The 21-cm signal from the Cosmic Dawn: metallicity dependence of high
  mass X-ray binaries
  X-rays from High-Mass X-ray Binaries (HMXBs) are likely the main source of
heating of the intergalactic medium (IGM) during Cosmic Dawn (CD), before the
completion of reionization. This Epoch of Heating (EoH; $z\sim 10-15$) should
soon be detected via the redshifted 21-cm line from neutral hydrogen, allowing
us to indirectly study the properties of HMXBs in the unseen, first galaxies.
Low-redshift observations, as well as theoretical models, imply that the
integrated X-ray luminosity to star formation rate of HMXBs ($L_{\rm X}/{\rm
SFR}$) should increase in metal-poor environments, typical of early galaxies.
Here we study the impact of the metallicity ($Z$) dependence of $L_{\rm X}/{\rm
SFR}$ during the EoH. For our fiducial models, galaxies with star formation
rates of order $10^{-3} - 10^{-1}$ $M_\odot$ yr$^{-1}$ and metallicities of
order $10^{-3} - 10^{-2}$ $Z_\odot$ are the dominant contributors to the X-ray
background (XRB) during this period. Different $L_{\rm X}/{\rm SFR}$-$Z$
relations result in factors of $\sim$ 3 differences in these ranges, as well as
in the mean IGM temperature and the large-scale 21-cm power, at a given
redshift. We compute mock 21-cm observations adopting as a baseline a 1000h
integration with the upcoming Square Kilometer Array (SKA), for two different
$L_{\rm X}/{\rm SFR}$-$Z$ relations. We perform inference on these mock
observations using the common simplification of a constant $L_{\rm X}/{\rm
SFR}$, finding that constant $L_{\rm X}/{\rm SFR}$ models can recover the IGM
evolution of the more complicated $L_{\rm X}/{\rm SFR}$-$Z$ simulations only
during the EoH. At $z<10$, where the typical galaxies are more polluted,
constant $L_{\rm X}/{\rm SFR}$ models over-predict the XRB and its relative
contribution to the early stages of the reionization.
