\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}