Radiative relativistic reconnection powering the hard-state emission of X-ray binaries: synchrotron-driven pair loading, MeV tail, and seed photons

In the hard state, X-ray emission from black hole X-ray binaries is attributed to Comptonization in the corona, a highly magnetized region near the black hole. Relativistic magnetic reconnection drives bulk motions that can upscatter soft photons and reproduce the spectral peak at $\sim 100$ keV for parameters relevant to Cygnus X-1. However, the origin of the seed photons and of the MeV tail above the peak remains unclear. In 3D reconnection, so-called "free" particles escape the flux ropes and accelerate at the maximum rate set by the reconnection electric field. Their synchrotron emission extends to tens of MeV, which enables $γγ$ pair production with the Compton-upscattered photons. We present 3D particle-in-cell simulations of relativistic reconnection in pair plasma, in which particles cool by inverse Compton (IC) scattering below the synchrotron self-absorption threshold and by synchrotron radiation above it. Of the incoming magnetic power, $\sim 40 \%$ is converted to IC radiation and $\gtrsim 10$-$20\%$ to synchrotron. Using analytical estimates and radiative calculations for Cygnus X-1, we model how the radiation from reconnection-accelerated particles is reprocessed in the corona. Pair production attenuates the synchrotron emission above $\sim 1$ MeV, and the escaping $γ$-rays form an MeV tail consistent with the observations, extending up to at least $\sim 10$ MeV. Most of the absorbed power goes into secondary pairs, whose Thomson optical depth can reach order unity. Their synchrotron emission, peaking at $\sim 0.1 \, \text{keV}$, can supply the seed photons for Comptonization. Our results support reconnection-based synchrotron self-Compton models of the hard-state emission in X-ray binaries.