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Appendix A: Review of the binary properties of OB stars

The current constraints on the binary fraction and distributions of orbital parameters of massive binaries are reviewed below.

Appendix A.1: Period distribution

Sana et al. (2012) showed that the intrinsic period distribution of their Galactic open clusters sample does not follow the widely used Öpik law (i.e., a flat distribution in the logarithm of the separation or, equivalently, of the period; Öpik 1924) but is instead overabundant in short-period systems. They found an exponent π =  −0.55 ± 0.22 for the power law of the period distribution for lower and upper bounds of 0.15 and 0.35 on log ₁₀P/d. For the same period range, Sana et al. (2013) also found from the 30 Doradus dataset a stronger preference for short periods than previously assumed, with a comparable value of π =  −0.45 ± 0.30. This is in contrast with the best-fit value of π = 0.2 ± 0.4 from Kiminki & Kobulnicky (2012) for Cyg OB2 binaries, which is consistent with the Öpik law to within 1σ, although these authors argued that no single power law adequately reproduces the data at the shortest periods (P < 14 days). Although this work assumes a power-law distribution valid between 1 and 1000 days, we must also highlight that the sample does not probe this full range of periods. The power-law exponent of the period distribution was determined from 22 binaries with periods shorter than 30 days, so the results had to be extrapolated over almost two orders of magnitude.

Appendix A.2: Mass ratio distribution

It has been reported that the mass ratio distribution of massive binaries tends to peak toward unity (Bosch & Meza 2001; Pinsonneault & Stanek 2006), but this has since been contested (Lucy 2006) and more recent studies tend to favor a flat distribution of mass ratios. Kiminki & Kobulnicky (2012) indeed inferred a value of κ = 0.1 ± 0.5 for the exponent of the power-law distribution of mass ratios for the known massive binaries in Cyg OB2. Similarly, Sana et al. (2012) found no preference for equal-mass binaries (κ =  −0.1 ± 0.6) in Galactic open clusters. In 30 Doradus, Sana et al. (2013) even found a mass ratio distribution that is slightly skewed toward systems with low mass ratios (κ =  −1.0 ± 0.4), although this only provides a weak constraint on the distribution of mass ratios, and these results still agree within 2σ with the two previous studies reporting flat distributions. These results are all incompatible with a random pairing from a classical mass function (i.e. κ =  −2.35; see Sana et al. 2013).

Appendix A.3: Eccentricity distribution

Because measuring the eccentricity of a spectroscopic binary requires many epochs of radial velocity data, we are only beginning to probe the eccentricity distribution of massive binaries. As expected from tidal dissipation that tends to circularize their orbit (Zahn 1977, 1978), a large portion of the short-period massive binary systems are found to have low eccentricities

(Sana & Evans 2011; Kiminki & Kobulnicky 2012). Kiminki & Kobulnicky (2012) found a value of η =  −0.6 ± 0.3 for the exponent of the power-law distribution of eccentricities, while Sana et al. (2012) obtained η =  −0.45 ± 0.17. Sana et al. (2013) could not constrain η in the 30 Doradus study and instead adopted the eccentricity distribution inferred by Sana et al. (2012) for the Galactic open clusters sample.

Appendix A.4: Binary fraction

A number of studies have investigated the observed fraction of spectroscopic binaries among massive stars. Mason et al. (2009) compiled results from the literature to show that 51% of the Galactic O-type stars investigated by multi-epoch spectroscopy are in fact spectroscopic binaries, while this fraction increases to 56% for objects in clusters or OB associations. Barbá et al. (2010) obtained a similar fraction, with 60% of the 240 Galactic O and WN stars in their survey of the southern sky displaying significant radial velocity variations (i.e. >10 km   s^-1). Chini et al. (2012) also observed a high binary fraction in their spectroscopic survey of Galactic O and B stars in the southern sky. Studies focusing on individual young open clusters or OB associations have reported observed binary fractions between 30 and 60% (e.g. De Becker et al. 2006; Hillwig et al. 2006; Sana et al. 2008, 2009; Mahy et al. 2009; Rauw et al. 2009; Sana et al. 2011; Mahy et al. 2013), with variations from one cluster to the other compatible with the statistical fluctuations expected given the size of the samples (Sana & Evans 2011). Thus, although it has been proposed that the spectroscopic binary fraction might be related to the cluster density (e.g. García & Mermilliod 2001), the current data are consistent with a common binary fraction in all clusters, at least for O-star-rich clusters (for details see Sana & Evans 2011).

To constrain the intrinsic fraction of spectroscopic binaries, one has to correct the observed fraction for observational biases that depend on the underlying distributions of orbital parameters. Kobulnicky & Fryer (2007) opted to fix the period distribution to the standard Öpik law because the solution of their Monte Carlo simulations for the period and mass-ratio distributions was degenerate. They inferred an intrinsic binary fraction of over 80%, but note that the range of separations considered in this study (up to 10 000 AU) extends well beyond the sensitivity domain of their spectroscopic observations. Kiminki & Kobulnicky (2012) observed a binary fraction of 21% in Cyg OB2 (24/114 objects) and inferred an intrinsic fraction of 44 ± 8% considering binaries with periods between 1 and 1000 days. Sana et al. (2012) identified 40 spectroscopic binaries for an observed binary fraction of 56% in their Galactic open clusters sample and found an intrinsic fraction of 69 ± 9% for periods in the range 0.15 < log ₁₀P/d < 3.5. Sana et al. (2013) observed a spectroscopic binary fraction of 35 ± 3% in 30 Doradus, compatible with what Bosch et al. (2009) found from a different but overlapping sample of 54 O and early B-type stars, and inferred an intrinsic binary fraction of 51 ± 4% for periods in the range 0.15 < log ₁₀P/d < 3.5. This binary fraction appears mostly uniform across the 30 Doradus region and independent of the spectral subtype and luminosity class.

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