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Formation of black-hole X-ray binaries in globular clusters

Inspired by the recent identification of the first candidate BH-WD X-ray binaries, where the compact accretors may be stellar-mass black hole candidates in extragalactic globular clusters, 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 to form BH-WD binaries is via coupling these usual formation channels with subsequent hardening and/or triple formation. Indeed, we find that the most important mechanism to make a BH-WD X-ray binary from an initially dynamically formed BH-WD binary is triple induced mass transfer via the Kozai mechanism. Even using the most optimistic estimates for the formation rates, we cannot match the observationally inferred production rates if black holes undergo significant evaporation from the cluster or form a completely detached subcluster of black holes. We estimate that at least 1% of all formed black holes, or presumably 10% of the black holes present in the core now, must be involved in interactions with the rest of the core stellar population.