\begin{table}%t3
\par
      \caption{Equations to derive the disk/torus properties from observations. 
	Velocities are in units of km~s$^{-1}$, radii in pc,
	masses in $M_{\odot}$, and star formation rates in $M_{\odot}$~yr$^{-1}$.}
         \label{tab:equations}
       \begin{tabular}{l}
        \hline \hline
        {\rm Present\ collisional\ torus}\\
	\hline
	$Q^{\rm pr}=(v_{\rm turb}^{\rm pr}/v_{\rm rot})~(M_{\rm dyn}/M_{\rm gas}^{\rm pr})$\\	$\vartheta^{\rm pr}=1.9 \times 10^{-9} Q^{\rm pr} R/(v_{\rm rot} v_{\rm turb}^{\rm pr} M_{\rm cl})$\\
	$\dot{M}^{\rm pr}=2~(v_{\rm turb}^{\rm pr})^{3}/(G Q^{\rm pr} \vartheta^{\rm pr})$\\\hline
	{\rm Massive\ turbulent\ gas\ disk}\\
	\hline
	$Q^{\rm disk}=9674~\dot{M}_*^{-\frac{2}{11}} v_{\rm rot}$\\
	$M_{\rm gas}^{\rm disk}=3.97 \times 10^{5} \dot{M}_*^{\frac{5}{11}} R$\\
	$v_{\rm turb}^{\rm disk}=18.2~\dot{M}_*^{\frac{3}{11}}$\\
	\hline
	{\rm Initial\ collisional\ torus}\\
	\hline
	$\dot{M}^{\rm init}=\dot{M} (M_{\rm gas}^{\rm disk}/M_{\rm gas}^{\rm pr})^{2}$\\
	$Q^{\rm init}=Q^{\rm pr} M_{\rm gas}^{\rm pr}/M_{\rm gas}^{\rm disk}$\\
	$\vartheta^{\rm init}=\vartheta^{\rm pr}~M_{\rm gas}^{\rm pr}/M_{\rm gas}^{\rm disk}$\\
	\hline
        \end{tabular}
\end{table}