Table 6: A model for the instrument bias of the Hipparcos catalogue, based on the analysis of Lindegren et al. (1997). The binary systems satisfying the above constraints are resolved with Hipparcos in our models. For the comparison between the observations and the simulated observations, we consider two sets of Hipparcos binaries: the visual binaries and the astrometric binaries. No orbital motion is detected for the (C) binaries; these are visually resolved and therefore technically visual binaries. The Hipparcos astrometric binaries contain the targets with (X), (O), (G), and optionally (S) entries. No difference between the latter categories is made for the comparison with the astrometric binaries. Binary systems that do not satisfy the constraints listed in this table remain undetected in our simulated observations for Hipparcos. We do not model the (V)-binaries (variability-induced movers; VIMs) and (S)-binaries (suspected non-single stars). Note that in our model we overpredict the number of binaries in categories (X), (O), and (S), as not all binaries with the properties above are detected by Hipparcos as such.
Constraints on $\rho $ and $\Delta H_{\rm p}$ Period constraints Solution Symbol Elements
$2 \leq \langle \rho \rangle \leq 100$ mas or $\Delta H_{\rm p} > 4$ $P \leq 0.1$ year Stochastic (X) no
$2 \leq \langle \rho \rangle \leq 100$ mas or $\Delta H_{\rm p} > 4$ $0.1 < P \leq 10$ year Orbital (O) yes
$2 \leq \rho \leq 100$ mas or $\Delta H_{\rm p} > 4$ $5 < P \leq 30$ year Acceleration (G) no
$0.1 \leq \rho \leq 100$ arcsec and $\Delta H_{\rm p} \leq 4$ P > 30 year Resolved (C) no
Not modeled Suspected (S) no
Not modeled VIM (V) no

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