The galaxy cluster system Abell 1689 has been well studied and yields good lensing and X-ray gas data. Modified gravity (MOG) is applied to the cluster Abell 1689 and the acceleration data is well fitted without assuming dark matter. Newtonian dynamics and Modified Newtonian dynamics (MOND) are shown not to fit the acceleration data, while a dark matter model based on the Navarro-Frenk-White (NFW) mass profile is shown not to fit the acceleration data below ~ 200 kpc.
J. W. Moffat and M. H. Zhoolideh Haghighi, "Modified gravity (MOG) can fit the acceleration data for the cluster Abell 1689" (16 Nov 2016).
The introduction observes that:
MOG has passed successful tests in explaining rotation velocity data of spiral and dwarf galaxies (Moffat & Rahvar (2013)), (Zhoolideh Haghighi & Rahvar (2016)), globular clusters (Moffat & Toth (2008b)) and clusters of galaxies (Moffat & Rahvar (2014)). Recently, it was claimed (Nieuwenhuizen (2016)) that no modified gravity theory can fit the Abell 1689 acceleration data without including dark matter or heavy (sterile) neutrinos. The cluster A1689 is important, for good lensing and gas data are available and we have data from 3kpc to 3Mpc. We will show that MOND (Milgrom (1983)) does not fit the A1689 acceleration data, nor does the dark matter model based on an NFW mass profile. However, MOG does fit the A1689 acceleration data without dark matter.
The conclusion of the paper notes:
The fully covariant and Lorentz invariant MOG theory fits galaxy dynamics data and cluster data. It also fits the merging clusters Bullet Cluster and the Train Wreck Cluster (Abell 520) without dark matter (Brownstein & Moffat (2007); Israel & Moffat (2016)). A MOG application to cosmology without dark matter can explain structure growth and the CMB data (Moffat & Toth (2013)). The fitting of the cluster A1689 data adds an important success for MOG as an alternative gravity theory without dark matter.I will leave a detailed explanation of MOG theory and any analysis of this paper's conclusions for another day.