Source Counts Spanning Eight Decades of Flux Density at 1.4 GHz

Abstract: Brightness-weighted differential source counts $S^2 n(S)$ spanning the eight decades of flux density between $0.25\,\mu\mathrm{Jy}$ and 25 Jy at 1.4 GHz were measured from (1) the confusion brightness distribution in the MeerKAT DEEP2 image below $10\,\mu\mathrm{Jy}$, (2) counts of DEEP2 sources between $10\,\mu\mathrm{Jy}$ and $2.5\,\mathrm{mJy}$, and (3) counts of NVSS sources stronger than $2.5\,\mathrm{mJy}$. We present our DEEP2 catalog of $1.7 \times 10^4$ discrete sources complete above $S = 10\,\mu\mathrm{Jy}$ over $\Omega = 1.04\,\mathrm{deg}^2$. The brightness-weighted counts converge as $S^2 n(S) \propto S^{1/2}$ below $S = 10\,\mu\mathrm{Jy}$, so $>99\%$ of the $\Delta T_\mathrm{b} \sim 0.06\,\mathrm{K}$ sky brightness produced by active galactic nuclei and $\approx96\%$ of the $\Delta T_\mathrm{b} \sim 0.04\,\mathrm{K}$ added by star-forming galaxies has been resolved into sources with $S \geq 0.25\,\mu\mathrm{Jy}$. The $\Delta T_\mathrm{b} \approx 0.4\,\mathrm{K}$ excess brightness measured by ARCADE 2 cannot be produced by faint sources smaller than $\approx 50\,\mathrm{kpc}$ if they cluster like galaxies.