We estimate the spectral index , \beta , of polarized synchrotron emission as observed in the 9 yr WMAP sky maps using two methods , linear regression ( “ T–T plot ” ) and maximum likelihood .
We partition the sky into 24 disjoint sky regions , and evaluate the spectral index for all polarization angles between 0 ^ { \circ } and 85 ^ { \circ } in steps of 5 ^ { \circ } .
Averaging over polarization angles , we derive a mean spectral index of \beta ^ { \textrm { all - sky } } = -2.99 \pm 0.01 in the frequency range of 23-33 GHz .
We find that the synchrotron spectral index steepens by 0.14 from low to high Galactic latitudes , in agreement with previous studies , with mean spectral indices of \beta ^ { \textrm { plane } } = -2.98 \pm 0.01 and \beta ^ { \textrm { high - lat } } = -3.12 \pm 0.04 .
In addition , we find a significant longitudinal variation along the Galactic plane with a steeper spectral index toward the Galactic center and anticenter than toward the Galactic spiral arms .
This can be well modeled by an offset sinusoidal , \beta ( l ) = -2.85 + 0.17 \sin ( 2 l - 90 ^ { \circ } ) .
Finally , we study synchrotron emission in the BICEP2 field , in an attempt to understand whether the claimed detection of large-scale B-mode polarization could be explained in terms of synchrotron contamination .
Adopting a spectral index of \beta = -3.12 , typical for high Galactic latitudes , we find that the most likely bias corresponds to about 2 % of the reported signal ( r = 0.003 ) .
The flattest index allowed by the data in this region is \beta = -2.5 , and under the assumption of a straight power-law frequency spectrum , we find that synchrotron emission can account for at most 20 % of the reported BICEP2 signal .