The deep diffuse extragalactic radio sky at 1.75 GHz

We present a study of diffuse extragalactic radio emission at $1.75\,$GHz from part of the ELAIS-S1 field using the Australia Telescope Compact Array. The resulting mosaic is $2.46\,$deg$^2$, with a roughly constant noise region of $0.61\,$deg$^2$ used for analysis. The image has a beam size of $150 \times60\,$arcsec and instrumental $\langle\sigma_{\rm n}\rangle= (52\pm5)\, \mu$Jy beam$^{-1}$. Using point-source models from the ATLAS survey, we subtract the discrete emission in this field for $S \ge 150\, \mu$Jy beam$^{-1}$. Comparison of the source-subtracted probability distribution, or \pd, with the predicted distribution from unsubtracted discrete emission and noise, yields an excess of $(76 \pm 23) \, \mu$Jy beam$^{-1}$. Taking this as an upper limit on any extended emission we constrain several models of extended source counts, assuming $\Omega_{\rm source} \le 2\,$arcmin. The best-fitting models yield temperatures of the radio background from extended emission of $T_{\rm b}=(10\pm7) \,$mK, giving an upper limit on the total temperature at $1.75\,$GHz of $(73\pm10)\,$mK. Further modelling shows that our data are inconsistent with the reported excess temperature of ARCADE2 to a source-count limit of $1\, \mu$Jy. Our new data close a loop-hole in the previous constraints, because of the possibility of extended emission being resolved out at higher resolution. Additionally, we look at a model of cluster halo emission and two WIMP dark matter annihilation source-count models, and discuss general constraints on any predicted counts from such sources. Finally, we report the derived integral count at $1.4\,$GHz using the deepest discrete count plus our new extended-emission limits, providing numbers that can be used for planning future ultra-deep surveys.