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 $μ$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.