Macias, Oscarvan Leijen, HarmSong, DehengAndo, Shin'ichiroHoriuchi, ShunsakuCrocker, Roland2023-03-072023-03-070035-8711http://hdl.handle.net/1885/286677The 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 CTAto this signature bymaking 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 ≥158 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±.OM acknowledges support by Japan Society for the Promotion of Science KAKENHI grant number JP20K14463. The work of DS is supported by the U.S. Department of Energy under the award number DE-SC0020262. SA is supported by Japan Society for the Promotion of Science KAKENHI grant numbers JP17H04836 and JP18H04340. The work of SH is supported by the United States Department of Energy under the award number DE-SC0020262 and National Science Foundation grant numbers AST-1908960 and PHY-1914409. This work was supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. RMC acknowledges support from the Australian Government through the Australian Research Council for grant DP190101258 shared with Prof. Mark Krumholz at the ANU. DMN acknowledges support from National Aeronautics and Space Administration under award number 80NSSC19K0589application/pdfen-AU© 2021 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society202110.1093/mnras/stab14502021-12-26