GMRT 610-MHz observations of the faint radio source population - and what these tell us about the higher-radio-frequency sky

We present 610-MHz Giant Metrewave Radio Telescope observations of 0.84 deg$^2$ of the AMI001 field (centred on $00^{\rm h} 23^{\rm m} 10^{\rm s}$, $+31^{\circ} 53'$) with an r.m.s. noise of 18 $\mu$Jy beam$^{-1}$ in the centre of the field. 955 sources are detected, and 814 are included in the source count analysis. The source counts from these observations are consistent with previous work. We have used these data to study the spectral index distribution of a sample of sources selected at 15.7 GHz from the recent deep extension to the Tenth Cambridge (10C) survey. The median spectral index, $\alpha$, (where $S \propto \nu^{-\alpha}$) between $0.08 < S_{15.7~\rm GHz} / \rm mJy < 0.2$ is $0.32 \pm 0.14$, showing that star-forming galaxies, which have much steeper spectra, are not contributing significantly to this population. This is in contrast to several models, but in agreement with the results from the 10C ultra-deep source counts; the high-frequency sky therefore continues to be dominated by radio galaxies down to $S_{15.7~\rm GHz} = 0.1$ mJy.