Cherenkov Telescope Array sensitivity to the putative millisecond pulsar population responsible for the Galactic Centre excess

The leading explanation of the Fermi Galactic Centre γ-ray excess is the extended emission from an unresolved population of millisecond pulsars (MSPs) in the Galactic bulge. Such a population would, along with the prompt γ-rays, also inject large quantities of electrons/positrons (e^±) into the interstellar medium. These e^± could potentially inverse-Compton (IC) scatter ambient photons into γ-rays that fall within the sensitivity range of the upcoming Cherenkov Telescope Array (CTA). In this article, we examine the detection potential of CTA to this signature by making a realistic estimation of the systematic uncertainties on the Galactic diffuse emission model at TeV-scale γ-ray energies. We forecast that, in the event that e^± injection spectra are harder than E^-2, CTA has the potential to robustly discover the IC signature of a putative Galactic bulge MSP population sufficient to explain the Galactic Centre excess for e^± injection efficiencies in the range of ≈2.9-74.1 per cent, or higher, depending on the level of mismodelling of the Galactic diffuse emission components. On the other hand, for spectra softer than E^-2.5, a reliable CTA detection would require an unphysically large e^± injection efficiency of ${\gtrsim} 158{{\ \rm per\ cent}}$. However, even this pessimistic conclusion may be avoided in the plausible event that MSP observational and/or modelling uncertainties can be reduced. We further find that, in the event that an IC signal were detected, CTA can successfully discriminate between an MSP and a dark matter origin for the radiating e^±.