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.