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

Jun 26, 2013
13 pages
Published in:
  • Mon.Not.Roy.Astron.Soc. 436 (2013) 1439-1451
e-Print:

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Abstract: (arXiv)
As an alternative to dark matter models, MOdified Gravity (MOG) theory can compensate for dark matter by 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 mass has a charge proportional to the inertial mass. In this work, we obtain the weak field approximation of MOG by perturbing the metric and the fields around Minkowski space-time. We derive an effective gravitational potential which yields the Newtonian attractive force plus a repulsive Yukawa force. This potential, in addition to the Newtonian gravitational constant, GNG_N, has two additional constant parameters α\alpha and μ\mu. We use the THINGS catalog of galaxies and fix the two parameters α\alpha and μ\mu of the theory to be α=8.89±0.34\alpha =8.89 \pm 0.34 and μ=0.04±0.004kpc1\mu =0.04 \pm 0.004 {\rm kpc}^{-1}. We then apply the effective potential with the fixed universal parameters to the Ursa-Major catalog of galaxies and obtain good fits to galaxy rotation curve data with an average value of χ2ˉ=1.07\bar{\chi^2} = 1.07 . In the fitting process, only the stellar mass-to-light ratio (M/L)(M/L) of the galaxies is a free parameter. As predictions of MOG, our derived M/LM/L is shown to be correlated with the color of galaxies, and we 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.
Note:
  • 14 pages, 5 figures, v2: Minor corrections, accepted in MNRAS
  • galaxy: rotation
  • approximation: weak field
  • gravitation: potential
  • force: Lorentz
  • force: Yukawa
  • space-time: Minkowski
  • dark matter
  • effective potential
  • covariance
  • Einstein