\begin{table}%t8
%\centering
\par
 \caption{The observed and expected number of brown dwarfs with $1'' \leq \rho \leq 4''$ and $12 \leq K_{\rm S} \leq 14$~mag for the sample of 199~target stars. The left columns shows the various models for which we simulated observations. Each model has a semi-major axis distribution $f_a(a) \propto a^{-1}$ with $15~R_\odot \leq a \leq 5\times 10^6$~$R_\odot$, and a multiplicity fraction of $F_{\rm M} =100\%$. 
%
Columns 3 and 4 show for a survey of intermediate mass stars (late-B and A stars; $1.4~{M}_\odot < M < 7.7~{M}_\odot$) the expected number of brown dwarfs $N_{\rm \star,BD,IM}$ and the substellar-to-stellar companion ratio $R_{\rm \star,IM}$, both with $1\sigma$ errors. 
%
By comparing the predicted values of $N_{\rm \star,BD,IM}$ and $R_{\rm \star,IM}$ with the observations, we can exclude models 1, 2, and 4. In \cite{kouwenhoven2005} we exclude random pairing from the Preibisch mass distribution (models 1$-$3) since these models are inconsistent with the observed mass ratio distribution of stellar companions. We additionally list the values $N_{\rm \star,BD,LM}$ and $R_{\rm \star,LM}$ that are expected for a survey amongst 199~low-mass stars ($0.3~{M}_\odot < M < 1.4~{M}_\odot$) in Cols. 5 and 6. For models with $F_{\rm M} < 100\%$ the expected number of brown dwarfs reduces to $F_{\rm M} \times N_{\rm \star,BD}$, while $R$ remains unchanged. Models with a smaller semi-major axis range and models with the log-normal period distribution found by \cite{duquennoy1991} have a larger expected value of $N_{\rm \star,BD,IM}$, $N_{\rm \star,BD,LM}$. Under the assumption that companion mass and semi-major axis are uncorrelated, the values of  $R_{\rm \star,IM}$ and  $R_{\rm \star,LM}$ are equal to those listed above, if the log-normal period distribution is chosen.
    \label{table: modelbackgroundstars}}
\begin{tabular}{llcccc}
    \hline\hline
    \# & Model & $N_{\rm \star,BD,IM}$ & $R_{\rm \star,IM}$  & $N_{\rm \star,BD,LM}$ & $R_{\rm \star,LM}$ \\
    \hline
    0 & ADONIS/NACO observations                                                                    & $1   \pm 1  $    & $0.036 \pm 0.036$ & unknown             & unknown \\
    \hline
    1 &  extended Preibisch  MF, $\alpha=-0.9$, random pairing             & $      5.50\pm       0.48 $&$     0.34\pm     0.03 $&$       7.19\pm      0.17 $&$      0.50 \pm    0.01  $ \\ 
    2 &  extended Preibisch  MF, $\alpha=-0.3$, random pairing             & $      4.50\pm       0.41 $&$     0.24\pm     0.03 $&$       5.08\pm      0.13 $&$      0.30 \pm    0.01  $ \\ 
    3 &  extended Preibisch  MF, $\alpha=+2.5$, random pairing            & $      1.07\pm       0.18 $&$     0.05\pm     0.01 $&$       1.42\pm      0.07 $&$      0.07 \pm    0.01  $ \\ 
    4 &  Salpeter MF, random pairing                                      & $     15.31\pm       2.79 $&$     6.00\pm     2.90 $&$      17.18\pm      0.88 $&$      3.95 \pm    0.45  $ \\ 
    5 &  extended Preibisch MF, $\alpha=-0.9$, $f_q(q) \propto q^{-0.33}$    & $      0.72\pm       0.24 $&$     0.04\pm     0.01 $&$       3.42\pm      0.14 $&$      0.18 \pm    0.01  $ \\
    6 &  extended Preibisch MF, $\alpha=-0.3$, $f_q(q) \propto q^{-0.33}$    & $      0.71\pm       0.22 $&$     0.04\pm     0.01 $&$       3.35\pm      0.14 $&$      0.18 \pm    0.01  $ \\ 
    7 &  extended Preibisch MF, $\alpha=+2.5$, $f_q(q) \propto q^{-0.33}$   & $      1.19\pm       0.27 $&$     0.06\pm     0.01 $&$       3.30\pm      0.13 $&$      0.18 \pm    0.01  $ \\ 
    8 &  Salpeter MF, $f_q(q) \propto q^{-0.33}$                            & $      1.00\pm       0.57 $&$     0.05\pm     0.02 $&$       3.70\pm      0.57 $&$      0.20 \pm    0.03  $ \\ 
    \hline
   \end{tabular}
\par
\end{table}