2011ApJ...728...11I

High energy gamma-ray emission from two nearby bright starburst galaxies, M82 and NGC 253, have recently been detected by Fermi, H. E. S. S., and VERITAS. Since starburst galaxies have a high star formation rate and plenty of dust in the central starburst region, infrared emissions are strong there. Gamma-ray photons are absorbed by the interstellar radiation field photons via electron and positron pair creation. The generated electron and positron pairs up-scatter the interstellar photons to very high energy gamma-ray photons via cascade emission through inverse Compton scattering. In this paper, we evaluate the contribution of this cascade emission to the gamma-ray spectra of M82 and NGC 253. Although it would be difficult to see direct gamma-ray evidence of cosmic-rays with an energy >10 TeV due to the gamma-ray attenuation, the resulting cascade emission would be indirect evidence. By including the cascade component, we find that the total flux above 1 TeV increases ∼18% and ∼45% compared with the absorbed flux assuming the maximum kinetic proton energy as 45.3 and 512 TeV, respectively. Future gamma-ray observatories such as CTA would be able to see the indirect evidence of cosmic-rays with energies >10 TeV by comparing with theoretical emission models including this cascade effect.