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.