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$\begin{figure} \par\includegraphics[width=8.4cm,clip]{7372fig1.ps}\end{figure}$ Figure 1: Separation of stable from unstable perturbations of a self-gravitating disk embedded in a live dark halo. $Q{_{\rm T}}$ denotes the usual Toomre stability index and $\lambda$ is the wavelength of the perturbation measured in units of $\lambda _{\rm crit}$ . Unstable perturbations are located in the parameter space below the dividing lines. Lines are shown for values of the $\beta$ parameter, which describes the dynamical responsiveness of the dark halo, $\beta =$ 0, 0.2, 0.25, and 0.3, respectively.
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In the text