Magnetic field disorder and Faraday effects on the polarization of extragalactic radio sources

We present a polarization catalog of 533 extragalactic radio sources with 2.3 GHz total intensity above 420 mJy from the S-band Polarization All Sky Survey, S-PASS, with corresponding 1.4 GHz polarization information from the NRAO VLA Sky Survey, NVSS. We studied selection effects and found that fractional polarization, $pi$, of radio objects at both wavelengths depends on the spectral index, source magnetic field disorder, source size and depolarization. The relationship between depolarization, spectrum and size shows that depolarization occurs primarily in the source vicinity. The median $pi_{2.3}$ of resolved objects in NVSS is approximately two times larger than that of unresolved sources. Sources with little depolarization are $sim2$ times more polarized than both highly depolarized and re-polarized sources. This indicates that intrinsic magnetic field disorder is the dominant mechanism responsible for the observed low fractional polarization of radio sources at high frequencies. We predict that number counts from polarization surveys will be similar at 1.4 GHz and at 2.3 GHz, for fixed sensitivity, although $sim$10% of all sources may be currently missing because of strong depolarization. Objects with $pi_{1.4}approx pi_{2.3} ge 4%$ typically have simple Faraday structures, so are most useful for background samples. Almost half of flat spectrum ($alpha ge -0.5$) and $sim$25% of steep spectrum objects are re-polarized. Steep spectrum, depolarized sources show a weak negative correlation of depolarization with redshift in the range 0 $<$ z $<$ 2.3. Previous non-detections of redshift evolution are likely due the inclusion of re-polarized sources as well.