X-ray gas in the galaxy cluster Abell 2029: conformal gravity versus dark matter

Abstract

Conformal gravity has a weak-field limit that augments the Newtonian potential -GM/R by a linear potential γc 2 R/2. Mannheim has shown that an appropriate choice of y enables a satisfying fit to the flat rotation curves of large spiral galaxies and simultaneously to the rising rotation curves of low surface brightness galaxies, without invoking dark matter. Here, we extend to larger scales the comparison of Newtonian and conformal gravity by analysis of X-ray gas in the Abell 2029 galaxy cluster. The Newtonian analysis yields a mass profile rising roughly as M α R 2 from 10 10 M ⊙ at 2kpc to 10 14 M ⊙ at 200kpc, and this can be interpreted as the profile of an extensive dark matter halo that dominates the cluster potential. In conformal gravity, the potential is non-uniform inside a spherical shell, so that both interior and exterior mass distributions must be taken into account. We derive the conformal gravity potential both inside and outside a spherical shell, enabling the evaluation of potentials for spherically symmetric mass distributions. A conformal gravity analysis of X-ray gas in Abell 2029 then yields a total mass profile that rises from 10 10 M ⊙ at 2kpc to 1.4 x 10 12 M ⊙ at 30 kpc, and then remains roughly constant out to 300 kpc. With this mass profile, conformal gravity is able to bind the X-ray gas with no need for dark matter. However, integrating the X-ray gas density profile gives a baryon mass of 10 13 M ⊙ inside 200 kpc, nearly 10 times more than what is required to hold the hot gas in hydrostatic equilibrium. This discrepancy may rule out conformal gravity unless there is a significant breakdown of hydrostatic equilibrium in the outskirts of the potential well. The required velocities, V ∼ 2000 km s -1 , may be observable via Doppler profiles in high-resolution X-ray spectroscopy. It is also possible that the mass distribution outside the cluster significantly reduces conformal gravity in the cluster outskirts. Our approximate treatment of this effect suggests that it is negligible, but a more sophisticated analysis might yield a different conclusion.