The synchrotron foreground and CMB temperature-polarization cross correlation power spectrum from the first year WMAP data

We analyse the temperature-polarization cross-correlation in the Galactic synchrotron template that we have recently developed, and between the template and CMB temperature maps derived from WMAP data. Since the polarized synchrotron template itself uses WMAP data, we can estimate residual synchrotron contamination in the CMB $C_\ell^{TE}$ angular spectrum. While $C_2^{TE}$ appears to be contamined by synchrotron, no evidence for contamination is found in the multipole range which is most relevant for the fit of the cosmological optical depth.