  The first population of X-ray binaries (XRBs) is expected to affect the
thermal and ionization states of the gas in the early Universe. Although these
X-ray sources are predicted to have important implications for high-redshift
observable signals, such as the hydrogen 21-cm signal from cosmic dawn and the
cosmic X-ray background, their properties are poorly explored, leaving
theoretical models largely uninformed. In this paper we model a population of
X-ray binaries arising from zero metallicity stars. We explore how their
properties depend on the adopted initial mass function (IMF) of primordial
stars, finding a strong effect on their number and X-ray production efficiency.
We also present scaling relations between XRBs and their X-ray emission with
the local star formation rate, which can be used in sub-grid models in
numerical simulations to improve the X-ray feedback prescriptions.
Specifically, we find that the uniformity and strength of the X-ray feedback in
the intergalactic medium is strongly dependant on the IMF. Bottom-heavy IMFs
result in a smoother distribution of XRBs, but have a luminosity orders of
magnitude lower than more top-heavy IMFs. Top-heavy IMFs lead to more spatially
uneven, albeit strong, X-ray emission. An intermediate IMF has a strong X-ray
feedback while sustaining an even emission across the intergalactic medium.
These differences in X-ray feedback could be probed in the future with
measurements of the cosmic dawn 21-cm line of neutral hydrogen, which offers us
a new way of constraining population III IMF.
