Effects of Bethe-Heitler pair production in ultraluminous X-ray sources

Some black holes in X-ray binaries accrete at rates far above the Eddington limit. In this supercritical regime, photons are trapped in a radiation-dominated, geometrically thick disk. The innermost regions form a complex environment of intense radiation, strong magnetic fields, and powerful outflows, where radiation-driven winds expel large amounts of mass. These conditions suppress primary relativistic electrons within the transparent funnel along the black hole's spin axis. We show that high-energy electrons can instead arise as secondary pairs from Bethe-Heitler interactions between relativistic protons and ambient photons. Using self-similar models of accretion disks with strong winds of ultraluminous X-ray sources (ULXs), we compute particle acceleration via magnetic reconnection and diffusive shocks, evaluate energy losses, and assess the efficiency and spectral imprint of Bethe-Heitler pair production. Our results suggest that secondary pairs can yield nonthermal radiation in the 0.1-100 MeV range with luminosities from $10^{34}$ up to $10^{38}$ erg s$^{-1}$. This emission could be detectable by future MeV instruments from Galactic ULXs, offering evidence of relativistic protons in their inner funnels and revealing misaligned, otherwise hidden, super-Eddington sources in the Milky Way.