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We study the reionization parameter space consistent with the currentmeasurement of the Thomson optical depth using a new parametrization of thereionization history. The mass-weighted ionization fraction is specified interms of the redshift midpoint, duration, and asymmetry shape parameters. Weperform an MCMC analysis using conservative flat priors and physicalconstraints. 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-weightedionization fraction $x_\text{i}(z)$ is asymmetric, but early contributions toreionization are minor.

The Reionization Parameter Space Consistent with the Thomson Optical Depth from Planck