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 ${\mathrm{\Delta }}_{\text{z}}<7.5$ 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.