Formation of black hole X-ray binaries in globular clusters

Inspired by the recent identification in extragalactic globular clusters of the first candidate black hole-white dwarf (BH-WD) X-ray binaries, where the compact accretorsmay be stellar-mass black holes (BHs), we explore how such binaries could be formed in a dynamical environment. We provide analyses of the formation rates via well-known formation channels like binary exchange and physical collisions and propose that the only possibility of forming BH-WD binaries is via coupling these usual formation channels with subsequent hardening and/or triple formation. In particular, we find that the most important mechanism for the creation of a BH-WD X-ray binary from an initially dynamically formed BH-WD binary is mass transfer induced in a triple system via the Kozai mechanism. Furthermore, we find that BH-WD binaries that evolve into X-ray sources can be formed by exchanges of a BH into a WD-WD binary or possibly by collisions of a BH and a giant star. If BHs undergo significant evaporation from the cluster or form a completely detached subcluster of BHs, then we cannot match the observationally inferred production rates even using the most optimistic estimates of formation rates. To explain the observations with stellar-mass BH-WD binaries, at least 1% of all formed BHs, or presumably 10% of the BHs present in the core now, must be involved in interactions with the rest of the core stellar population.