Dynamically formed black hole+millisecond pulsar binaries in globular clusters

The discovery of a binary comprising a black hole (BH) and a millisecond pulsar (MSP) would yield insights into stellar evolution and facilitate exquisitely sensitive tests of general relativity. Globular clusters (GCs) are known to harbour large MSP populations and recent studies suggest that GCs may also retain a substantial population of stellar mass BHs. We modelled the formation of BH+MSP binaries in GCs through exchange interactions between binary and single stars. We found that in dense, massive clusters most of the dynamically formed BH+MSP binaries will have orbital periods of 2-10 d, regardless of the mass of the BH, the number of BHs retained by the cluster, and the nature of the GC's binary population. The size of the BH+MSP population is sensitive to several uncertain parameters, including the BH mass function, the BH retention fraction, and the binary fraction in GCs. Based on our models, we estimate that there are 0.6 ± 0.2 dynamically formed BH+MSP binaries in the MilkyWay GC system, and place an upper limit on the size of this population of ∼10. Interestingly, we find that BH+MSP binaries will be rare even if GCs retain large BH populations.