A hint on the metal-free star formation rate density from 21-cm-EDGES data

ABSTRACT We aim to provide here the first data-constrained estimate of the metal-free (Population III; Pop III) star formation rate density $\dot{\rho }_{*}^{III}$ required at high redshifts ($z \lower.5ex\hbox{$\,\, \buildrel\gt \over \sim \,\,$}16$) in order to reproduce both the amplitude and the redshift of the EDGES 21-cm global signal. Our model accounts for the Ly α, radio, and X-ray backgrounds from both Pop III and metal-enriched Population II (Pop II) stars. For the latter, we use the star formation rate density estimates (and the Ly α background) from the Delphi semi-analytic model that has been shown to reproduce all key observables for galaxies at $z \lower.5ex\hbox{$\,\, \buildrel\gt \over \sim \,\,$}5$; the radio and X-ray backgrounds are fixed using low-z values. The constraints on the free parameters characterizing the properties of the Pop III stars are obtained using a Markov Chain Monte Carlo analysis. Our results yield a $\dot{\rho }_{*}^{III}$ that while increasing from z ∼ 21 to 16 thereafter shows a sharp decline which is in excellent agreement with the results found by Valiante et al. to simulate the growth of z ∼ 6–7 quasars and their host galaxies, suggesting that the bulk of Pop III star formation occurs in the rarest and most massive metal-poor haloes at z ≲ 20. This allows Pop III stars to produce a rapidly growing Ly α background between z ∼ 21 and 15. Further, Pop III stars are required to provide a radio background that is about 3–4 orders of magnitude higher than that provided by Pop II stars although Pop II stars dominate the X-ray background.