The high-redshift tail of stellar reionization in LCDM is beyond the
  reach of the low-$\ell$ CMB
  The first generation (Pop-III) stars can ionize 1-10% of the universe by
$z=15$, when the metal-enriched (Pop-II) stars may contribute negligibly to the
ionization. This low ionization tail might leave detectable imprints on the
large-scale CMB E-mode polarization. However, we show that physical models for
reionization are unlikely to be sufficiently extended to detect any parameter
beyond the total optical depth through reionization. This result is driven in
part by the total optical depth inferred by Planck, indicating a reionization
midpoint around $z=8$, which in combination with the requirement that
reionization completes by $z\approx 5.5$ limits the amplitude of an extended
tail. To demonstrate this, we perform semi-analytic calculations of
reionization including Pop-III star formation in minihalos with Lyman-Werner
feedback. We find that standard Pop-III models need to produce very extended
reionization at $z>15$ to be distinguishable at 2-$\sigma$ from Pop-II-only
models, assuming a cosmic variance-limited measurement of the low-$\ell$ EE
power spectrum. However, we show that unless there is (1) a late-time quenching
mechanism such as from strong X-ray feedback or (2) some other extreme Pop-III
scenario, structure formation makes it quite challenging to produce high enough
Thomson scattering optical depth from $z>15$, $\tau(z>15)$, and still be
consistent with other observational constraints on reionization.
