On the hard $γ$-ray spectrum of the potential PeVatron supernova remnant G106.3+2.7

Abstract: The Tibet AS$\gamma$ experiment has measured $\gamma$-ray flux of supernova remnant G106.3+2.7 up to 100 TeV, suggesting it {being} potentially a "PeVatron". Challenge arises when the hadronic scenario requires a hard proton spectrum (with spectral index $\approx 1.8$), while {usual observations and numerical simulations prefer} a soft proton spectrum {(with spectral index $\geq 2$)}. In this paper, we explore an alternative scenario to explain the $\gamma$-ray spectrum of G106.3+2.7 within the current understanding of acceleration and escape processes. We consider that the cosmic ray {particles} are scattered by the turbulence driven via Bell instability. The resulting hadronic $\gamma$-ray spectrum is novel, dominating the contribution to the emission above 10\,TeV, and can explain the bizarre broadband spectrum of G106.3+2.7 in combination with leptonic emission from the remnant.