\begin{table}%t1 \caption{Summary of the parameter grid used in our model$^{{a}}$.} \label{tb:pgrid} \small%\centerline { \begin{tabular}{ccccccc} \hline\hline\noalign{\smallskip} Case$^{{b}}$ & $\Omega_0$ & $\cs$ & $M_0$ & $\tacc$ & $\tau_\el{ads}$ & $M_\el{d}$ \\ & (\ps) & (km~\ps) & ($M_\odot$) & (\ten{5}~yr) & (\ten{5}~yr) & ($M_\odot$) \\ \hline\noalign{\smallskip} 1 \phantom{(std)} & \ten{-14} & 0.19 & 1.0 & 6.3 & 14.4 & 0.22\phantom{0} \\ 2 \phantom{(std)} & \ten{-14} & 0.19 & 0.5 & 3.2 & \phantom{0}3.6 & 0.08\phantom{0} \\ 3 (std) & \ten{-14} & 0.26 & 1.0 & 2.5 & \phantom{0}2.3 & 0.05\phantom{0} \\ 4 \phantom{(std)} & \ten{-14} & 0.26 & 0.5 & 1.3 & \phantom{0}0.6 & 0.001 \\ 5 \phantom{(std)} & \ten{-13} & 0.19 & 1.0 & 6.3 & 14.4 & 0.59\phantom{0} \\ 6 \phantom{(std)} & \ten{-13} & 0.19 & 0.5 & 3.2 & \phantom{0}3.6 & 0.25\phantom{0} \\ 7 (ref) & \ten{-13} & 0.26 & 1.0 & 2.5 & \phantom{0}2.3 & 0.43\phantom{0} \\ 8 \phantom{(std)} & \ten{-13} & 0.26 & 0.5 & 1.3 & \phantom{0}0.6 & 0.16\phantom{0} \\ \hline \end{tabular}} \smallskip $^{a}$ $\Omega_0$: solid-body rotation rate; $\cs$: effective sound speed; $M_0$: initial envelope mass; $\tacc$: accretion time; $\tau_\el{ads}$: adsorption timescale for \w{} at the edge of the initial cloud; $M_\el{d}$: disk mass at $\tacc$.\\ $^{{b}}$ Case 3 is our standard parameter set and Case 7 is our reference set. \end{table}