tokens: datasets with Gammapy by generating random count maps from a Poisson distribution taking into account the expected residual hadronic background and the physical model. The expected γ -ray profile alongthe Galactic longitude from those simulations for H.E.S.S and CTA is represented in Fig. 4 in two energy bands: 0.5–5 TeV and 5–100 TeV. We can see the variation of the profile morphology in the two energy bands for H.E.S.S. and CTA simulations, but it appears that the statistical errors with H.E.S.S. at high energy are too high to enable us to distinguish any variation between the low- and high-energy profiles (see Fig. 4 a). On the other hand, this simulation clearly demonstrates that CTA will be able to measure such a morphology variation with energy thanks to the SST and the strong increase of the statistic in the high-energy range ( Fig. 4 b). In the near future, CTA observations will therefore establish a clear constraint on the origin of this VHE diffuse emission and on the CR acceleration mechanism in the CMZ. Fig. 4 Expected γ -ray profile along the Galactic longitude from the simulation of 100 GC datasets of 250 h between 0.5–5 TeV (blue) and 5–100 TeV (orange). On the top those profiles are simulated using H.E.S.S. IRFs and on the bottom using CTA IRFs (version prod3b-v2, http://www.cta-observatory.org/science/cta-performance/ ). The solid lines represent the median of the 100 simulated datasets and the colored region the dispersion around the median. The dispersion contains 50% of the realizations in each longitude bin independently. 5 Conclusions Supernova remnants are natural candidates for Galactic CR acceleration. With a 3D model of CR injection and propagation in the GC, we already showed that the SNe alone can reproduce the total VHE γ -ray flux of the diffuse emission, by considering typical values for the SN rate, the diffusion coefficient, the total mass of the matter in the region, and a low CR acceleration efficiency of approximately 2% ( Jouvin et al. 2017 ). Besides, we showed that SNRs, concentrated at the position of the massive stellar clusters, the Quintuplet, and the central disk, creates a pronounced CR gradient but can only marginally reproduce the data obtained by the H.E.S.S. Collaboration in the inner 30 pc ( Abramowski et al. 2016 ; H.E.S.S. Collaboration 2018a ). Yet, we considered only a burst-like injection in which all the CRs are emitted at the same time in the ISM independently of their energy. The deceleration of the shock wave in the adiabatic phase of the SNR evolution leads to a progressive energy-dependent CR escape in the surrounding medium. To add this more realistic time-energy-dependent escape from the SNR, we followed thework of Gabici et al. (2009) who assume that the time dependency of the proton energy loss in this phase follows a power law. With this approach, the low-energy CRs remain confined a longer time in the remnant than the high energy CRs. At lower energies, the CRs do not
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