\begin{table}%t2 \caption{\label{run-table}Overview of runs using the proposed approximate radiation transport module.} %\centering \small \begin{tabular}{lccccc} \hline\hline \noalign {\smallskip} Run & G0.1 & G100 & F100 & GD100 & FD100\\ \hline Optical depth $\tau_{550{\rm nm}}$ & 0.1 & 100 & 100 & 100 & 100\\ %\hline Comparison run & MC0.1-full & MC100-A & MC100-A & MC100-full & MC100-full\\ %\hline Ray-tracing Irradiation & gray & gray & freq.~dep. & gray & freq.~dep.\\ Flux Limited Diffusion & no & no & no & yes & yes\\ %\hline Theory Sect. & \ref{sect:irradiation} & \ref{sect:irradiation} & \ref{sect:irradiation} \& \ref{sect:freqdepirradiation} & \ref{sect:fld} \& \ref{sect:irradiation} & \ref{sect:fld} - \ref{sect:freqdepirradiation}\\ Comparison Sect. & \ref{sect:irradiation_thin} & \ref{sect:irradiation_thick} & \ref{sect:irradiation_thick} & \ref{sect:full_thick} & \ref{sect:full_thick} \& \ref{sect:radiativeforce}\\ \hline Deviation $\left(\Delta T\right)/T$ [\%] & $<$+2.0 & +10.9 $\rightarrow$ --57.2 & +5.0 $\rightarrow$ -0.6 & +5.0 $\rightarrow$ --38.4 & +9.3 $\rightarrow$ --11.1\\ \hline \end{tabular} \tablefoot{The overview table of the runs discussed contains the corresponding optical depth of the test case and the Monte-Carlo run, which is used for comparison (see also Table~\ref{MC-runs} and referred theory and comparison Sects.). Furthermore, the applied radiative modules (gray or frequency dependent absorption as well as possible diffusion) of our proposed approximate radiation transport method and the corresponding sections, in which this modules and the final results are discussed, are given. The deviations in the resulting temperature profiles of the approximate radiation transport from the corresponding Monte-Carlo comparison run are shown in the lower row.} \end{table}