  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.
