  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
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. 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 degrees, 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.
