  Recently, Tseliakhovich and Hirata (2010) showed that during the cosmic Dark
Ages the baryons were typically moving supersonically with respect to the dark
matter with a spatially variable Mach number. Such supersonic motion may source
shocks that heat the Universe. This motion may also suppress star formation in
the first halos. Even a small amount of coupling of the 21cm signal to this
motion has the potential to vastly enhance the 21cm brightness temperature
fluctuations at 15<z<40 as well as to imprint acoustic oscillations in this
signal. We present estimates for the size of this coupling, which we calibrate
with a suite of cosmological simulations. Our simulations, discussed in detail
in a companion paper, are initialized to self-consistently account for gas
pressure and the dark matter-baryon relative velocity, v_bc (in contrast to
prior simulations). We find that the supersonic velocity difference
dramatically suppresses structure formation at 10-100 comoving kpc scales, it
sources shocks throughout the Universe, and it impacts the accretion of gas
onto the first star-forming minihalos (even for halo masses as large as ~10^7
Msun). However, we find that the v_bc-sourced temperature fluctuations can
contribute only as much as ~10% of the fluctuations in the 21cm signal. We do
find that v_bc could source an O(1) component in the power spectrum of the 21cm
signal via the X-ray (but not ultraviolet) backgrounds produced once the first
stars formed. In a scenario in which ~10^6 Msun minihalos reheated the Universe
via their X-ray backgrounds, we find that the pre-reionization 21cm signal
would be larger than previously anticipated and exhibit significant acoustic
features. We show that structure formation shocks are unable to heat the
Universe sufficiently to erase a strong 21cm absorption trough at z ~ 20 that
is found in most models of the sky-averaged 21cm intensity.
