\begin{table}%t1 \caption{\label{tab_systems}Models for $\beta$~Pic, HD~32297, and AU~Mic.} \par \small%\centerline { \begin{tabular}{l|cccccccccc|cc|cc} \hline\hline & \multicolumn{10}{|c|}{\makebox[3cm]{$\beta$~Pic}} & \multicolumn{2}{|c|}{\makebox[1.2cm]{HD~32297}} & \multicolumn{2}{|c}{\makebox[1.2cm]{AU~Mic}}\\ \hline \multicolumn{15}{l}{\em Star} \\ Luminosity, $L_\odot$ & \multicolumn{10}{|c|}{$8.70$} & \multicolumn{2}{|c|}{$5.40$} & \multicolumn{2}{|c}{$.092$}\\ Mass, $M_\odot$ & \multicolumn{10}{|c|}{$1.75$} & \multicolumn{2}{|c|}{$1.80$} & \multicolumn{2}{|c}{$.50$}\\ Age, Myr & \multicolumn{10}{|c|}{$12$} & \multicolumn{2}{|c|}{$30$} & \multicolumn{2}{|c}{$12$}\\ \hline \multicolumn{14}{l}{\em Planetesimals and dust} \\ Birth ring, AU & \multicolumn{10}{|c|}{110-130} & \multicolumn{2}{|c|}{60--80} & \multicolumn{2}{|c}{30--40}\\ Max optical depth & \multicolumn{10}{|c|}{$5 \times 10^{-3}$} & \multicolumn{2}{|c|}{$4 \times 10^{-3}$} & \multicolumn{2}{|c}{$6 \times 10^{-4}$}\\ Init. surf. density slope & \multicolumn{10}{|c|}{$-1.5$} & \multicolumn{2}{|c|}{$-1.5$} & \multicolumn{2}{|c}{$-1.5$}\\ $[s_{\rm min}, s_{\rm max}]$, $\mum$ & \multicolumn{10}{|c|}{$[1, 86]$} & \multicolumn{2}{|c|}{$[0.6, 52]$} & \multicolumn{2}{|c}{$[0.04, 3.2]$}\\ \hline \multicolumn{15}{l}{\em Gas} \\ Model identifier &\tb{000}&\tb{tns}&\tb{t0ns}&\tb{t1ns}&\tb{rns}&\tb{r0ns}&\tb{r1ns}&\tb{ths}&\tb{thf}&\tb{tvs} &\tb{tns}&\tb{ths} &\tb{tns} &\tb{ths} \\ t- or r-support & -- & t & t & t & r & r & r & t & t & t & t & t & t & t \\ Temperature slope $p$ & -- & $1/2$ & $0$ & $1$ & $1/2$ & $0$ & $1$ & $1/2$ & $1/2$ & $1/2$ & $1/2$ & $1/2$ & $1/2$ & $1/2$ \\ Mass, $M_\oplus$ & -- & $.05$ & $.05$ & $.05$ & $.05$ & $.05$ & $.05$ & 5 & 5 & 50 & .15 & 15 & $2\times 10^{-4}$ & $2\times 10^{-2}$ \\ Surface density slope & -- & --1.5 & --1.5 & --1.5 & --1.5 & --1.5 & --1.5 & --1.5 & --1.0 & --1.5 & --1.5 & --1.5 & --1.5 & --1.5 \\ Outer edge, AU$^\star$ & \multicolumn{10}{|c|}{$600$} & \multicolumn{2}{|c|}{$350$} & \multicolumn{2}{|c}{$175$}\\ \hline \end{tabular}} \medskip $^\star$ The arbitrary truncation distance (we set it to five times the central distance of the respective birth ring). It only affects the conversion of total gas mass to gas density. In that conversion, we also use a constant semi-opening angle of~$15^\circ$ for all disks, assuming the density to be constant with height. \vspace*{-2.5mm} \end{table}