In this work, we consider the possible presence of a large population of millisecond pulsars in the Galactic Centre. Their direct detection would be challenging due to severe pulse broadening caused by scattering of radiation.
We propose a new method to constrain
their population with neutrino imaging
of the Galactic Centre.
Millisecond pulsars are proposed cosmic-ray accelerators. The high-energy protons they produce will collide with the baryonic matter in the central molecular zone to create charged and neutral pions that decay into neutrinos and $\gamma$-rays, respectively.
The specific neutrino and $\gamma$-ray fluxes
must be below their corresponding observed values, allowing us to put a conservative upper limit on the millisecond pulsar population
of $N_{\rm MSP} < 10{,}000$ within a galacto-centric radius of $20\,$pc.
This upper limit is sensitive to
the proton acceleration efficiency
of the pulsars, but is less dependent on
the particle injection spectral index and
the choice of mass tracers.
The population will be better constrained
when high resolution
neutrino observations
of the Galactic Centre become
available.
The presence of these millisecond pulsars
can account for the $\gamma$-ray excess
in the Galactic Centre.