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A hard $\gamma$-ray spectrum of supernova remnant G106.3+2.7 can be explainedby using the hadronic model with the gluon condensation effect. This impliesthat not only PeVatrons but also EeVatrons generally exist in the universeincluding our galaxy, and they can accelerate protons to beyond "ankle"($10^{19}~eV$). Although these proton beams are very weak in the galaxy andcannot be observed individually on the earth, the gluon condensation effect maygreatly enhance the proton-proton cross section, which can compensate for theweak proton flux and produce the observed $\gamma$-rays. We also show that thegluon condensation effect in proton provides an efficient conversion mechanismfor kinetic energy into $\gamma$-rays in the universe.

The current recorded signals of ultrahigh-energy $\gamma$-rays may come from EeVatrons in the galaxy