BeyondPlanck XV. Polarized foreground emission between 30 and 70 GHz
  We constrain polarized foreground emission between 30 and 70 GHz with the
Planck Low Frequency Instrument (LFI) and WMAP data within the global Bayesian
BeyondPlanck framework. We combine for the first time full-resolution Planck
LFI time-ordered data with low-resolution WMAP sky maps at 33, 40 and 61 GHz.
Spectral parameters are fit with a likelihood defined at the native resolution
of each frequency channel. This analysis represents the first implementation of
true multi-resolution component separation applied to CMB observations for both
amplitude and spectral energy distribution (SED) parameters. For synchrotron
emission, we approximate the SED as a power-law in frequency and find that the
low signal-to-noise ratio of the current data strongly limits the number of
free parameters that may be robustly constrained. We partition the sky into
four large disjoint regions (High Latitude; Galactic Spur; Galactic Plane; and
Galactic Center), each associated with its own power-law index. We find that
the High Latitude region is prior-dominated, while the Galactic Center region
is contaminated by residual instrumental systematics. The two remaining regions
appear to be signal-dominated, and for these we derive spectral indices of
$\beta_{\mathrm s}^{\mathrm{Spur}}=-3.17\pm0.06$ and $\beta_{\mathrm
s}^{\mathrm{Plane}}=-3.03\pm0.07$, in good agreement with previous results. For
thermal dust emission we assume a modified blackbody model and we fit a single
power-law index across the full sky. We find $\beta_{\mathrm{d}}=1.64\pm0.03$,
which is slightly steeper than reported from Planck HFI data, but still
statistically consistent at the 2$\sigma$ confidence level.
