On the hadronic origin of the very high energy $γ$-ray emission surrounding the young massive stellar cluster Westerlund 1

The Westerlund 1 (Wd 1) is the most massive known young star cluster in the Galaxy, and an extended $γ$-ray source HESS J1646-458 surrounding it has been detected up to 80 TeV in the very high energy, implying that cosmic rays (CRs) are accelerated effectively in the region. However, the dominant radiation process contributing to the $γ$-ray emission is not well constrained. In the present work, we develop a model of CR acceleration at the termination shock in the superbubble inflated by the interaction of the cluster wind from the Wd 1 with the surrounding interstellar medium. We then calculate the flux and radial profile of $γ$ rays produced by the inelastic collisions of the hadronic CRs with the ambient gas. Our results with reasonable parameters can explain well the spectrum and radial profile of the $γ$-ray emission of HESS J1646-458, and consequently the $γ$-ray emission of HESS J1646-458 is likely to be of hadronic origin.