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Most active galactic nuclei (AGNs) are radio-quiet, and the origin of theirradio emission is not well-understood. One hypothesis is that this radioemission is a by-product of quasar-driven winds. In this paper, we present theradio properties of 108 extremely red quasars (ERQs) at $z=2-4$. ERQs are amongthe most luminous quasars ($L_{bol} \sim 10^{47-48}$ erg/s) in the Universe,with signatures of extreme ($\gg 1000$ km/s) outflows in their[OIII]$\lambda$5007 \AA\ emission, making them the best subjects to seek theconnection between radio and outflow activity. All ERQs but one are unresolvedin the radio on $\sim 10$ kpc scales, and the median radio luminosity of ERQsis $\nu L_\nu [{\rm 6\,GHz}] = 10^{41.0}$ erg/s, in the radio-quiet regime, butone to two orders of magnitude higher than that of other quasar samples. Theradio spectra are steep, with a mean spectral index $\langle \alpha \rangle =-1.0$. In addition, ERQs neatly follow the extrapolation of the low-redshiftcorrelation between radio luminosity and the velocity dispersion of[OIII]-emitting ionized gas. Uncollimated winds, with a power of one per centof the bolometric luminosity, can account for all these observations. Suchwinds would interact with and shock the gas around the quasar and in the hostgalaxy, resulting in acceleration of relativistic particles and the consequentsynchrotron emission observed in the radio. Our observations support thepicture in which ERQs are signposts of extremely powerful episodes of quasarfeedback, and quasar-driven winds as a contributor of the radio emission in theintermediate regime of radio luminosity $\nu L_\nu = 10^{39}-10^{42}$ erg/s.

Winds as the origin of radio emission in $z=2.5$ radio-quiet extremely red quasars