\begin{table}%t4 %\centering \par \caption{\label{best_fit_phy_param}Summary of the dust radiative transfer analysis for the five IM protostars.} \begin{tabular}{lrrrrrrr} \hline\hline\noalign{\smallskip} \multicolumn{2}{c}{Fixed input parameters} \\ \hline Stellar temperature, $T_{\star}$ & 5000~K\\ Dust temperature at $r_{{\rm in}}$, $T_{{\rm in}}$ & 300~K\\ Dust opacity (OH5) at 100~$\mu$m, $\kappa_{100}$ & 86.5~cm$^2$~g$^{-1}$ \\ \hline \multicolumn{2}{c}{Best\textendash fit\ parameters \& physical\ quantities} \\ \hline Source & CB3\ & Cep\ E\ & IC1396\ N\ & NGC7129\ & Serpens\ & OMC2\ \\ & mm\ & mm\ & BIMA2\ & FIRS\ 2\ & FIRS\ 1 & FIR4\ \\ \hline Distance, (${\rm pc}$) & 2500 & 730 & 750 & 1250 & 230 & 450 \\ Luminosity, (${L}_{\sun}$) & 1000 & 100 & 150 & 500 & 33 & 1000 \\ Dust optical depth at 100~$\mu$m, $\tau_{100}$ & 5.8 & 5.0 & 1.4 & 2.3 & 3.0 & 0.6 \\ Density power law index, $\alpha$ & 2.2 & 1.9 & 1.2 & 1.4 & 1.5 & 0.6 \\ Envelope thickness, $Y$ (= $r_{{\rm out}}$/$r_{{\rm in}}$) & 400 & 500 & 630 & 180 & 200 & 120 \\ $\chi^2_{\rm red}$-maps & 0.43 & 0.11 & 0.55 & 0.21 & 0.20 & 1.2 \\[2mm] $\chi^2_{\rm red}$-SED & 0.85 & 0.80 & 1.2 & 0.87 & 4.4 & 0.55 \\ \hline Inner envelope radius, $r_{{\rm in}}$, (${\rm AU}$) & 260 & 70 & 50 & 100 & 30 & 100 \\ Outer envelope radius, $r_{{\rm out}}$, (${\rm AU}$) & 103~000 & 35~800 & 29~600 & 18~600 & 5900 & 12~000 \\ Radius at $T_{\rm dust} = 100$~K, $r_{{\rm 100~K}}$, (${\rm AU}$) & 700 & 223 & 180 & 373 & 102 & 440 \\ H$_2$ density at $r_{100~{\rm K}}$, $n_0$, (cm$^{-3}$) & $7.5\times10^{7}$ & $2.0 \times 10^{8}$ & $4.3 \times 10^{7}$ & $4.4 \times 10^{7}$ & $2.2 \times 10^{8}$ & $4.3 \times 10^{6}$ \\ Envelope mass, $M_{\rm env}$, ($M_{\sun}$) & 120 & 35& 90 & 50 & 5.0 & 30 \\ ($T_{\rm dust}$--$T_{\rm gas}$)$_{\max}$, (K) & 6 & 5 & 40 & 40 & 10 & 150 \\ \hline \end{tabular} \tablefoot{The top section lists the fixed input parameters, the lower section reports the best-fit parameters, and some relevant physical quantities corresponding to the best-fit model. The last column reports the same parameters for the IM~protostar OMC2-FIR4, found with a similar analysis \citep{Crimier2009a}, for comparison.} \end{table}