Average fractional polarization of extragalactic sources at Planck frequencies

Recent detailed simulations have shown that an insufficiently accurate characterization of the contamination of unresolved polarized extragalactic sources can seriously bias measurements of the primordial cosmic microwave background (CMB) power spectrum if the tensor-to-scalar ratio $r\sim 0.001,$ as predicted by models currently of special interest (e.g., Starobinsky's $R^2$ and Higgs inflation). This has motivated a reanalysis of the median polarization fraction of extragalactic sources (radio-loud AGNs and dusty galaxies) using data from the \textit{Planck} polarization maps. Our approach, exploiting the intensity distribution analysis, mitigates or overcomes the most delicate aspects of earlier analyses based on stacking techniques. By means of simulations, we have shown that the residual noise bias on the median polarization fraction, $\Pi_{\rm median}$, of extragalactic sources is generally $\simlt 0.1\%$. For radio sources, we have found $\Pi_{\rm median} \simeq 2.83\%$, with no significant dependence on either frequency or flux density, in good agreement with the earlier estimate and with high-sensitivity measurements in the frequency range 5--40\,GHz. No polarization signal is detected in the case of dusty galaxies, implying 90\% confidence upper limits of $\Pi_{\rm dusty}\simlt 2.2\%$ at 353\,GHz and of $\simlt 3.9\%$ at 217\,GHz. The contamination of CMB polarization maps by unresolved point sources is discussed.