Constraints on very high energy gamma-ray emission from the Fermi bubbles with future ground-based experiments

The origin of sub-TeV gamma rays detected by the Fermi-Large Area Telescope (LAT) from the Fermi bubbles (FBs) at the Galactic center is still uncertain. In a hadronic model, acceleration of protons and/or nuclei and their subsequent interactions with gas in the bubble volume can produce the observed gamma rays. Recently the High Altitude Water Cherenkov (HAWC) observatory reported an absence of gamma-ray excess from the Northern FB at b6° Galactic latitude, which resulted in flux upper limits in the energy range of 1.2-126 TeV. These upper limits are consistent with the gamma-ray spectrum measured by Fermi-LAT at |b|≥10°, where an exponential cutoff at energies 100 GeV is evident. However, the FB gamma-ray spectrum at |b|≤10°, without showing any sign of cutoff up to around 1 TeV in the latest results, remains unconstrained. The upcoming Cherenkov Telescope Array (CTA) will perform a Galactic center survey with unprecedented sensitivity in the energy between 20 GeV and 300 TeV. In this work, we perform both morphological and classic on/off analyses with planned CTA deep central and extended survey and estimate the sensitivity of CTA to the FB hadronic gamma-ray flux models that best fit the spectrum at |b|≤10° and whose counterpart neutrino flux model best fits the optimistic neutrino spectrum from IceCube Neutrino Observatory. We also perform sensitivity analysis with a future ground-based Cherenkov detector the Large High Altitude Air Shower Observatory (LHAASO). We find that CTA will be able to discover or constrain the FB gamma-ray flux at |b|≤10° in the ≈200 GeV-100 TeV range with planned observation strategy, while LHAASO may constrain emission in the ≈100 GeV-100 TeV range if 10% systematic uncertainties can be achieved.