Feedback from High-Mass X-Ray Binaries on the High Redshift
  Intergalactic Medium : Model Spectra
  Massive stars at redshifts z > 6 are predicted to have played a pivotal role
in cosmological reionization as luminous sources of ultra-violet (UV) photons.
However, the remnants of these massive stars could be equally important as
X-ray luminous (L_X 1e38 erg/s) high-mass X-ray binaries (HMXBs). Because the
absorption cross section of neutral hydrogen decreases sharply with photon
energy (proportional to the inverse cube), X-rays can escape more freely than
UV photons from the star-forming regions in which they are produced, allowing
HMXBs to make a potentially significant contribution to the ionizing X-ray
background during reionization. In this paper, we explore the ionizing power of
HMXBs at redshifts z > 6 using a Monte Carlo model for a coeval stellar
population of main sequence stars and HMXBs. Using the archetypal Galactic HMXB
Cygnus X-1 as our template, we propose a composite HMXB spectral energy
distribution consisting of black-body and power-law components, whose
contributions depend on the accretion state of the system. We determine the
time-dependent ionizing power of a combined population of UV-luminous stars and
X-ray luminous HMXBs, and deduce fitting formulae for the boost in the
population's ionizing power arising from HMXBs; these fits allow for simple
implementation of HMXB feedback in numerical simulations. Based on this
analysis, we estimate the contribution of high redshift HMXBs to the
present-day soft X-ray background, and we show that it is a factor of ~100-1000
smaller than the observed limit. Finally, we discuss the implications of our
results for the role of HMXBs in reionization and in high redshift galaxy
formation.
