Decoding the X-ray Properties of Pre-Reionization Era Sources
  Evolution in the X-ray luminosity -- star formation rate ($L_X$-SFR) relation
could provide the first evidence of a top-heavy stellar initial mass function
in the early universe, as the abundance of high-mass stars and binary systems
are both expected to increase with decreasing metallicity. The sky-averaged
(global) 21-cm signal has the potential to test this prediction via constraints
on the thermal history of the intergalactic medium, since X-rays can most
easily escape galaxies and heat gas on large scales. A significant complication
in the interpretation of upcoming 21-cm measurements is the unknown spectrum of
accreting black holes at high-$z$, which depends on the mass of accreting
objects and poorly constrained processes such as how accretion disk photons are
processed by the disk atmosphere and host galaxy interstellar medium. Using a
novel approach to solving the cosmological radiative transfer equation (RTE),
we show that reasonable changes in the characteristic BH mass affects the
amplitude of the 21-cm signal's minimum at the $\sim 10-20$ mK level ---
comparable to errors induced by commonly used approximations to the RTE ---
while modifications to the intrinsic disk spectrum due to Compton scattering
(bound-free absorption) can shift the position of the minimum of the global
signal by $\Delta z \approx 0.5$ ($\Delta z \approx 2$), and modify its
amplitude by up to $\approx 10$ mK ($\approx 50$ mK) for a given accretion
history. Such deviations are larger than the uncertainties expected of current
global 21-cm signal extraction algorithms, and could easily be confused with
evolution in the $L_X$-SFR relation.
