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In this work, we consider the possible presence of a large population ofmillisecond pulsars in the Galactic Centre. Their direct detection would bechallenging due to severe pulse broadening caused by scattering of radiation.We propose a new method to constrain their population with neutrino imaging ofthe Galactic Centre. Millisecond pulsars are proposed cosmic-ray accelerators.The high-energy protons they produce will collide with the baryonic matter inthe central molecular zone to create charged and neutral pions that decay intoneutrinos and $\gamma$-rays, respectively. The specific neutrino and$\gamma$-ray fluxes must be below their corresponding observed values, allowingus to put a conservative upper limit on the millisecond pulsar population ofN_MSP < 10,000 within a galacto-centric radius of 20 pc. This upper limit issensitive to the proton acceleration efficiency of the pulsars, but is lessdependent on the particle injection spectral index and the choice of masstracers. The population will be better constrained when high resolutionneutrino observations of the Galactic Centre become available. The presence ofthese millisecond pulsars can account for the $\gamma$-ray excess in theGalactic Centre.

Neutrino Imaging of the Galactic Centre and Millisecond Pulsar Population