Using varying models for the star formation rate (SFR) of Population (Pop) III and II stars at z > 6 we derive the expected redshift history of the global 21-cm signal from the intergalactic medium (IGM). To recover the observed Thomson scattering optical depth of the cosmic microwave background (CMB) requires SFRs at the level of ~10-3M⊙ yr-1 Mpc-3 at z ~ 15 from Pop III stars, or ~10-1M⊙ yr-1 Mpc-3 at z ~ 7 from Pop II stars. In the case the SFR is dominated by Pop III stars, the IGM quickly heats above the CMB at z ≳ 12 due to heating from supernovae. In addition, Lyα photons from haloes hosting Pop III stars couple the spin temperature to that of the gas, resulting in a deep absorption signal. If the SFR is dominated by Pop II stars, the IGM slowly heats and exceeds the CMB temperature at z ~ 10. However, the larger and varying fraction of Pop III stars are able to break this degeneracy. We find that the impact of the initial mass function (IMF) of Pop III stars on the 21-cm signal results in an earlier change to a positive signal if the IMF slope is ~-1.2. Measuring the 21-cm signal at z ≳ 10 with next generation radio telescopes such as the Square Kilometre Array will be able to investigate the contribution from Pop III and Pop II stars to the global SFR.
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