Particle acceleration and multi-messenger radiation from ultra-luminous X-ray sources

Super-Eddington accretion onto stellar-mass compact objects powers fast outflows in ultra-luminous X-ray sources (ULXs). Such outflows, which can reach mildly relativistic velocities, are often observed forming bubble structures. Wind bubbles are expected to develop strong wind termination shocks, which are sites of great interest for diffusive shock acceleration. We developed a model of diffusive shock acceleration in the wind bubbles powered by ULXs. We find that the maximum energy in these objects can easily reach the PeV range, promoting winds from ULXs as a new class of PeVatrons. We specialized our model in the context of the Galactic source SS 433 and show that high-energy protons in the bubble might explain the highest energy photons (>100 TeV) and their morphology recently observed by LHAASO. In this paper, we discuss the detectability of such a source in neutrinos, and we analyze the possible radio counterpart of ULXs focusing on the case of W50, the nebula surrounding SS 433. Finally, we discuss the possible contribution of Galactic ULXs to the cosmic-ray flux at the knee, concluding that their role could be significant only if one of these sources, currently undetected, were sufficiently close.