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

Most active galactic nuclei (AGNs) are radio-quiet, and the origin of their radio emission is not well-understood. One hypothesis is that this radio emission is a by-product of quasar-driven winds. In this paper, we present the radio properties of 108 extremely red quasars (ERQs) at $z=2-4$. ERQs are among the 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 the connection between radio and outflow activity. All ERQs but one are unresolved in the radio on $\sim 10$ kpc scales, and the median radio luminosity of ERQs is $\nu L_\nu [{\rm 6\,GHz}] = 10^{41.0}$ erg/s, in the radio-quiet regime, but one to two orders of magnitude higher than that of other quasar samples. The radio spectra are steep, with a mean spectral index $\langle \alpha \rangle = -1.0$. In addition, ERQs neatly follow the extrapolation of the low-redshift correlation between radio luminosity and the velocity dispersion of [OIII]-emitting ionized gas. Uncollimated winds, with a power of one per cent of the bolometric luminosity, can account for all these observations. Such winds would interact with and shock the gas around the quasar and in the host galaxy, resulting in acceleration of relativistic particles and the consequent synchrotron emission observed in the radio. Our observations support the picture in which ERQs are signposts of extremely powerful episodes of quasar feedback, and quasar-driven winds as a contributor of the radio emission in the intermediate regime of radio luminosity $\nu L_\nu = 10^{39}-10^{42}$ erg/s.