The Formation of Binaries Containing Black Holes by the Exchange of Companions and the X-ray Sources in Globular Clusters

Clark's suggestion that the X-ray sources in globular clusters are binaries containing black holes or neutron stars is viable if we consider their formation by an exchange of companions with primordial binaries rather than by three-star encounters as originally suggested. In this process, which is similar to charge exchange among atomic particles, the black hole or neutron star makes a close encounter with a primordial binary, ejects one of its components, and becomes itself bound to the binary. The model is capable of producing the observed number of X-ray sources in globular clusters if a fraction $${f}_\text{b}\,={10}^{-3}-{10}^{-2}$$ of the ordinary stars in the clusters are binaries with semimajor axes less than 1 AU. However, a consideration of the relative reaction rates reveals that X-ray sources powered by the tidal break-up and capture of ordinary stars by the black holes and neutron stars are likely to radiate several orders of magnitude more energy than that emitted by the X-ray binaries.