Table 8: 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 Kouwenhoven et al. (2005) 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 Duquennoy & Mayor (1991) 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.
# Model $N_{\rm\star ,BD,IM}$ $R_{\rm\star ,IM}$ $N_{\rm\star ,BD,LM}$ $R_{\rm\star ,LM}$
0 ADONIS/NACO observations $1 \pm 1 $ $0.036 \pm 0.036$ unknown unknown
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 $


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