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\end{equation}  If we define the disk Mach number as the ratio of the isothermal sound speed to the keplerian orbital velocity $v_K=sqrt{GM/r}$, then we have an expression for the Mach number in terms of disk sound speed,  \begin{equation}  \mathcal{M} = \frac{v_K}{c^{\rm{iso}_s} \frac{v_K}{c^{\rm{iso}}_s}  \end{equation}