Complete Reionization Constraints from Planck 2015 Polarization
  We conduct an analysis of the Planck 2015 data that is complete in
reionization observables from the large angle polarization $E$-mode spectrum in
the redshift range $6 < z < 30$. Based on 5 principal components, all of which
are constrained by the data, this single analysis can be used to infer
constraints on any model for reionization in the same range; we develop an
effective likelihood approach for applying these constraints to models. By
allowing for an arbitrary ionization history, this technique tests the
robustness of inferences on the total optical depth from the usual step-like
transition assumption, which is important for the interpretation of many other
cosmological parameters such as the dark energy and neutrino mass. The Planck
2015 data not only allow a high redshift $z>15$ component to the optical depth
but prefer it at the $2\sigma$ level. This preference is associated with excess
power in the multipole range $10 \lesssim \ell \lesssim 20$ and may indicate
high redshift ionization sources or unaccounted for systematics and foregrounds
in the 2015 data.
