\begin{table}%t1 \caption{Parameters of models~A,~B,~C (from Kaufmann \&~Contopoulos \cite{Kaufmann1996}). The units are $\mbox{km}^2~\mbox{s}^{-2}~\mbox{kpc}^{-1}$ for $A$, $\mbox{kpc}^{-1}$ for $\varepsilon_{\rm s}$, $\varepsilon_{\rm d}$, $\kappa_1$ and $\kappa_2$, $\mbox{kpc}$ for $r_1$, $r_2$, $\Delta$, $a$, $b$, $c$, and $b_{\rm h}$, $10^{10}~M_\odot$ for $M_{\rm h}$, $M_{\rm b}$, $\mbox{km}~\mbox{s}^{-1}~\mbox{kpc}^{-1}$ for $\Omega_{\rm p}$, and $M_\odot$/pc$^2$ for $\Sigma_0$. Model~A$'$ has the same parameters as model~A, except for the spiral amplitude $A=1000$ and the pitch angle $i_0=-9^\circ$. Model~B$'$ has the same parameters as model~B except for $A=2500$, $M_{\rm b}=0.09$, $i_0=-8^\circ$, $\Omega_{\rm p}=30.5~$$\mbox{km}~\mbox{s}^{-1}~\mbox{kpc}^{-1}$.} \small%\centering \par \begin{tabular}[c]{c c c c c c c c c} \hline \hline \multicolumn{9}{c}{Model~A} \\ \hline \hline Spiral: &~A & $\varepsilon_{\rm s}$ & $i_0$ & $r_1$ & $r_2$ & $\kappa_1$ & $\kappa_2$ & $\Delta$ \\ & 2000 & 0.4 & --10$^\circ$ & 1.5 & 10.6 & 1 & 1 & 0.1 \\ ~Bar: & $M_{\rm b}$ & $a$ & $b$ & $c$ & $\Omega_{\rm p}$ & & & \\ & 1.5 & 5.5 & 2.1 & 0.55 & 43.6 & & & \\ Disk: & $\Sigma_0$ & $\varepsilon_{\rm d}$ & & & & & & \\ & 750 & 0.235 & & & & & & \\ Halo: & $M_{\rm h}$ & $b_{\rm h}$ & & & & & & \\ & 27.5 & 12 & & & & & & \\ \hline \multicolumn{9}{c}{Model~B} \\ \hline Spiral: &~A & $\varepsilon_{\rm s}$ & $i_0$ & $r_1$ & $r_2$ & $\kappa_1$ & $\kappa_2$ & $\Delta$ \\ & 9000 & 1.2 & --10$^\circ$ & 3 & 5.6 & 0.5 & 0.5 & 0.1 \\ ~Bar: & $M_{\rm b}$ & $a$ & $b$ & $c$ & $\Omega_{\rm p}$ & & & \\ & 0.18 & 3 & 0.4 & 0.3 & 32.2 & & & \\ Disk: & $\Sigma_0$ & $\varepsilon_{\rm d}$ & & & & & & \\ & 250 & 0.305 & & & & & & \\ Halo: & $M_{\rm h}$ & $b_{\rm h}$ & & & & & & \\ & 1.0 & 9 & & & & & & \\ \hline \multicolumn{9}{c}{Model~C} \\ \hline Spiral: &~A & $\varepsilon_{\rm s}$ & $i_0$ & $r_1$ & $r_2$ & $\kappa_1$ & $\kappa_2$ & $\Delta$ \\ & 3000 & 0.4 & --6$^\circ$ & 1 & 10 & 0.5 & 0.5 & 0.1 \\ ~Bar: & $M_{\rm b}$ & $a$ & $b$ & $c$ & $\Omega_{\rm p}$ & & & \\ & 1.2 & 4.8 & 1.6 & 0.48 & 54.2 & & & \\ Disk: & $\Sigma_0$ & $\varepsilon_{\rm d}$ & & & & & & \\ & 1475 & 0.185 & & & & & & \\ Halo: & $M_{\rm h}$ & $b_{\rm h}$ & & & & & & \\ & 60.0 & 35 & & & & & & \\ \hline \end{tabular} \end{table}