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$\begin{figure} \par\includegraphics[width=7.7cm,clip]{0336fig1.eps} \end{figure}$ Figure 1: Mass density contours in the meridional plane of the torus model. Contour levels are stepping down a factor of 2 from the peak in density. The model assumes $x_H = \sqrt {2 \pi } H/(0.56 R)$ implied by the discussion at the end of Sect. 3.4. The vertical collision depth is set to $\tau =1$ and the largest clouds are at the shear limit (Eq. (27)). The potential described in Sect. 6 for NGC 1068 is used and the inner radius for dust sublimation is set to 1 pc. For simplicity the sound speed in clouds is assumed to follow an r^-1/4-law. The radial distribution follows from Eq. (30) and the vertical distribution is described in Sect. 3.2. The mass accretion rate in the torus is taken to $\dot{M} = 20 \dot{M}_{\rm Edd}$ for a $1.2\times 10^7~M_\odot$ black hole and corresponds to the solid-lines in Figs. 2 and 3.
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In the text

$\begin{figure} \includegraphics[width=11cm,clip]{0336fig2.eps} \end{figure}$ Figure 2: The radial structure of the torus described in Sect. 4.1 with the mass distribution from Sect. 6 for NGC 1068 with $\tau =1$ and Q at its local maximum (Eq. (27)). Three different accretion rates are assumed $\dot{m} =$ [30 (solid line), 10 (dashed), 3 (dash-dotted)], where $\dot{m}$ is the accretion rate in units of the Eddington rate for the central black hole. On the top left a) the velocity dispersion $\sigma$ can be compared to the Keplerian circular velocity (dashed-3 $\times$ dotted). The top right b) shows the volume filling fraction of dusty clouds $\phi _V$ to be in the range of $0.5\%$ to $10\%$ . The star formation time-scale (Eq. (44)) is plotted bottom left c) which smaller than the accretion time-scale $t_{\rm acc}$ (Eq. (42)) displayed bottom right d) only in the innermost region. Plot d) also gives the dissipation or collapse time (Eq. (45)) in the absence of heating (dotted) for $\dot{M} = 30\dot{m}$ , which is the shortest timescale considered.
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In the text

$\begin{figure} \includegraphics[width=10.7cm,clip]{0336fig3.eps} \end{figure}$ Figure 3: For the same specific model assumed in Figs. 1 and 2 we plot the relative scale H/R at the top left a) for the three accretion rates $\dot{m} =$ [30 (solid line), 10 (dashed), 3 (dash-dotted)] as a function of radius. The cloud mass at top right b) is seen to be independent of $\dot{m}$ . The coefficient of restitution $\epsilon$ or elasticity in cloud collisions required by our model (Eq. (37)) is shown bottom left c). The variation of the limiting value of Toomre-Q is given bottom right d).
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{0336fig4.eps} \end{figure}$ Figure 4: The obscuration angle i_N and $i_{\rm Obsc}$ as function of mass accretion rate derived from the model adapted for NGC 1068 with vertical density structure given by Eq. (15). The outer radius of the torus is set to $R_{\rm out} = 100$ pc. The dashed lines show the angle i_N for having on average N=[1,2,3,4,5,6] clouds along the line of sight. Due to the vertical stratification of the torus the probability of seeing more clouds increases for smaller angles and the dashed lines are ordered accordingly. The solid lines show the obscuration angle $i_{\rm Obsc}$ for finding an average hydrogen column density of $N_{\rm H} = [10^{22}, 10^{23}, 10^{24}, 2\times 10^{24}, 4\times 10^{24}, 6\times 10^{24}]$ per cm². Again the stratification leads to an increased column for smaller angles and the identification of lines with column density is obvious.
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In the text