Author:Â Jordan Mirocha
Abstract: Evolution in the X-ray luminosity–star formation rate (LX–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 (BHs) at high-z, which depends on the mass of accreting objects and poorly constrained processes such as how accretion disc photons are processed by the disc 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 ∼10–20 mK level – comparable to errors induced by commonly used approximations to the RTE – while modifications to the intrinsic disc spectrum due to Compton scattering (bound-free absorption) can shift the position of the minimum of the global signal by  Δz ≈ 0.5 (Δz ≈ 2), and modify its amplitude by up to ≈10 mK (≈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 LX–SFR relation.