Testing MOdified Gravity (MOG) theory and dark matter model in Milky Way
  using the local observables
  In this paper, we have investigated one of the alternative theories to dark
matter named MOdified Gravity (MOG) by testing its ability to describe the
local dynamics of the Milky Way in vertical and transverse directions with the
baryonic matter. MOG is designed to interpret the dynamics of galaxies and
cluster of galaxies without the need for dark matter. We use local
observational data such as the vertical dispersion, rotation curve, surface
density and number density of stars in the Milky Way to obtained the parameters
of MOG and the baryonic component of MW by implementing a Bayesian approach to
the parameter estimation based on a Markov Chain Monte Carlo method. We compare
our results with the dark matter model of MW. The two models of MOG and CDM are
able to describe equally well the rotation curve and the vertical dynamics of
stars in the local MW. The best values for the free parameters of MOG in this
analysis is obtained as $\alpha = 8.99 \pm 0.02 $ and $\mu =0.054\pm 0.005$
kpc$^{-1}$. Also, we obtain the parameters of the generalized gNFW model in the
dark matter model. Our best value of bulge mass from MOG is $(1.06 \pm
0.26)\times10^{10}\rm M_{\odot}$ which is consistent with the estimations form
the microlensing observations.
