We use very long baseline interferometry to measure the proper motions of three black hole Xray binaries (BHXBs). Using these results together with data from the literature and Gaia DR2 to collate the best available constraints on proper motion, parallax, distance, and systemic radial velocity of 16 BHXBs, we determined their threedimensional Galactocentric orbits. We extended this analysis to estimate the probability distribution for the potential kick velocity (PKV) a BHXB system could have received on formation. Constraining the kicks imparted to BHXBs provides insight into the birth mechanism of black holes (BHs). Kicks also have a significant effect on BH–BH merger rates, merger sites, and binary evolution, and can be responsible for spin–orbit misalignment in BH binary systems. 75 per cent of our systems have potential kicks $\gt 70\, \rm {km\,s^{1}}$. This suggests that strong kicks and hence spin–orbit misalignment might be common among BHXBs, in agreement with the observed quasiperiodic Xray variability in their power density spectra. We used a Bayesian hierarchical methodology to analyse the PKV distribution of the BHXB population, and suggest that a unimodal Gaussian model with a mean of 107 $\pm \,\,16\, \rm {km\,s^{1}}$ is a statistically favourable fit. Such relatively high PKVs would also more »
 Publication Date:
 NSFPAR ID:
 10121273
 Journal Name:
 Monthly Notices of the Royal Astronomical Society
 Volume:
 489
 Issue:
 3
 Page Range or eLocationID:
 p. 31163134
 ISSN:
 00358711
 Publisher:
 Oxford University Press
 Sponsoring Org:
 National Science Foundation
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