Within standard $Lambda$CDM cosmology, Population III (Pop III) star formation in minihalos of mass $M_mathrm{halo}gtrsim 5times10^5$ M$_odot$ provides the first stellar sources of Lyman$alpha$ (Ly$alpha$) photons. The Experiment to Detect the Global Epoch of Reionization Signature (EDGES) has measured a strong absorption signal of the redshifted 21 cm radiation from neutral hydrogen at $zapprox 17$, requiring efficient formation of massive stars before then. In this paper, we investigate whether star formation in minihalos plays a significant role in establishing the early Ly$alpha$ background required to produce the EDGES absorption feature. We find that Pop III stars are important in providing the necessary Ly$alpha$-flux at high redshifts, and derive a best-fitting average Pop III stellar mass of $sim$ 750M$_odot{}$ per minihalo, corresponding to a star formation efficiency of 0.1%. Further, it is important to include baryon-dark matter streaming velocities in the calculation, to limit the efficiency of Pop~III star formation in minihalos. Without this effect, the cosmic dawn coupling between 21 cm spin temperature and that of the gas would occur at redshifts higher than what is implied by EDGES.
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