Implication of the Shape of the EDGES Signal for the 21 cm Power
  Spectrum
  We revisit the 21 cm power spectrum from the epoch of cosmic dawn in light of
the recent EDGES detection of the 21 cm global signal at frequencies
corresponding to $z\sim20$. The shape of the signal suggests that the spin
temperature of neutral hydrogen was coupled to the kinetic temperature of the
gas relatively rapidly ($19\lesssim z \lesssim 21$). We therefore consider
models in which the UV photons were dominantly produced in the rarest and most
massive halos ($M\gtrsim 10^9M_\odot$), since their abundance grows fast enough
at those redshifts to account for this feature of the signal. We show that
these models predict large power spectrum amplitudes during the inhomogeneous
coupling, and then inhomogeneous heating by CMB and Lyman-$\alpha$ photons due
to the large shot noise associated with the rare sources. The power spectrum is
enhanced by more than an order of magnitude compared to previous models which
did not include the shot noise contribution, making it a promising target for
upcoming radio interferometers that aim to detect high-redshift 21 cm
fluctuations.
