Unveiling the weak radio quasar population at |$z\ge 4$|.

We applied image stacking on empty field Faint Images of the Radio Sky at Twenty-Centimeters (FIRST) survey maps centred on optically identified high-redshift quasars at |$z\ge 4$| to uncover the hidden |$\mu$| Jy radio emission in these active galactic nuclei (AGN). The median stacking procedure for the full sample of 2229 optically identified AGN uncovered an unresolved point source with an integrated flux density of 52  |$\mu$| Jy, with a signal-to-noise ratio |${\sim} 10$|⁠. We co-added the individual image centre pixels to estimate the characteristic monochromatic radio power at 1.4 GHz considering various values for the radio spectral index, revealing a radio population with |$P_\mathrm{1.4\, GHz}\sim 10^{24}$|  W Hz |$^{-1}$|⁠. Assuming that the entire radio emission originates from star-forming (SF) activity in the nuclear region of the host galaxy, we obtained an upper limit on the characteristic star formation rate, |${\sim} 4200$|  M |$_\odot$|  yr |$^{-1}$|⁠. The angular resolution of FIRST images is insufficient to distinguish between the SF and AGN origin of radio emission at these redshifts. However, a comparison with properties of individual sources from the literature indicates that a mixed nature is likely. Future very long baseline interferometry radio observations and ultradeep Square Kilometre Array surveys are expected to be sensitive enough to detect and resolve the central |$1\!-\!10$|  kpc region in the host galaxies, and thus discriminate between SF and AGN related emission. [ABSTRACT FROM AUTHOR]