Constraints on the spectral index of polarized synchrotron emission from
  WMAP and Faraday-corrected S-PASS data
  We constrain the spectral index of polarized synchrotron emission, $\beta_s$,
by correlating the recently released 2.3 GHz S-Band Polarization All Sky Survey
(S-PASS) data with the 23 GHz 9-year Wilkinson Microwave Anisotropy Probe
(WMAP) sky maps. We subdivide the S-PASS field, which covers the southern
ecliptic hemisphere, into 95 $15^{\circ}\times15^{\circ}$ regions and estimate
the spectral index of polarized synchrotron emission within each region using a
simple but robust T-T plot technique. Three different versions of the S-PASS
data are considered, corresponding to: no correction for Faraday rotation;
Faraday correction based on the rotation measure model presented by the S-PASS
team; or Faraday correction based on a rotation measure model presented by
Hutschenreuter and En{\ss}lin. We find that the correlation between S-PASS and
WMAP is strongest when applying the S-PASS model. Adopting this correction
model, we find that the mean spectral index of polarized synchrotron emission
gradually steepens from $\beta_s\approx-2.8$ at low Galactic latitudes to
$\beta_s\approx-3.3$ at high Galactic latitudes, in good agreement with
previously published results. Finally, we consider two special cases defined by
the BICEP2 and SPIDER fields and obtain mean estimates of
$\beta_{BICEP2}=-3.22\pm0.06$ and $\beta_{SPIDER}=-3.21\pm0.03$, respectively.
A comparison with a similar analysis performed in the 23-33 GHz range suggests
a flattening of about $\Delta\beta_s \sim 0.1 \pm 0.2$ from low to higher
frequencies, but with no statistical significance due to high uncertainties.
