There remain significant uncertainties in the origin and evolution of black holes in binary systems, in particular regarding their birth sites and the influence of natal kicks. These are long-standing issues, but their debate has been reinvigorated in the era of gravitational wave detections and the improving precision of astrometric measurements. Using recent and archival characterisation of Galactic black hole X-ray binaries (BHXBs), we report here an apparent anticorrelation between P{orb} (system orbital periods) and scatter in z (elevation above the Galactic plane). The absence of long period sources at high z is not an obvious observational bias, and two possible explanatory scenarios are qualitatively explored: (1) a disc origin for BHXBs followed by natal kicks producing the scatter in z, with only the tightest binaries preferentially surviving strong kicks; (2) a halo origin, with P{orb} shortening through dynamical interactions in globular clusters (GCs). For the latter case, we show a correspondence in z-scatter between BHXBs and the GCs with most compact core radii of <0.1pc. However, the known absence of outbursting BHXB transients within Galactic GCs remains puzzling in this case, in contrast to the multitude of known GC neutron star XRBs. These results provide an interesting observational constraint for any black hole binary evolutionary model to satisfy.
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