Ionizing radiation from hydrogen recombination strongly suppresses the lithium scattering signature in the CMB

It has been suggested that secondary CMB anisotropies generated by neutral lithium could open a new observational window into the universe around the redshift $z\sim 400$, and permit a determination of the primordial lithium abundance. The effect is due to resonant scattering in the allowed Li i doublet ($2s^2{S}_{1/2}-2p^2{P}_{1/2,3/2}$), so its observability depends on the formation history of neutral lithium. Here we show that the ultraviolet photons produced during hydrogen recombination are sufficient to keep lithium in the Li ii ionization stage in the relevant redshift range and suppress the neutral fraction by $\sim 3$ orders of magnitude from previous calculations, making the lithium signature unobservable.

Figure 1

The distortion field generated by $n=2$ decays of hydrogen during recombination dwarfs the high-energy tail of the CMB (shown in black dotted line). The ionization energy of lithium is shown to emphasize that even at late times, there is a large number of distortion photons above the ionization energy.

Figure 2

The photoionization rate of lithium as a function of redshift, showing the contribution of nonthermal (distortion) photons, beginning to dominate shortly after hydrogen recombination. The nonthermal rate is fast compared to the inverse Hubble time, allowing a steady-state solution.

Figure 3

Lithium recombination history in the presence of an ionizing flux from the $n=2$ hydrogen recombinations to the ground state. Lithium recombines much more slowly than for a purely thermal CMB, as $(1+z{)}^{-3/2}$, and remains largely ionized up until late times. This reduces the optical depth, and significantly reduces the imprint left on the CMB.

Figure 4

A comparison of the optical depth through the resonance of neutral lithium, with and without the ionizing flux from hydrogen recombination.

Figure 5

The maximum number of photons that lithium recombinations can remove from the distortion population is significantly less than the total distortion population, based on $X_{\mathrm{Li}}=4.15\times {10}^{-10}$. The distortion spectrum is well-approximated by just those photons which are generated by hydrogen, without lithium feedback.

Figure 6

For a spectral distortion produced by only Lyman-$\alpha$ decays, the spectral distortion is much harder, and lithium recombines less readily at early times. Alternately, for a distortion produced by only two photon decays, the softer radiation allows lithium to recombine more efficiently. This simulates the effect of hydrogen $2p$ and $2s$ falling out of equilibrium in its most extreme form. In both cases, lithium remains largely ionized up to late times.