Figure 1

Fits to the observed rotational velocities of the Milky Way galaxy using various theories. The data [6] are represented with red crosses ($\beta =0$), blue hollow circles ($\beta =0.5$) and green hollow squares ($\beta =1.0$). The solid red line is the Newtonian fit with a central mass of $M=5\times 10^{11}{M}_{\odot }$. The blue medium dashed and green short dashed lines correspond to MOG using the values of $M=4\times 10^{10}{M}_{\odot }$, $\alpha =15.01$, $\mu =0.0313{\mathrm{kpc}}^{-1}$, and $M=5\times 10^{10}{M}_{\odot }$, $\alpha =8.89$, $\mu =0.04{\mathrm{kpc}}^{-1}$, respectively, which correspond to the values calculated according to Ref. [7], or given by Ref. [3]. The purple dash-dotted line and the yellow dash-double-dot line correspond to fits using MOND, the mass of $M=5\times 10^{10}{M}_{\odot }$, $a_0=1.21\times 10^{-8}\mathrm{cm}/{\mathrm{s}}^2$, and the interpolation functions given by Eqs. (5) and (6), respectively. Finally, the black long-dashed line is the dark matter halo prediction given in Ref. [13].