  Very-high-energy gamma-ray observations of the Galactic center (GC) show
extended emission that is strongly correlated with the morphology of the
central molecular zone (CMZ). The best explanation for that emission is a
hadronic interaction between cosmic rays (CRs) and ambient gas, where a CR
central and continuous source accelerates protons up to 1 PeV ("PeVatron").
However, current models assume very simplistic CR dynamics. Our goal is to
verify if more realistic CR dynamics for the GC environment are consistent with
current gamma-ray observations, and whether they could be constrained by
upcoming observations with the Cherenkov Telescope Array (CTA). We generated
synthetic gamma-ray maps using a CR transport model with spherical injection,
different diffusion regimes (in and out of the CMZ), polar advection, and
mono-energetic particles of 1 PeV, and including different CR populations
injected from the Arches, Quintuplet, and nuclear clusters of young massive
stars, plus supernova Sgr A East. We adopted two different 3D gas distributions
consistent with the observed gas column density, either with or without an
inner cavity. In order to reproduce the existing observations detected by the
High Energy Stereoscopic System (HESS), a ring-like gas distribution, with its
mass set by the standard Galactic CO-to-H$_2$ conversion factor, and CR
acceleration from all relevant sources are required. For a conversion factor
one order of magnitude lower, injection rates that are ten times higher are
needed. We show that CTA will be able to differentiate between models with
different CR dynamics, proton sources, and CMZ morphology, owing to its
unprecedented sensitivity and angular resolution. More realistic CR dynamics
suggest that the CMZ has a large inner cavity and that the GC PeVatron is a
composite CR population accelerated by the Arches, Quintuplet, and nuclear star
clusters, and Sgr A East.
