All Figures

$\begin{figure} \par\includegraphics[width=8.25cm,clip]{fig0a.ps}\hspace*{1cm} \includegraphics[width=8.25cm,clip]{fig0b.ps}\end{figure}$ Figure 1: Schematic diagram for the Keplerian specific angular momentum $\ell _{_{\rm K}}$ in a Schwarzschild-de Sitter spacetime ( left panel) and the corresponding effective potential W ( right panel) once a constant value for $\ell$ has been chosen (cf. Fig. 2). The figure reports the different radial locations that are relevant for our discussion: the inner and outer cusp points $r_{\rm ci}, r_{\rm co}$ , the inner and outer radii for the torus $r_{\rm in}, r_{\rm out}$ , the inner and outer marginally stable orbits $r_{\rm ms,i}, r_{\rm ms,o}$ , and the location of the maximum pressure in the torus $r_{\rm max}$ (see text for details). Note that $r_{\rm ci}, r_{\rm co}$ and $r_{\rm max}$ are determined once a value for the constant specific angular momentum has been chosen (this is shown with the long-dashed line in the left panel) and that the inner and outer radii need not coincide with the corresponding locations of the cusps but are set by the value chosen for the potential $W_{\rm {in}}$ (this is shown with the long-dashed line in the right panel). Reported for comparison with a short-dashed line are $\ell _{_{\rm K}}$ and W in a Schwarzschild spacetime; the radial coordinate is shown on a logarithmic scale.
Open with DEXTER

In the text

$\begin{figure} \mbox{ \includegraphics[height=6.3cm,width=6.1cm,clip]{fig1.ps}\i... ...{fig2.ps}\includegraphics[height=6.3cm,width=6.2cm,clip]{fig3.ps} } \end{figure}$ Figure 2: Radial profiles of the potential at the equatorial plane for models labelled A ( left), B ( centre) and C ( right), respectively. The local maxima in each plot indicate the location of the cusps. The horizontal lines fix the potential of the fluid element at the edges of the torus for each of the models considered. Models A, B and C differ among each other by the value of the angular momentum $\ell$ which is reported in the lower right corners of the different panels.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{fig4.ps}\hspace*{0.5cm} \includegraphics[width=8cm,clip]{fig5.ps}\end{figure}$ Figure 3: Time evolution of the inner ( left panel) and of the outer ( right panel) mass outflows for the models of class A. The data is shown in units of solar masses per second, while the time is expressed in units of the orbital period. Note that only models A₁ (solid line) and A₂(dotted line) are runaway unstable. The solid circles in the two panels indicate the time at which $\dot{m}_{\rm i} > \dot{m}_{\rm o}$ for model A₂.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics{figure4.EPS}\end{figure}$ Figure 4: Velocity field and equally spaced isocontours of the logarithm of the rest-mass density for model A₂ at an early time ( left panel) and at a later time ( right panel); the times reported are in units of the orbital period. Initially the outer mass flux dominates the dynamics of the torus. However, the gravitational attraction of the black hole eventually overcomes the effect of the cosmological constant and the runaway instability takes place. This leads to the large inward-directed fluxes and to the disappearance of the torus inside the black hole in a few orbital periods.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{fig6.ps}\hspace*{0.5cm} \includegraphics[width=8.2cm,clip]{fig7.ps}\end{figure}$ Figure 5: Same as Fig. 3 but for the models of class B.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics{figure6.EPS}\end{figure}$ Figure 6: Same as Fig. 4 but for model B₂. The intense mass ouflow across the outer edge of the disc removes a large fraction of its mass, and suppresses the runaway instability. The final disc reaches a quasi-steady state.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.45cm,clip]{fig8.ps}\hspace*{0.5cm} \includegraphics[width=8.45cm,clip]{fig9.ps}\end{figure}$ Figure 7: Same as Fig. 3 but for the models of class C.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{fig6.ps}\hspace*{0.5cm} \includegraphics[width=8.2cm,clip]{fig7.ps}\end{figure}$	Figure 5: Same as Fig. 3 but for the models of class B.
Open with DEXTER

$\begin{figure} \par\includegraphics{figure6.EPS}\end{figure}$	Figure 6: Same as Fig. 4 but for model B₂. The intense mass ouflow across the outer edge of the disc removes a large fraction of its mass, and suppresses the runaway instability. The final disc reaches a quasi-steady state.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8.45cm,clip]{fig8.ps}\hspace*{0.5cm} \includegraphics[width=8.45cm,clip]{fig9.ps}\end{figure}$	Figure 7: Same as Fig. 3 but for the models of class C.
Open with DEXTER