All Figures

$\begin{figure} { \includegraphics[height=9.cm,angle=-90]{dur4a4b.ene.eps} }\end{figure}$ Figure 1: Internal energy (i) for a disc irradiated by a uniform $10~{\rm K}$ background radiation field (bottom, red line) and (ii) for a disc irradiated by its central star ( $T_{_{\rm BGR}}(R)\sim R^{-1}$ ; top, blue line).
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In the text

$\begin{figure} \par\includegraphics[height=9cm,angle=-90]{dens.xy.4b.ps}\par\includegraphics[height=8.3cm,angle=-90]{dens.xz.4b.ps} \end{figure}$ Figure 2: Logarithmic column density in ${\rm g}~{\rm cm}^{-2}$ , projected on the xy-plane ( top), and volume density in ${\rm g}~{\rm cm}^{-3}$ on the xz-plane ( bottom) for a disc irradiated by a $10~{\rm K}$ background radiation field.
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In the text

$\begin{figure} \par\includegraphics[height=9cm,angle=-90]{temp.xy.4b.ps}\par\includegraphics[height=8.3cm,angle=-90]{temp.xz.4b.ps} \end{figure}$ Figure 3: Logarithmic temperature on the xy-plane ( top), and on the xz-plane ( bottom) for a disc irradiated by a $10~{\rm K}$ background radiation field.
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In the text

$\begin{figure} { \includegraphics[height=9cm,angle=-90]{toomre.xy.4b.ps} } \end{figure}$ Figure 4: Toomre parameter for a disc irradiated by a $10~{\rm K}$ background radiation field.
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In the text

$\begin{figure} { \includegraphics[height=9cm,angle=-90]{cool.xy.4b.ps} }\end{figure}$ Figure 5: Net cooling time (in units of the local orbital period, and averaged vertically) for a disc irradiated by a $10~{\rm K}$ background radiation field.
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In the text

$\begin{figure} \par\includegraphics[height=6.9cm,angle=-90]{dur4b.qsigma.eps}\par\includegraphics[height=6.9cm,angle=-90]{dur4b.qtemp.eps} \end{figure}$ Figure 6: Surface density (azimuthally averaged) and temperature (azimuthally and vertically averaged) at five times ( $t=500, 1000,\dots ,2500$ yr; green, red, blue, cyan, black) during the evolution of a disc irradiated by a $10~{\rm K}$ background radiation field. The dotted lines correspond to the initial conditions.
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In the text

$\begin{figure} \par\includegraphics[height=6.9cm,angle=-90]{dur4b.qtoom.eps}\par\includegraphics[height=6.9cm,angle=-90]{dur4b.qcool.eps} \end{figure}$ Figure 7: As, Fig. 6, the Toomre parameter (azimuthally averaged) and net cooling time (in units of the local orbital period, also azimuthally averaged).
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In the text

$\begin{figure} \par\includegraphics[width=9cm]{mode.comp.eps} \end{figure}$ Figure 8: The mean strengths, F, of the m=1,2,3 and 4 spiral modes during the quasi-steady phase, against $\zeta=-m/\tan(\beta)$ , where $\beta$ is the pitch angle, for a disc irradiated by a $10~{\rm K}$ blackbody background radiation field (solid lines), a disc irradiated by the central star ( $\times 10$ ; dashed lines), and the Boley et al. (2006) disc which is irradiated by a $3~{\rm K}$ blackbody background radiation field ( $\times 0.1$ ; dotted lines).
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In the text

$\begin{figure} { \includegraphics[width=7.2cm]{dur4b.hube.high.eps} } { \includegraphics[width=7.2cm]{dur4b.hube.low.eps} }\end{figure}$ Figure 9: Vertical temperature profiles, $T(\tau )$ , at different radii (6, 9, 11 AU, top to bottom, top plot; 14, 20, 25, 30, 33 AU, top to bottom, bottom plot). Points correspond to the results of our model (azimuthally averaged), the solid lines to the Hubeny (1990) solution, and the dashed lines to the Hubeny solution corrected for the fact that radiation diffuses both vertically and radially.
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In the text

$\begin{figure} \includegraphics[height=9cm,angle=-90]{dens.xy.4a.ps}\par\includegraphics[height=8.3cm,angle=-90]{dens.xz.4a.ps} \end{figure}$ Figure 10: As Fig. 2, but taking account of radiation from the central star.
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In the text

$\begin{figure} \par\includegraphics[height=9cm,angle=-90]{temp.xy.4a.ps}\par\includegraphics[height=8.3cm,angle=-90]{temp.xz.4a.ps} \end{figure}$ Figure 11: As Fig. 3, but taking account of radiation from the central star.
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In the text

$\begin{figure} \par\includegraphics[height=9cm,angle=-90]{toomre.xy.4a.ps} \end{figure}$ Figure 12: As Fig. 4, but taking account of radiation from the central star.
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In the text

$\begin{figure} \par { \includegraphics[height=9cm,angle=-90]{cool.xy.4a.ps} }\end{figure}$ Figure 13: As Fig. 5, but taking account of radiation from the central star.
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In the text

$\begin{figure} { \includegraphics[height=6.9cm,angle=-90]{dur4a.qsigma.eps}\par\includegraphics[height=6.9cm,angle=-90]{dur4a.qtemp.eps} }\end{figure}$ Figure 14: As Fig. 6, but taking account of radiation from the central star.
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In the text

$\begin{figure} { \includegraphics[height=6.9cm,angle=-90]{dur4a.qtoom.eps}\par\includegraphics[height=6.9cm,angle=-90]{dur4a.qcool.eps} }\end{figure}$ Figure 15: As Fig. 7, but taking account of radiation from the central star.
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In the text

$\begin{figure} { \includegraphics[height=9.cm,angle=-90]{dur4a4b.ene.eps} }\end{figure}$	Figure 1: Internal energy (i) for a disc irradiated by a uniform $10~{\rm K}$ background radiation field (bottom, red line) and (ii) for a disc irradiated by its central star ( $T_{_{\rm BGR}}(R)\sim R^{-1}$ ; top, blue line).
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$\begin{figure} \par\includegraphics[height=9cm,angle=-90]{dens.xy.4b.ps}\par\includegraphics[height=8.3cm,angle=-90]{dens.xz.4b.ps} \end{figure}$	Figure 2: Logarithmic column density in ${\rm g}~{\rm cm}^{-2}$ , projected on the xy-plane ( top), and volume density in ${\rm g}~{\rm cm}^{-3}$ on the xz-plane ( bottom) for a disc irradiated by a $10~{\rm K}$ background radiation field.
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$\begin{figure} \par\includegraphics[height=9cm,angle=-90]{temp.xy.4b.ps}\par\includegraphics[height=8.3cm,angle=-90]{temp.xz.4b.ps} \end{figure}$	Figure 3: Logarithmic temperature on the xy-plane ( top), and on the xz-plane ( bottom) for a disc irradiated by a $10~{\rm K}$ background radiation field.
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$\begin{figure} { \includegraphics[height=9cm,angle=-90]{toomre.xy.4b.ps} } \end{figure}$	Figure 4: Toomre parameter for a disc irradiated by a $10~{\rm K}$ background radiation field.
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$\begin{figure} { \includegraphics[height=9cm,angle=-90]{cool.xy.4b.ps} }\end{figure}$	Figure 5: Net cooling time (in units of the local orbital period, and averaged vertically) for a disc irradiated by a $10~{\rm K}$ background radiation field.
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$\begin{figure} \par\includegraphics[height=6.9cm,angle=-90]{dur4b.qsigma.eps}\par\includegraphics[height=6.9cm,angle=-90]{dur4b.qtemp.eps} \end{figure}$	Figure 6: Surface density (azimuthally averaged) and temperature (azimuthally and vertically averaged) at five times ( $t=500, 1000,\dots ,2500$ yr; green, red, blue, cyan, black) during the evolution of a disc irradiated by a $10~{\rm K}$ background radiation field. The dotted lines correspond to the initial conditions.
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$\begin{figure} \par\includegraphics[height=6.9cm,angle=-90]{dur4b.qtoom.eps}\par\includegraphics[height=6.9cm,angle=-90]{dur4b.qcool.eps} \end{figure}$	Figure 7: As, Fig. 6, the Toomre parameter (azimuthally averaged) and net cooling time (in units of the local orbital period, also azimuthally averaged).
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$\begin{figure} \includegraphics[height=9cm,angle=-90]{dens.xy.4a.ps}\par\includegraphics[height=8.3cm,angle=-90]{dens.xz.4a.ps} \end{figure}$	Figure 10: As Fig. 2, but taking account of radiation from the central star.
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$\begin{figure} \par\includegraphics[height=9cm,angle=-90]{temp.xy.4a.ps}\par\includegraphics[height=8.3cm,angle=-90]{temp.xz.4a.ps} \end{figure}$	Figure 11: As Fig. 3, but taking account of radiation from the central star.
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$\begin{figure} \par\includegraphics[height=9cm,angle=-90]{toomre.xy.4a.ps} \end{figure}$	Figure 12: As Fig. 4, but taking account of radiation from the central star.
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$\begin{figure} \par { \includegraphics[height=9cm,angle=-90]{cool.xy.4a.ps} }\end{figure}$	Figure 13: As Fig. 5, but taking account of radiation from the central star.
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$\begin{figure} { \includegraphics[height=6.9cm,angle=-90]{dur4a.qsigma.eps}\par\includegraphics[height=6.9cm,angle=-90]{dur4a.qtemp.eps} }\end{figure}$	Figure 14: As Fig. 6, but taking account of radiation from the central star.
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$\begin{figure} { \includegraphics[height=6.9cm,angle=-90]{dur4a.qtoom.eps}\par\includegraphics[height=6.9cm,angle=-90]{dur4a.qcool.eps} }\end{figure}$	Figure 15: As Fig. 7, but taking account of radiation from the central star.
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