In the last decade, the detection by diverse experiments of diffuse $\gamma$-ray emissions toward several galactic young massive star clusters has renewed attention to these objects as potential galactic cosmic ray accelerators. Indeed, the conversion of a few percent of the power supplied by the strong winds from the massive stars into accelerated particles is enough to explain the observed $\gamma$-ray luminosities in a purely hadronic scenario. Cygnus OB2 is one of the massive star clusters found in coincidence with diffuse $\gamma$-ray emission detected in a broad range of energies, from a few GeV up to 1.4 PeV.
In this work, we aim to compare the morphology and spectrum of the observed gamma emission with those predicted from a theoretical model where particles are accelerated at the termination shock of the cluster wind. The expected properties of the $\gamma$-ray emission depend on the distribution of accelerated cosmic rays, which is determined by the physics of acceleration at the termination shock and propagation in the hot expanding bubble created by the cluster wind. Propagation and acceleration are in turn strongly linked to the type of turbulence spectrum in the hot plasma filling the bubble.
After testing different turbulence spectra, we found our model predictions to reproduce the observed spectral energy distribution well in the case of Kraichnan turbulence. The predicted radial profile agrees well with HAWC observations but not with Fermi results. According to our best fit model, Cygnus OB2 should be able to accelerate cosmic rays up to 1 PeV, and would hence be a PeVatron.