Effect of Template Uncertainties on the WMAP and Planck Measures of the
  Optical Depth Due To Reionization
  The reionization optical depth is the most poorly determined of the six
$\Lambda$CDM parameters fit to CMB anisotropy data. Instrumental noise and
systematics have prevented uncertainties from reaching their cosmic variance
limit. At present, the datasets providing the most statistical constraining
power are the WMAP, Planck LFI, and Planck HFI full-sky polarization maps. As
the reprocessed HFI data with reduced systematics are not yet publicly
unavailable, we examine determinations of $\tau$ using 9-year WMAP and 2015
Planck LFI data, with an emphasis on characterizing potential systematic bias
resulting from foreground template and masking choices. We find evidence for a
low-level systematic in the LFI polarization data with a roughly common-mode
morphology across the LFI frequencies and a spectrum consistent with leakage of
intensity signal into the polarization channels. We demonstrate significant
bias in the optical depth derived when using the LFI 30 GHz map as a template
to clean synchrotron from WMAP data, and recommend against use of the 2015 LFI
30 GHz polarization data as a foreground template for non-LFI datasets. We find
an inconsistency between versions of the 2015 polarized 353 GHz dust templates
reconstructed from the Planck likelihood and those from delivered maps, which
can affect $\tau$ at the 1$\sigma$ level. The spread in $\tau$ values over the
ensemble of data combinations we study suggests that systematic uncertainties
still contribute significantly to the current uncertainty in $\tau$, but all
values are consistent with the range of $\tau$ = 0.07 +/- 0.02.
