The formation of the black hole in the X-ray binary system V404 Cyg

Using new and archival radio data, we have measured the proper motion of the black hole X-ray binary V404 Cyg to be 9.2 +/- 0.3 mas yr(-1). Combined with the systemic radial velocity from the literature, we derive the full three-dimensional heliocentric space velocity of the system, which we use to calculate a peculiar velocity in the range 47-102 km s(-1), with a best-fitting value of 64 km s(-1). We consider possible explanations for the observed peculiar velocity and find that the black hole cannot have formed via direct collapse. A natal supernova is required, in which either significant mass (similar to 11 M-circle dot) was lost, giving rise to a symmetric Blaauw kick of up to similar to 65 km s(-1), or, more probably, asymmetries in the supernova led to an additional kick out of the orbital plane of the binary system. In the case of a purely symmetric kick, the black hole must have been formed with a mass similar to 9 M-circle dot, since when it has accreted 0.5-1.5 M-circle dot from its companion.