Motivated by recent interest in redshifted 21 cm emission of intergalactic hydrogen, we investigate the 8.7 GHz ${}^2\mathrm{S}_{1/2}$ $F=0-1$ hyperfine transition of ${}^3\mathrm{He}^{+}$. While the primordial abundance of ${}^3\mathrm{He}$ relative to hydrogen is ${10}^{-5}$, the hyperfine spontaneous decay rate is 680 times larger. Furthermore, the antenna temperature is much lower at the frequencies relevant for the ${}^3\mathrm{He}^{+}$ transition compared to that of $z>6$ 21 cm emission. We find that the spin temperature of this 8.7 GHz line in the intergalactic medium is approximately the cosmic microwave background temperature, such that this transition is best observed in absorption against high-redshift, radio-bright quasars. We show that intergalactic 8.7 GHz absorption is a promising, unsaturated observable of the ionization history of intergalactic helium (for which $\mathrm{He}\mathrm{II}\to \mathrm{He}\mathrm{III}$ reionization is believed to complete at $z\sim 3$) and of the primordial ${}^3\mathrm{He}$ abundance. Instruments must reach $\sim 1\mu \mathrm{Jy}$ RMS noise in bands of 1 MHz on a 1 Jy source to directly resolve this absorption. However, in combination with H i $\mathrm{Ly}\alpha$ forest measurements, an instrument can statistically detect this absorption from $z>3$ with $30\mu \mathrm{Jy}$ RMS noise in 0.1 MHz spectral bands over 100 MHz, which may be within the reach of present instruments.

• Received 22 May 2009

DOI:https://doi.org/10.1103/PhysRevD.80.063010