We present deep VLA observations of the polarization of radio sources in the GOODS-N field at 1.4 GHz at resolutions of 1.6″and 10″ .
At 1.6″ , we find that the peak flux cumulative number count distribution is N ( > p ) \sim 45 * ( p/30 \mu Jy ) ^ { -0.6 } per square degree above a detection threshold of 14.5 \mu Jy .
This represents a break from the steeper slopes at higher flux densities , resulting in fewer sources predicted for future surveys with the SKA and its precursors .
It provides a significant challenge for using background RMs to study clusters of galaxies or individual galaxies .
Most of the polarized sources are well above our detection limit , and are radio galaxies which are well-resolved even at 10″ , with redshifts from \sim 0.2 - 1.9 .
We determined a total polarized flux for each source by integrating the 10″ polarized intensity maps , as will be done by upcoming surveys such as POSSUM .
These total polarized fluxes are a factor of 2 higher , on average , than the peak polarized flux at 1.6″ ; this would increase the number counts by \sim 50 % at a fixed flux level .
The detected sources have rotation measures ( RMs ) with a characteristic rms scatter of \sim 11 \frac { rad } { m ^ { 2 } } around the local Galactic value , after eliminating likely outliers .
The median fractional polarization from all total intensity sources does not continue the trend of increasing at lower flux densities , as seen for stronger sources .
The changes in the polarization characteristics seen at these low fluxes likely represent the increasing dominance of star-forming galaxies .