\begin{table}%T10
%\centering
\small
  \caption{The simulated observed binary fraction for models with a different assumption for the tightest and widest binaries. The first and second column list the properties of the tightest and widest orbits, respectively. The third and fourth column list the visual binary fraction for the simulated combined KO5/SHT observations and the spectroscopic binary fraction for the simulated LEV observations, respectively. For each model we adopt an intrinsic binary fraction $\binfrac=100\%$ and a thermal eccentricity distribution. The values listed in Cols.~3 and~4 are proportional to $\binfrac$. The statistical errors on the listed binary fraction are $0.5$--$1\%$. The values listed in this table provide error estimates for our results in Table~\ref{table: fm_inferred}. The uncertainties in the limits of $f_a(a)$ and $f_{P}(P)$ result in a systematic error of ${<}2$--$4\%$ in the inferred intrinsic binary of the binary population. \label{table: limitsdependence}}
  \begin{tabular}{cccc}
    \hline
    \hline\\[-3.2mm]
    \multicolumn{2}{l}{$f_{\tiny\mbox{\"{O}pik}}(a)$ limits} & $\tilde{F}_{M,\rm ~KO5,~SHT}$ (\%) & $\tilde{F}_{M,\rm ~LEV}$ (\%)  \\
    \hline\\[-3.2mm]
    $2\rsun$  & $2.0\times 10^6\rsun$ & 25  & 42 \\
    $2\rsun$  & $8.9\times 10^6\rsun$ & 24  & 37 \\
    $10\rsun$ & $2.0\times 10^6\rsun$ & 27  & 34 \\
    $10\rsun$ & $8.9\times 10^6\rsun$ & 25  & 30 \\
    \hline\\[-3.2mm]
     \multicolumn{2}{l}{$f_{\rm DM}(P)$ limits} & $\binfracobs$ VB (\%)  & $\binfracobs$ SB (\%)\\
    \hline
    $0.5$ day & $0.15$ Myr & 38  & 25 \\
    $0.5$ day & $4.00$ Myr & 35  & 22 \\
    $2.0$ day & $0.15$ Myr & 39  & 22 \\
    $2.0$ day & $4.00$ Myr & 36  & 20 \\
    \hline
  \end{tabular}
\end{table}