  Within standard $\Lambda$CDM cosmology, Population III (Pop III) star
formation in minihalos of mass $M_\mathrm{halo}\gtrsim 5\times10^5$ 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 $z\approx 17$, 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.
