Hard X-ray emission of the Earth's atmosphere: Monte Carlo simulations

We perform Monte Carlo simulations of cosmic ray-induced hard X-ray radiation from the Earth's atmosphere. We find that the shape of the spectrum emergent from the atmosphere in the energy range 25-300 keV is mainly determined by Compton scatterings and photoabsorption, and is almost insensitive to the incident cosmic-ray spectrum. We provide a fitting formula for the hard X-ray surface brightness of the atmosphere as would be measured by a satellite-born instrument, as a function of energy, solar modulation level, geomagnetic cutoff rigidity and zenith angle. A recent measurement by the INTEGRAL observatory of the atmospheric hard X-ray flux during the occultation of the cosmic X-ray background by the Earth agrees with our prediction within 10%. This suggests that Earth observations could be used for in-orbit calibration of future hard X-ray telescopes. We also demonstrate that the hard X-ray spectra generated by cosmic rays in the crusts of the Moon, Mars and Mercury should be significantly different from that emitted by the Earth's atmosphere.