Past activity of Sgr A ⋆ is unlikely to affect the local cosmic-ray spectrum up to the TeV regime

Context The presence of kiloparsec-sized bubble structures on both sides of the Galactic plane suggests active phases of Sgr A ⋆ , the central supermassive black hole of the Milky Way in the last 1–6 Myr. We investigated the contribution of such events to the cosmic-ray (CR) flux measured in the solar neighborhood with numerical simulations. Aims. We evaluate whether the population of high-energy charged particles emitted by the Galactic center could be sufficient to significantly impact the CR flux measured in the solar neighborhood. Methods. We present a set of 3D magnetohydrodynamical simulations following the anisotropic propagation of CRs in a Milky Way-like Galaxy. We followed independent populations of CRs through time. We followed CRs originating from two different source types, namely supernovae and the Galactic center. To assess the evolution of the CR flux spectrum properties, we split these populations into two independent energy groups of 100 GeV and 10 TeV. Results. We find that the anisotropic nature of CR diffusion dramatically affects the amount of CR energy received in the solar neighborhood. The typical timescale required to observe measurable changes in the CR spectrum slope is of the order 10 Myr, largely surpassing estimated ages of the Fermi bubbles in the active galactic nuclei (AGN) jet-driven scenario. Conclusions. We conclude that a CR outburst from the Galactic center in the last few million years is unlikely have produced any observable feature in the local CR spectrum in the TeV regime within times consistent with current estimates of the age of the Fermi bubbles.