  In order to understand the role of radio-quiet quasars (RQQs) in galaxy
evolution, we must determine the relative levels of accretion and
star-formation activity within these objects. Previous work at low radio
flux-densities has shown that accretion makes a significant contribution to the
total radio emission, in contrast with other quasar studies that suggest star
formation dominates. To investigate, we use 70 RQQs from the Spitzer-Herschel
Active Galaxy Survey. These quasars are all at $z$ ~ 1, thereby minimising
evolutionary effects, and have been selected to span a factor of ~100 in
optical luminosity, so that the luminosity dependence of their properties can
be studied. We have imaged the sample using the Karl G. Jansky Very Large Array
(JVLA), whose high sensitivity results in 35 RQQs being detected above 2
$\sigma$. This radio dataset is combined with far-infrared luminosities derived
from grey-body fitting to Herschel photometry. By exploiting the
far-infrared--radio correlation observed for star-forming galaxies, and
comparing two independent estimates of the star-formation rate, we show that
star formation alone is not sufficient to explain the total radio emission.
Considering RQQs above a 2-$\sigma$ detection level in both the radio and the
far-infrared, 92 per cent are accretion-dominated, and the accretion process
accounts for 80 per cent of the radio luminosity when summed across the
objects. The radio emission connected with accretion appears to be correlated
with the optical luminosity of the RQQ, whilst a weaker luminosity-dependence
is evident for the radio emission connected with star formation.
