Systematic offset between the best-fit velocity dispersion (σfitted) and the input velocity dispersion (σinp) relative to the input velocity dispersion due to the uncertainties in the orbital parameter distributions of OB stars for a single epoch of radial velocity data. From top to bottom we have generated the radial velocity data using the orbital parameter distributions from Sana et al. (2012), Sana et al. (2013), and Kiminki & Kobulnicky (2012). The colors of the lines indicate the set of orbital parameter distributions assumed for the fit: blue line for Sana et al. (2012); green line for Sana et al. (2013); red line for Kiminki & Kobulnicky (2012). When the orbital parameter distributions used to generate the data are the same as those assumed in the fit, there is no systematic offset in the fitted velocity dispersion. The error bars represent the remaining uncertainty on the systematic offset after ~30 Monte Carlo simulations, each of which included a sample of 2000 radial velocities. The simulations for which we find a best-fit binary fraction of 100% in the majority of cases are marked with a black cross (see upper panel) to indicate that the fitted velocity dispersion is most likely overestimated in this case (see the main text).
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