Formation of Black Hole–White Dwarf X-Ray Binaries in Globular Clusters

Globular clusters are host to significant populations of dynamically active stellar remnants that connect to a variety of astrophysical sources. Using simulations performed with the Cluster Monte Carlo dynamics code, we study the formation of ultracompact binaries in which a stellar-mass black hole accretes material from a white dwarf companion in an orbit of less than an hour. These binary systems are prime multimessenger targets, as they can be observed both as luminous X-ray sources and as millihertz gravitational-wave sources detectable by the Laser Interferometer Space Antenna (LISA). We find that black hole+giant collisions are the primary mechanism through which such systems form. We model the outcomes of these “common envelope”-like events using the smoothed particle hydrodynamics code StarSmasher , and verify that these collisions yield black hole+white dwarf binaries that enter Roche contact on timescales ≲1 Gyr via gravitational-wave inspiral. We construct a mock catalog of local ultracompact X-ray sources and compare to candidate sources observed in globular clusters in the Milky Way (e.g., 47 Tuc X9) and external galaxies (e.g., RZ 2109 in NGC 4472). Finally, we compute the gravitational-wave strain for these sources, and show that of order one source may be resolvable in the Milky Way by LISA, representing a potentially powerful tool for observing new black holes in globular clusters.