While there are an estimated 100 million black holes in our Galaxy, there are relatively few observational constraints on the mechanisms by which such exotic objects form. Theoretical work suggests that the most massive black holes should form via direct collapse, whereas those less massive should undergo a natal supernova. During a supernova, different magnitude velocity kicks can be imparted to the black hole, depending on the nature of the supernova. We propose to continue our successful program of high angular resolution LBA observations (triggered by our joint ATCA proposal) to test these predictions by measuring the proper motion of a black hole X-ray binary, which, when combined with the optically-determined systemic radial velocity and source distance, will provide the full three-dimensional space velocity of the system. Comparison with the predicted velocity from Galactic rotation will determine whether the system received a natal kick during a supernova, and hence place observational constraints on the formation mechanism of black holes. Natal kick distributions are a key parameter in simulating the expected rates of black hole mergers, which give rise to gravitational waves. With only a handful of BH proper motions having been measured to date, the sample size must be increased if we are to test the theoretical predictions for BH formation. We therefore request up to 24 hours of time with the LBA over the next year to perform high-precision astrometric observations during the hard states of the outburst of a black hole X-ray binary.
