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tokens: II stars (as modelled in Delphi ). Indeed, a larger contribution from Pop III stars would lead to a faster coupling between the spin and CMB temperatures, resulting in a higher redshift at which the signal would tend to 0. Finally, in all panels, we also show by the grey shaded regions the models that are consistent with the EDGES data. As expected, while the range of histories naturally shows a dispersion, their redshift-evolution remains unaffected. The Pop III SFRD and the radio emissivity show the least dispersion (since they effectively govern the brightness temperature from Pop III stars) while, given their negligible contribution to the X-ray emissivity, the value of shows the largest dispersion. It is worth pointing out here that the depth of the EDGES signal is highly controversial (see, e.g. Hills et al. 2018 ; Sims Pober 2020 ). In case the amplitude of the signal turns out to be much smaller than what is assumed in this work (say |δ T b | ≲ 100 mK), then the Pop II stars with conventional choice of efficiency parameters are sufficient to explain the observations. Hence our conclusions on the Pop III stars hold only in the case where the amplitude and redshift extent of the 21-cm signal are similar to those reported by the EDGES experiment. Finally, we compare our predicted redshift evolution of the Pop III SFRD with some theoretical models in Fig. 3 . Most models predict a Pop III SFRD that either rises between z ∼ 22 and 13 (Jaacks et al. 2018 ; Sarmento et al. 2019 ) or shows a relatively constant behaviour for z ∼ 20 − 13 (Johnson et al. 2013 ). The only exceptions are the predictions by Valiante et al. ( 2016 ), Valiante et al. ( 2018 ), whose amplitude and redshift dependence are very similar to our predicted shape. Interestingly, the Valiante et al. ( 2016 ), Valiante et al. ( 2018 ) models aim to describe the formation histories of z ∼ 6–7 quasars and their host galaxies. They therefore describe rapidly evolving and biased regions of the Universe. In these models, Pop III stars (and their black hole remnants) start to form at z > 20 in dark matter mini-haloes with mass [10 6 –10 7 ]M ⊙ . However, their formation efficiency is small, as Lyman-Werner radiation limits gas cooling due to H 2 photo-dissociation. Because of this, the bulk of Pop III stars form at redshift 15 z 20 in metal poor ( Z Z cr = 10 −3.8 Z ⊙ ) Ly α-cooling haloes, with mass [10 7.5 − 10 8.5 ] M ⊙ that are able to self-shield and cool the gas more efficiently (see the top panel of Fig. 1 in Valiante et al. 2018 ). At z ≤ 15 Pop III star formation is suppressed by metal enrichment, as Z Z cr = 10 −3.8 Z ⊙ star forming regions become increasingly rare. Hence, the shape of the EDGES signal suggests that the rapid coupling between the spin temperature and the gas kinetic temperature is driven by Ly α photons produced by Pop III stars that form in relatively massive and rare haloes, whose abundance grows fast, due to the exponential growth of the massive-end