Fermi has detected gamma-ray emission from eight globular clusters. We suggest that the gamma-ray emission from globular clusters may result from the inverse Compton scattering between relativistic electrons/positrons in the pulsar wind of MSPs in the globular clusters and background soft photons including cosmic microwave/relic photons, background star lights in the clusters, the galactic infrared photons and the galactic star lights. We show that the gamma-ray spectrum from 47 Tuc can be explained equally well by upward scattering of either the relic photons, the galactic infrared photons or the galactic star lights whereas the gamma-ray spectra from other seven globular clusters are best fitted by the upward scattering of either the galactic infrared photons or the galactic star lights. We also find that the observed gamma-ray luminosity is correlated better with the combined factor of the encounter rate and the background soft photon energy density. Therefore the inverse Compton scattering may also contribute to the observed gamma-ray emission from globular clusters detected by Fermi in addition to the standard curvature radiation process. Furthermore, we find that the emission region of high energy photons from globular cluster produced by inverse Compton scattering is substantially larger than the core of globular cluster with a radius >10pc. The diffuse radio and X-rays emitted from globular clusters can also be produced by synchrotron radiation and inverse Compton scattering respectively. We suggest that future observations including radio, X-rays, and gamma-rays with energy higher than 10 GeV and better angular resolution can provide better constraints for the models.
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