Probing the presence of a single or binary black hole in the globular cluster NGC 6752 with pulsar dynamics

The five millisecond pulsars that inhabit NGC 6752 display locations or accelerations that are quite unusual compared to all other known pulsars in globular clusters. In particular, PSR A, a binary pulsar, lives in the cluster halo, while PSR B and PSR E, located in the core, show remarkably high negative spin derivatives. This suggests that some uncommon dynamical process is at play in the cluster core, which we attribute to the presence of a massive perturber. Here we investigate whether a single intermediate-mass black hole, lying on the extrapolation of the mass M-BH versus sigma relation observed in galaxy spheroids, or a less massive binary black hole could play the requested role. To this purpose we simulated binary-binary encounters involving PSR A, its companion star, and the black hole(s). A stellar-mass binary black hole of (50 M., 10 M.) can impart the right thrust to propel PSR A into the halo during a flyby. The flyby is gentle and does not alter the internal properties of the binary pulsar. An intermediate-mass binary black hole of (200 M., 10 M.) tends to impart a recoil speed larger than the escape speed: it can release PSR A on the right orbit if its separation is wide. A single intermediate-mass black hole of mass M(BH)greater than or similar to500 M. may have ejected PSR A at the periphery of NGC 6752 in a close dynamical encounter involving the binary pulsar, the black hole, and a star belonging to its cusp. The encounter gives correct speeds but alters significantly the eccentricity of the impinging binary, so that it must occur before the neutron star of PSR A is recycled via accretion torque. The influence of an intermediate-mass binary black hole on the acceleration of the two core pulsars is studied, and the ejection of stars by the binary is briefly explored. In inspecting our close four-body encounters, we have found that a single or binary black hole may attract on a long-term stable orbit a millisecond pulsar. Timing measurements on the captured "satellite'' pulsar, either a member of a hierarchical triple or a member of the cusp, could unambiguously unveil the presence of a black hole(s) in the core of a globular cluster.