Properties of Compact Faint Radio Sources as a Function of Angular Size
  from Stacking
  The polarization properties of radio sources powered by an Active Galactic
Nucleus (AGN) have attracted considerable attention because of the significance
of magnetic fields in the physics of these sources, their use as probes of
plasma along the line of sight, and as a possible contaminant of polarization
measurements of the cosmic microwave background. For each of these
applications, a better understanding of the statistics of polarization in
relation to source characteristics is crucial. In this paper, we derive the
median fractional polarization, $\Pi_{0, \rm med}$, of large samples of radio
sources with 1.4 GHz flux density $6.6 < S_{1.4} < 70$ mJy, by stacking 1.4 GHz
NVSS polarized intensity as a function of angular size derived from the FIRST
survey. Five samples with deconvolved mean angular size 1.8" to 8.2" and two
samples of symmetric double sources are analyzed. These samples represent most
sources smaller than or near the median angular size of the mJy radio source
population We find that the median fractional polarization $\Pi_{0,\rm med}$ at
1.4 GHz is a strong function of source angular size less than ~5" and a weak
function of angular size for larger sources up to ~8". We interpret our results
as depolarization inside the AGN host galaxy and its circumgalactic medium. The
curvature of the low-frequency radio spectrum is found to anti-correlate with
$\Pi_{0,\rm med}$, a further sign that depolarization is related to the source.
