We constrain the spectral index of polarized synchrotron emission , \beta _ { \mathrm { 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 sub-divide the S-PASS field , which covers the Southern Ecliptic hemisphere , into 15 ^ { \circ } \times 15 ^ { \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 either 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 Enßlin .
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 _ { \mathrm { s } } \approx - 2.8 at low Galactic latitudes to \beta _ { \mathrm { s } } \approx - 3.2 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 _ { \textrm { BICEP 2 } } = -3.22 \pm 0.06 and \beta _ { \textrm { SPIDER } } = -3.21 \pm 0.03 , respectively .
Adopting the WMAP 23 GHz sky map bandpass filtered to including angular scales only between 2 ^ { \circ } and 10 ^ { \circ } as a spatial template , we constrain the root-mean-square synchrotron polarization amplitude to be less than 0.03 \thinspace \mu \textrm { K } ( 0.009 \thinspace \mu \textrm { K } ) at 90 GHz ( 150 GHz ) for the BICEP2 field , corresponding roughly to a tensor-to-scalar ratio of r \lesssim 0.02 ( r \lesssim 0.005 ) , respectively .
Very similar constraints are obtained for the SPIDER field .