Nonthermal emission from the plunging region: a model for the high-energy tail of black hole X-ray binary soft states

X-ray binaries exhibit a soft spectral state comprising thermal blackbody emission at 1 keV and a power-law tail above 10 keV. Empirical models fit the high-energy power-law tail to radiation from a nonthermal electron distribution, but the physical location of the nonthermal electrons and the reason for their power-law index and high-energy cut-off are still largely unknown. Here, we propose that the nonthermal electrons originate from within the black hole's innermost stable circular orbit (the ''plunging region''). Using an analytic model for the plunging region dynamics and electron distribution function properties from particle-in-cell simulations, we outline a steady-state model that can reproduce the observed spectral features. In particular, our model reproduces photon indices of $\Gamma\gtrsim2$ and power-law luminosities on the order of a few percent of the disk luminosity for strong magnetic fields, consistent with observations of the soft state. Because the emission originates so close to the black hole, we predict that the power-law luminosity should strongly depend on the system inclination angle and black hole spin. This model could be extended to the power-law tails observed above 400 keV in the hard state of X-ray binaries.