\begin{table}%t4 \caption{\label{tab4}Temperature-density ($T$-$n$) profiles from Crimier et~al. (\cite{Crimier2010}).} \small%\centering \par \begin{tabular}{llllll} \hline\hline\noalign{\smallskip} Source & CB3 & Cep- E\ & IC\ 1396\ N\ & NGC\ 7129\ & Serpens \\ & mm\ & mm\ & BIMA2\ & FIRS\ 2\ & FIRS\ 1 \\ \hline \multicolumn{1}{l}{RA(J2000) } & \multicolumn{1}{c}{00:28:42.1} & \multicolumn{1}{c}{23:03:12.7} & \multicolumn{1}{c}{21:40:41.8} & \multicolumn{1}{c}{21:43:01.5} & \multicolumn{1}{c}{18:29:49.8} \\ \multicolumn{1}{l}{Dec(J2000)} & \multicolumn{1}{c}{56:41:59.4} & \multicolumn{1}{c}{61:42:27.4} & \multicolumn{1}{c}{58:16:13.5} & \multicolumn{1}{c}{66:03:25.0} & \multicolumn{1}{c}{01:15:18.4} \\ Dust optical depth at 100~$\mu$m, $\tau_{100}$ & 5.8 & 5.0 & 1.4 & 2.3 & 3.0 \\ Density power law index, $\alpha$ & 2.2 & 1.9 & 1.2 & 1.4 & 1.5 \\ Envelope thickness, $r_{{\rm out}}$/$r_{{\rm i}}$ & 400 & 500 & 630 & 180 & 200 \\ \noalign{\smallskip} Inner envelope radius, $r_{{\rm in}}$, (${\rm AU}$) & 260 & 70 & 50 & 100 & 30 \\ Outer envelope radius, $r_{{\rm out}}$, (${\rm AU}$) & 103~000 & 35~800 & 29~600 & 18~600 & 5900 \\ Radius at $T_{\rm dust}$ = 100 K, $r_{{\rm 100~K}}$, (${\rm AU}$) & 700 & 223 & 180 & 373 & 102 \\ H$_2$ density at $r_{{\rm 100~K}}$, $n_0$, (${\rm cm}^{-3}$) & 7.5~$\times$~10$^{7}$ & 2.0~$\times$~10$^{8}$ & 4.3~$\times$~10$^{7}$ & 4.4~$\times$~10$^{7}$ & 2.2~$\times$~10$^{8}$ \\ Envelope mass, $M_{{\rm env}}$, (${\rm M}_{\odot}$) & 120 & 35 & 90 & 50 & 5.0 \\ \hline \end{tabular} \end{table}