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We develop a model for a possible origin of hard very high energy spectrafrom a distant blazar. In the model, both the primary photons produced in thesource and secondary photons produced outside the source contribute to theobserved high energy $\gamma$-rays emission. That is, the primary photons areproduced in the source through the synchrotron self-Compton (SSC) process, andthe secondary photons are produced outside the source through high energyprotons interaction with the background photons along the line of sight. Weapply the model to a characteristic case was the very high energy (VHE)$\gamma$-ray emissions in distant blazar 1ES 1101-232. Assuming a suitableelectron and proton spectra, we obtain excellent fits to observed spectra ofdistant blazar 1ES 1101-232. This indicated that the surprisingly lowattenuation of high energy $\gamma$-rays, especially for the shape of the veryhigh energy $\gamma$-rays tail of the observed spectra, can be explained bysecondary $\gamma$-rays produced in interactions of cosmic-ray protons withbackground photons in the intergalactic space.

Evidence for the Secondary Emission as the Origin of Hard Spectra in TeV Blazars