Probing the high-z IGM with the hyperfine transition of $^3$He$^+$
  The hyperfine transition of $^3$He$^+$ at 3.5cm has been thought as a probe
of the high-z IGM since it offers a unique insight into the evolution of the
helium component of the gas, as well as potentially give an independent
constraint on the 21cm signal from neutral hydrogen. In this paper, we use
radiative transfer simulations of reionization driven by sources such as stars,
X-ray binaries, accreting black holes and shock heated interstellar medium, and
simulations of a high-z quasar to characterize the signal and analyze its
prospects of detection. We find that the peak of the signal lies in the range
1-50 $\mu$K for both environments, but while around the quasar it is always in
emission, in the case of cosmic reionization a brief period of absorption is
expected. As the evolution of HeII is determined by stars, we find that it is
not possible to distinguish reionization histories driven by more energetic
sources. On the other hand, while a bright QSO produces a signal in 21cm that
is very similar to the one from a large collection of galaxies, its signature
in 3.5cm is very peculiar and could be a powerful probe to identify the
presence of the QSO. We analyze the prospects of the signal's detectability
using SKA1-mid as our reference telescope. We find that the noise power
spectrum dominates over the power spectrum of the signal, although a modest S/N
ratio can be obtained when the wavenumber bin width and the survey volume are
sufficiently large.
