All Tables

Table 1: Properties of the subgroups Upper Scorpius (US), Upper Centaurus Lupus (UCL), and Lower Centaurus Crux (LCC) of Sco OB2, and of our model for Sco OB2. Columns 2-4 list for each subgroup its distance, effective radius, and age. Column 5 lists the median interstellar extinction towards each subgroup. Column 6 lists the number of confirmed Hipparcos members of each subgroup, and is followed by the observed number of singles, binaries, triples, and higher-order systems among the confirmed members in Cols. 7-10, taken from Kouwenhoven et al. (2007). Finally, Cols. 11-13 list the observed multiplicity fraction, non-single star fraction, and companion star fraction among the confirmed members (see Kouwenhoven et al. 2005, for a definition of these fractions). Note that the latter quantities are lower limits due to the presence of unresolved binary and multiple systems. In the bottom row we list the properties of our Sco OB2 model. The number of systems N=S+B (i.e., singles and binaries) used in our model includes substellar objects with masses down to $0.02 ~{M}_\odot$ . References: (1) de Zeeuw et al. (1999); (2) de Geus et al. (1989); (3) Preibisch et al. (2002); (4) Mamajek et al. (2002); (5) de Bruijne (1999).
Table 2: References to literature data with spectroscopic, astrometric, eclipsing, and visual binaries among the Hipparcos members of Sco OB2. The data for a number of binary systems in Sco OB2 is taken from several catalogues. This table is similar to the one presented in Kouwenhoven et al. (2005), but is updated with recent discoveries.
Table 3: An overview of the datasets used to derive the properties of the binary population in Sco OB2. Columns 1-3 list the dataset acronym, the reference, and the type of binary studied in the dataset. Columns 4 and 5 list the number of targets in the original dataset, and the number of companions found for these targets. Columns 6 and 7 list the number of targets and companions used in our analysis. This dataset is smaller than the original dataset, as we do not include the non-members of Sco OB2 in our analysis and at most one companion per targeted star in the case of a multiple systems. The datasets partially overlap, which is taken into account when these are combined in the following sections. We list in this table the total number of spectroscopic binaries, including the radial velocity variables (RVVs; irrespective of their true nature), SB1s, and SB2s. For the Hipparcos observations we list the number of entries in the categories (X), (O), (G), (C), and (S), among the confirmed members of Sco OB2.
Table 4: An overview of the models for the selection effects used to generate simulated observations of simulated OB associations, for the six major datasets discussed in Sects. 4.1 to 4.6. The sample bias, resulting from the choice of the sample alone, includes the observer's choice and the brightness constraint. All other constraints result from the properties of the telescope, detector, atmospheric conditions, and confusion with background stars, and are in this paper referred to as the instrument bias. For a detailed description of the constraints mentioned in this table we refer to Sect. 4.5 of Kouwenhoven (2006).
Table 5: Candidate and confirmed astrometric binaries in the Hipparcos catalogue. For each subgroup we list the number $N_\star$ of known members, the number of stochastic (X); orbital (O); acceleration (G); component (C); and suspected (S) binaries in the Hipparcos catalogue. For each (S) binary we list between brackets how many of these are also (X)-flagged. The last three columns list the "astrometric binary fraction'' - including the (X), (O), (G) binaries - without the (S) binaries and with the (S) binaries included, and the Hipparcos "visual'' binary fraction, for the (C) binaries only. (V) binaries are not present in Sco OB2.
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.
Table 7: The five known binaries in Sco OB2 with an orbital period less than two days. Columns 1-3 list the primary star, the primary spectral type, and the measured orbital period. Columns 4 and 5 list the primary mass estimate as derived from the V-band magnitude, under the assumption that the mass ratio is $q\approx 0$ and q=1, respectively. Columns 6 and 7 list extremes for the semi-major axis of the binary, as derived using Kepler's third law, under the assumption of a mass ratio $q\approx 0$ (6th column), and q=1 (7th column). Finally, Cols. 8 and 9 list the subgroup of which the binary is a member and the reference for the orbital period. It is possible that a small number of closer, yet undiscovered binaries exist in Sco OB2.
Table 8: The widest known binary systems in Sco OB2. For each of these binary systems we list the angular separation, the Hipparcos parallax, an estimate for the semi-major axis $a_{\rm est} \equiv D\tan \rho$ , the subgroup, and the spectral type of the primary. The last column lists the reference. Note that this list must be incomplete, as very wide binaries are difficult to detect. Furthermore, several of these binaries may be optical due to confusion with background stars, i.e., not physically bound. References: (1) Lindroos (1985); (2) Worley (1978); (3) Worley & Douglass (1997); (4) Oblak (1978); (5) Tokovinin (1997).
Table 9: The observed binary fraction (in %) and inferred intrinsic binary fraction (in %) for the different datasets discussed in this paper. Columns 1 and 2 list the dataset and the observed binary fraction. The predicted observed binary fraction resulting from Öpik's law for each dataset (adopting $F_{M}=100\%$ ) is listed in Col. 3, followed by the inferred $1\sigma$ , $2\sigma$ and $3\sigma$ confidence ranges of the inferred binary fraction. The predicted observed binary fraction for the log-normal period distribution with $\mu =4.8$ and $\sigma =2.3$ (adopting $F_{M}=100\%$ ) and corresponding confidence ranges for the intrinsic binary fraction are listed in Cols. 7-10. The adopted association parameters are listed in Table 1. For models in Cols. 3-6 the semi-major axis range is $5~{R}_\odot\leq a \leq 5\times 10^6 ~{R}_\odot$ . For models in Cols. 7-10 the period range is $0.7~\mbox{day} \leq P \leq 3\times 10^8~\mbox{day}$ . For each model we assume a mass ratio distribution of the form $f_q(q) \propto q^{\gamma _q}$ with $\gamma _q=-0.4$ and a thermal eccentricity distribution. The comparison between observations and simulated observations indicates that the binary fraction among intermediate-mass binaries in Sco OB2 is close to 100% ( $\protect\ga$ 70% with $3\sigma$ confidence).
Table 10: 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 $F_{M}=100\%$ and a thermal eccentricity distribution. The values listed in Cols. 3 and 4 are proportional to F_M. 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 9. 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.
Table 11: The number of background stars expected per field of view for each of the three imaging surveys discussed in this paper, according to our model. The field of view size is 361.2 arcsec² for KO5, 196.0 arcsec² for KO6, and 280.1 arcsec² for SHT. We list the results for three different pointings: to the centers of the three subgroups US, UCL, and LCC, and for the intersection of LCC with the Galactic plane. Columns 4, 6, and 8 list the number of background stars brighter than $K_{\rm S}=12$ mag per field of view. Columns 5, 7, and 9 list the number of background stars brighter than $K_{\rm S}=18$ mag per field of view. The last column lists for each group the value of the normalization constant C in Eq. (34).
Table A.1: Properties of the KO5 dataset that we use in our analysis. Note that not all candidate companions are listed here, as in our analysis we only consider single stars and binary systems. The members HIP 68532 and HIP 69113 (marked with a star) both have two companions with a similar separation, position angle, and brightness. In our analysis we consider these "double companions'' as a single companion.
Table A.2: Properties of the KO6 dataset that we use in our analysis. Note that not all candidate companions are listed here, as in our analysis we only consider single stars and binary systems. The members HIP 68532 and HIP 69113 (marked with a star) both have two companions with a similar separation, position angle, and brightness. In our analysis we consider these "double companions'' as a single companion.
Table A.3: Properties of the SHT dataset that we use in our analysis. Note that not all candidate companions are listed here, as in our analysis we only consider single stars and binary systems. The six members at the bottom of the list were not explicitly observed by SHT. Due to the presence of (known) close companions these were not suitable for wavefront sensing. We have included these targets for our analysis to avoid a bias towards low binarity.
Table A.4: The LEV dataset used in this sample, consisting of 16 binaries with orbital elements (SB1 or SB2), and 23 radial velocity variables (RVV), for which no orbital elements are available. Left: the 16 spectroscopic binaries with orbital elements among the confirmed members of Sco OB2, in the LEV dataset. LEV observed 53 confirmed members of Sco OB2, of which 8 SB1s, 8 SB2s, 23 RVVs, and 14 targets with a constant radial velocity. Right: the 23 RVVs. Note that several of the RVVs may not be spectroscopic binaries, as radial velocity variation may also be caused by line profile variability.