Accelerated protons produced by magnetic Penrose process in Sgr A*

Typical mechanisms to extract energies from a rotating black hole are the Blandford-Znajek process and the Penrose process. The Penrose process requires a special condition that is difficult to occur in common astrophysical situations. However, the magnetic Penrose process (MPP) does not require such a special condition, and can produce ultra-high energy cosmic rays. When neutrons decay near a rotating black hole, the MPP efficiency of the produced proton is maximized. The supermassive black hole in Sagittarius A* (Sgr A*) is likely to have a radiatively inefficient accretion flow that is hot enough to produce neutrons by nuclear reactions, which can be subsequently accelerated to high-energy by the MPP. We calculate the production rate of accelerated protons from the Sgr A* to estimated the gamma-ray flux at Earth produced by these accelerated protons and the flux of the accelerated protons themselves transported from Sgr A* to Earth. We find that these very high-energy gamma rays ($E_{\gamma}\gtrsim10\,\mathrm{TeV}$) amount to a significant fraction of the flux of the gamma-ray from the HESS J1745-290 and the central molecular zone around $100\,\mathrm{TeV}$. The accelerated proton flux, when the dimensionless spin parameter $a_{*}=0.5$ and the magnetic field strength in the vicinity of the black hole $B_{0}=100\,\mathrm{G}$, is about $1.6-4.1\%$ of the cosmic ray proton flux from KASCADE experiment at about $1\,\mathrm{PeV}$. Due to the finite decay time of neutrons which need to be transported from the accretion flow to the acceleration zone, our acceleration model can operate only around black holes with mass not much greater than $\sim10^8\,M_\odot$.