  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 degree 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, computing it 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 beta=-2.59+-0.03 for alpha=30 degrees, and
beta=-2.03+-0.01 for alpha=50 degrees. 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
degree 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.
