The MOG weak field approximation and observational test of galaxy rotation curves

Abstract

As an alternative to dark matter models, Modified Gravity (MOG) theory is a covariant modification of Einstein gravity. The theory introduces two additional scalar fields and one vector field. The aim is to explain the dynamics of astronomical systems based only on their baryonic matter. The effect of the vector field in the theory resembles a Lorentz force where each particle has a charge proportional to its inertial mass. The weak field approximation of MOG is derived by perturbing the metric and the fields around Minkowski space-time. We obtain an effective gravitational potential which yields the Newtonian attractive force plus a repulsive Yukawa force. This potential, in addition to the Newtonian gravitational constant, GN, has two additional constant parameters α and μ. We use The HI Nearby Galaxy Survey catalogue of galaxies and fix the two parameters α and μ of the theory to be α = 8.89 ± 0.34 and μ = 0.042 ± 0.004 kpc-1. We then apply the effective potential with the fixed universal parameters to the Ursa Major catalogue of galaxies and obtain good fits to galaxy rotation curve data with an average value of χ2 = 1.07. In the fitting process, only the stellar massto- light ratio (M/L) of the galaxies is a free parameter. As predictions of MOG, our derived M/L is shown to be correlated with the colour of galaxies.We also fit the Tully-Fisher relation for galaxies. As an alternative to dark matter, introducing an effective weak field potential for MOG opens a new window to the astrophysical applications of the theory. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.