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 (∼11 M_⊙) was lost, giving rise to a symmetric Blaauw kick of up 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 ∼9 M_⊙, since when it has accreted 0.5-1.5 M_⊙ from its companion.