Modeling of proton-induced radioactivation background in hard X-ray telescopes: Geant4-based simulation and its demonstration by Hitomi's measurement in a low Earth orbit

Hard X-ray astronomical observatories in orbit suffer from a significant amount of background due to radioactivation induced by cosmic-ray protons and/or geomagnetically trapped protons. Within the framework of a full Monte Carlo simulation, we present modeling of in-orbit instrumental background which is dominated by radioactivation. To reduce the computation time required by straightforward simulations of delayed emissions from activated isotopes, we insert a semi-analytical calculation that converts production probabilities of radioactive isotopes by interaction of the primary protons into decay rates at measurement time of all secondary isotopes. Therefore, our simulation method is separated into three steps: (1) simulation of isotope production, (2) semi-analytical conversion to decay rates, and (3) simulation of decays of the isotopes at measurement time. This method is verified by a simple setup that has a CdTe semiconductor detector, and shows a 100-fold improvement in efficiency over the straightforward simulation. To demonstrate its experimental performance, the simulation framework was tested against data measured with a CdTe sensor in the Hard X-ray Imager onboard the Hitomi X-ray Astronomy Satellite, which was put into a low Earth orbit with an altitude of 570 km and an inclination of 31^°, and thus experienced a large amount of irradiation from geomagnetically trapped protons during its passages through the South Atlantic Anomaly. The simulation is able to treat full histories of the proton irradiation and multiple measurement windows. The simulation results agree very well with the measured data, showing that the measured background is well described by the combination of proton-induced radioactivation of the CdTe detector itself and thick Bi₄Ge₃O₁₂ scintillator shields, leakage of cosmic X-ray background and albedo gamma-ray radiation, and emissions from naturally contaminated isotopes in the detector system.