Sub-mJy radio emission from high-redshift active galactic nuclei in the footprint of the VLA Sky Survey

Using empty-field `Quick Look' images from the first two epochs of the VLA Sky Survey (VLASS) observations, centred on the positions of $\sim3700$ individually radio-non-detected active galactic nuclei (AGNs) at $z\ge4$, we performed image stacking analysis to examine the sub-mJy emission at $3$ GHz. We found characteristic monochromatic radio powers of $P_\mathrm{char}=(2-13) \times 10^{24}$ W Hz$^{-1}$, $P_\mathrm{char}=2\times10^{24}-1.3\times10^{25}$ W Hz$^{-1}$, indicating that AGN-related radio emission is widespread in the sample. The signal-to-noise ratios of the redshift-binned median stacked maps are between $4-6$, and we expect that with the inclusion of the yet to be completed third-epoch VLASS observations, the detection limit defined as signal-to-noise ratio $\mathrm{SNR}\ge6$ could be reached, and the redshift dependence can be determined. To obtain information on the general spectral properties of the faint radio emission in high-redshift AGNs, we confined the sample to $\sim3000$ objects covered by both the VLASS and the Faint Images of the Radio Sky at Twenty-centimeters (FIRST) survey. We found that the flux densities from the median stacked maps show a characteristic spectral index of $\alpha^*=-0.30\pm0.15$, which is in agreement with the median spectral index of the radio-detected $z\ge4$ AGNs from our high-redshift AGN catalogue. The three-band mid-infrared colour--colour diagram based on Wide-field Infrared Survey Explorer observations provides further support regarding the AGN contribution to the radio emission in the sub-mJy sample.