All Figures

$\begin{figure} \par\mbox{\includegraphics[width=4.2cm,clip]{2951fig1.ps}\hspace*{3mm} \includegraphics[width=4.2cm,clip]{2951fig2.ps} }\end{figure}$ Figure 1: A uniform-density spherical cloud, represented by 20 000 SPH particles, is illuminated by an isotropic blackbody radiation field at $T=15~{\rm K}$ , using 10⁸ L-packets. RT cells are constructed with $N_{_{\rm MAX}}=60$ , giving $N_{_{\rm CELLS}} =1484$ . a) Triangles give the densities of the individual RT cells, the horizontal dotted line marks the mean density, and the vertical line marks the boundary of the cloud. b) Triangles give the temperatures of the individual RT cells, the horizontal dotted line marks $T=15~{\rm K}$ , and the vertical line marks the boundary of the cloud. c) The percentage error in the computed temperature.
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=4.05cm,clip]{2951fig3.ps}\hspace*{3mm} \includegraphics[width=4.2cm,clip]{2951fig4.ps} }\end{figure}$ Figure 2: A uniform-density spherical cloud, represented by 200 000 SPH particles, is illuminated by the BISRF radiation field, using 10⁸ L-packets. RT cells are constructed with $N_{_{\rm MAX}}=100$ giving $N_{_{\rm CELLS}} = 11~862$ . a) Triangles give the temperatures of the individual RT cells and the solid line gives the accurate temperature profile. b) The computed SED (solid line) is compared with the accurate SED (dashed line) and the illuminating BISRF (dotted line).
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2951fig5.ps} \end{figure}$ Figure 3: a) The square cells represent the global grid derived from the SPH tree, and the concentric circles represent the additional star grid. b) The dashed horizontal lines show the temperature computed (inaccurately) using the global grid on its own, whilst the solid curve shows the (accurate) temperature profile computed using the additional star grid.
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=4.1cm,clip]{2951fig6.ps}\hspace*{4mm} \includegraphics[width=4.17cm,clip]{2951fig7.ps} } \end{figure}$ Figure 4: Ivezic test with $\tau _{_{\rm V}}=1$ , using $5\times 10^7$ L-packets. The envelope is represented by 20 000 SPH particles and a global grid of $N_{_{\rm CELLS}} = 1276$ RT cells (with ${\bar N} = 15$ ), but no additional star grid around the star. a) The triangles represent the temperatures of the individual RT cells plotted against radius, whilst the solid line represents the benchmark calculation. The global grid on its own fails to capture the temperature profile close to the star. b) The solid line shows the SED computed here, and the dotted line shows the benchmark calculation. c) The percentage difference between the flux computed here and the benchmark calculation.
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=4.1cm,clip]{2951fig8.ps}\hspace*{4mm} \includegraphics[width=4.17cm,clip]{2951fig9.ps} }\end{figure}$ Figure 5: Same as Fig. 4 but with an additional star grid around the star, i.e. a volume devoid of matter inside $R_{_{\rm DEST}}$ and 30 concentric spherical RT cells between $R_{_{\rm DEST}}$ and $R_{_{\rm SG}} = 20~R_{_{\rm DEST}}$ . Agreement with the benchmark calculation is now very good. Small differences are due to statistical noise.
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=4.2cm,clip]{2951fig10.ps}\hspace*{4mm} \includegraphics[width=4.12cm,clip]{2951fig11.ps} }\end{figure}$ Figure A.1: A uniform-density spherical cloud, represented by 200 000 SPH particles, is heated by a central low-temperature star with $L_* = 7~{L}_\odot$ and $T_* = 30~{\rm K}$ , which emits 10⁸ L-packets. RT cells are constructed with $N_{_{\rm MAX}}=60$ , giving $N_{_{\rm CELLS}} = 13~050$ . a) Triangles give the temperatures of the individual RT cells and the solid line gives the accurate temperature profile. b) The computed SED (solid line) is compared with the accurate SED (dashed line). c) The precentage error in the SED.

In the text

$\begin{figure} \par\mbox{\includegraphics[width=4.08cm,clip]{2951fig12.ps}\hspace*{4mm} \includegraphics[width=4.2cm,clip]{2951fig13.ps} }\end{figure}$ Figure A.2: Ivezic test with $\tau _{{\rm V}}={100}$ , using 10⁷ L-packets. The envelope is represented by 20 000 SPH particles and a global grid of $N_{_{\rm CELLS}} = 1310$ RT cells (with ${\bar N} = 15$ ), but no additional star grid around the star. a) The triangles represent the temperatures of the individual RT cells plotted against radius, whilst the solid line represents the benchmark calculation. The global grid on its own fails to capture the temperature profile close to the star. b) The solid line shows the SED computed here, and the dotted line shows the benchmark calculation. c) The percentage difference between the flux computed here and the benchmark calculation.

In the text

$\begin{figure} \par\mbox{\includegraphics[width=4.08cm,clip]{2951fig14.ps}\hspace*{4mm} \includegraphics[width=4.2cm,clip]{2951fig15.ps} }\end{figure}$ Figure A.3: Same as Fig. A.2 but with an additional star grid around the star, i.e. a volume devoid of matter inside $R_{_{\rm DEST}}$ and 30 concentric spherical RT cells between $R_{_{\rm DEST}}$ and $R_{_{\rm SG}} = 20~R_{_{\rm DEST}}$ . Agreement with the benchmark calculation is now very good. Small differences are due to statistical noise.

In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{2951fig5.ps} \end{figure}$	Figure 3: a) The square cells represent the global grid derived from the SPH tree, and the concentric circles represent the additional star grid. b) The dashed horizontal lines show the temperature computed (inaccurately) using the global grid on its own, whilst the solid curve shows the (accurate) temperature profile computed using the additional star grid.
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$\begin{figure} \par\mbox{\includegraphics[width=4.1cm,clip]{2951fig8.ps}\hspace*{4mm} \includegraphics[width=4.17cm,clip]{2951fig9.ps} }\end{figure}$	Figure 5: Same as Fig. 4 but with an additional star grid around the star, i.e. a volume devoid of matter inside $R_{_{\rm DEST}}$ and 30 concentric spherical RT cells between $R_{_{\rm DEST}}$ and $R_{_{\rm SG}} = 20~R_{_{\rm DEST}}$ . Agreement with the benchmark calculation is now very good. Small differences are due to statistical noise.
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