Probing the formation history of the nuclear star cluster at the Galactic Centre with millisecond pulsars

The origin of the nuclear star cluster in the centre of our Galaxy is still unknown. One possibility is that it formed after the disruption of stellar clusters that spiralled into the Galactic Centre due to dynamical friction. We trace the formation of the nuclear star cluster around the central black hole, using state-of-the-art N-body simulations, and follow the dynamics of the neutron stars born in the clusters. We then estimate the number of millisecond pulsars (MSPs) that are released in the nuclear star cluster during its formation. The assembly and tidal dismemberment of globular clusters lead to a population of MSPs distributed over a radius of about 20 pc, with a peak near 3 pc. No clustering is found on the subparsec scale. We simulate the detectability of this population with future radio telescopes like the MeerKAT radio telescope and SKA1, and find that about an order of 10 MSPs can be observed over this large volume, with a paucity of MSPs within the central parsec. This helps discriminating this scenario from the in situ formation model for the nuclear star cluster that would predict an overabundance of MSPs closer to the black hole. We then discuss the potential contribution of our MSP population to the gamma-ray excess at the Galactic Centre.