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.