Redshifted intergalactic 3He+ 8.7 GHz hyperfine absorption
  Motivated by recent interest in redshifted 21 cm emission of intergalactic
hydrogen, we investigate the 8.7 GHz ^2S_{1/2} F=0-1 hyperfine transition of
^3He^+. While the primordial abundance of 3He 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 ^3He^+
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 HeII->HeIII
reionization is believed to be complete at z~3) and of the primordial 3He
abundance. Instruments must reach ~1 \mu Jy RMS noise in bands of 1 MHz on a 1
Jy source to directly resolve this absorption. However, in combination with HI
Ly\alpha forest measurements, an instrument can statistically detect this
absorption from z > 3 with 30 \mu Jy RMS noise in 0.1 MHz spectral bands over
100 MHz, which may be within the reach of present instruments.
