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, G N , has two additional constant parameters α and µ. We use the 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 χ 2 = 1.07. In the fitting process, only the stellar mass-to-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.

On the Gravitational Stability of the Maclaurin Disk

“…The observational values of the free parameters α and µ 0 are known from rotation curve data of spiral galaxies. It has been shown by Moffat & Rahvar (2013) that the best values for these parameters are α = 8.89 ± 0.34 and µ 0 = 0.042 ± 0.004kpc −1 . In order to study the global stability of the Maclaurin disk, in addition to the generalized Poisson equations, we need also the continuity and Euler equations in the context of MOG.…”

Compact stars in vector–tensor-Horndeski theory of gravity

“…This Lagrangian has a non-trivial coupling between the astrophysical vector field and the metric, which was not present in other vector-tensor theories of gravity [34][35][36][37][38][39]. The static spherically symmetric solutions for a vector field has been studied using the Horndeski formalism [16,17].…”

Dark Matter as a Metric Perturbation

“…[See Moffat & Rahvar [21] for MOG fits of THINGS data.] Gentile et al describe these data as "the most reliable for mass modelling, and they are the highest quality RC's currently available for a sample of galaxies spanning a wide range of luminosities."…”

“…These are two aspects of the dark matter problem [5], making this one of the most persistent problems in physics. As a consequence, many approaches have been brought to bear on the dark matter problem, typically by way of new particles [6,7], but also by way of modifications to existing theories of gravity, e.g., modified Newtonian dynamics (MOND) [8][9][10] and relativistic counterparts [11][12][13][14][15], Moffat's modified gravity (MOG), i.e., metric skew-tensor gravity (MSTG) and scalar-tensor-vector gravity (STVG) [16][17][18][19][20][21][22][23], Renormalization Group corrected General Relativity [24], and nonlocal general relativity [25]. No one disputes the existence of baryonic dark matter, e.g., brown dwarfs, black holes, and molecular hydrogen, but there is wide agreement that baryonic dark matter does not exist in large enough supply to resolve the dark matter problem [26].…”

“…Indeed, Cooperstock et al used GR instead of Newtonian gravity in fitting galactic RC's and found that the non-luminous matter in galaxies "is considerably more modest in extent than the DM extent claimed on the basis of Newtonian gravitational dynamics" [48][49][50]. And, Moffat & Rahvar used "The weak field approximation of MOG" as a perturbation of "the metric and the fields around Minkowski space-time" in fitting galactic RC's [21] and X-ray cluster mass profiles [22] without DM. Certainly MOND can be viewed in this fashion, since MOND advocates an extremely small modification to acceleration on astronomical scales in the context of flat spacetime (Newtonian gravity), and acceleration due to gravity in flat spacetime is replaced by curved spacetime in GR.…”