We study four particularly bright polarized compact objects ( Tau A , Virgo A , 3C273 and Fornax A ) in the 7-year WMAP sky maps , with the goal of understanding potential systematics involved in estimation of foreground spectral indices .
We estimate the spectral index , the polarization angle , the polarization fraction and apparent size and shape of these objects when smoothed to a nominal resolution of 1 ^ { \circ } FWHM .
Second , we compute the spectral index as a function of polarization orientation , \alpha .
Because these objects are approximately point sources with constant polarization angle , this function should be constant in the absence of systematics .
However , for the K- and Ka-band WMAP data we find strong index variations for all four sources .
For Tau A , we find a spectral index of \beta = -2.59 \pm 0.03 for \alpha = 30 ^ { \circ } , and \beta = -2.03 \pm 0.01 for \alpha = 50 ^ { \circ } .
On the other hand , the spectral index between Ka- and Q-band is found to be stable .
A simple elliptical Gaussian toy model with parameters matching those observed in Tau A reproduces the observed signal , and shows that the spectral index is in particular sensitive to the detector polarization angle .
Based on these findings , we first conclude that estimation of spectral indices with the WMAP K-band polarization data at 1 ^ { \circ } scales is not robust .
Second , we note that these issues may be of concern for ground-based and sub-orbital experiments that use the WMAP polarization measurements of Tau A for calibration of gain and polarization angles .