fields, {\it i.e.\/} Higgs fields. Thus the observational claim that clusters of galaxies deflect light much more strongly than would be expected from the observable matter contained by them, cannot be interpreted in terms of some scalar-tensor unconventional gravity theory with no dark matter. If the observations eventually show that the matter distribution inferred via general relativity from the lensing is very much like that determined from the dynamics of test objects, then scalar--tensor unconventional gravity will be irrelevant for understanding the mass discrepancy in clusters. However, even a single system in which the dynamically determined mass significantly exceeds the lensing mass suggested by general relativity, would be very problematic for the dark matter picture, but would be entirely consistent with unconventional scalar--tensor gravity.

On the Mass Discrepancy in Clusters of Galaxies

AbstractThe change of the slope in the luminosity function of the members of the Coma cluster near M ≈ — 21 is interpreted as an evolutionary effect. Originally there should have existed many luminous objects now being evolved to invisible masses in form of “black holes”. If the faint part of the luminosity function is extrapolated beyond M ≈ — 21 the observed discrepancy in the mass of the cluster determined by the virial theorem and by summing up the individual masses of the galaxies vanishes. The comparison of the hypothetical frequency of the black holes with the estimated numbers of the strong extragalactic radio sources encourages us to the assumption of a relation between the two groups of objects.