tokens: correlations between the p -values for each formation channel provided in Table 1 and the half-mass relaxation time, t rh . Fig. 8 shows that there is no strong correlation between the p -values obtained for the mass-transfer channel and the cluster half-mass relaxation time. If such a correlation were present, 2 one interpretation would be that the initial BS velocity distribution immediately after formation is not Maxwellian, but instead evolves towards a dynamically relaxed state over a relaxation time. This would, in principle, be more consistent with the collisional hypothesis, since the binary mass-transfer hypothesis predicts that BSs descended directly from internal evolution within (relatively) old binaries that have had plenty of time to relax towards a Maxwellian velocity distribution. Thus, the results from this component of our analysis are most consistent with a mass-transfer origin for the majority of the BSs in our samples, since the observed BS velocity distributions are typically consistent with having formed from a dynamically relaxed population. However, as already discussed, this is insufficient to fully exclude the collisional channel, because collisions among the dynamically relaxed binary population would yield the same Maxwellian velocity distribution of the collision products in very relaxed clusters. As shown in Table 1 and Fig. 8 , the 2+2 collisional velocity distributions best match the observed BS velocity distributions for the post-core collapse GCs in our sample, namely NGC 6624, NGC 6681 and NGC 7099. The latter being our strongest candidate for having a large fraction of BSs formed via 2+2 collisions. This provides good independent evidence to support the claim of a strong contribution from collisions to BS formation in NGC 7099, as found by Ferraro et al. ( 2009 ). 4 SUMMARY AND DISCUSSION In this paper, we have performed a thorough statistics-based search to answer the question: What are the origins of BS stars in GCs? The BS catalogue of Simunovic Puzia ( 2016 ) provides us with observational measurements for BS velocities (from their proper motions) and masses (from isochrone-fitting and assuming they are single isolated objects). We compare these observed BS masses and velocities to analogous theoretical predictions for BSs formed from MS–MS collisions during single–binary (1+2) and binary–binary (2+2) interactions, obtained via a suite of numerical scattering experiments performed with the FEWBODY code (Fregeau et al. 2004 ). The results of this analysis are ultimately consistent with the BS samples having been derived from a dynamically relaxed population. At face value, this appears to favour the mass-transfer (and/or binary merger) hypothesis for BS formation. This is because the p -values obtained from Kolmogorov–Smirnov tests suggest that the observed BS velocity distributions most closely resemble Maxwellian velocity distributions, adjusted to account for the slightly higher masses of the
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