The Reionization Parameter Space Consistent with the Thomson Optical
  Depth from Planck
  We study the reionization parameter space consistent with the current
measurement of the Thomson optical depth using a new parametrization of the
reionization history. The mass-weighted ionization fraction is specified in
terms of the redshift midpoint, duration, and asymmetry shape parameters. We
perform an MCMC analysis using conservative flat priors and physical
constraints. Our analysis yields a redshift midpoint of
$z_{50}=7.66\substack{+0.57-0.61}\text{(68%)}\substack{+1.26-1.02}\text{(95%)}$,
and upper limits on the duration $\Delta_\text{z} < 7.5$ and asymmetry
$A_\text{z}<5.3$ for $\tau = 0.054 \pm 0.007$. The reconstructed mass-weighted
ionization fraction $x_\text{i}(z)$ is asymmetric, but early contributions to
reionization are minor.
