We used the 1.4 GHz NVSS to study radio sources in two color-selected QSO samples : a volume-limited sample of 1313 QSOs defined by M _ { i } < -23 in the redshift range 0.2 < z < 0.45 and a magnitude-limited sample of 2471 QSOs with m _ { r } \leq 18.5 and 1.8 < z < 2.5 .
About 10 % were detected above the 2.4 mJy NVSS catalog limit and are powered primarily by AGNs .
The space density of the low-redshift QSOs evolves as \rho \propto ( 1 + z ) ^ { 6 } .
In both redshift ranges the flux-density distributions and luminosity functions of QSOs stronger than 2.4 mJy are power laws , with no features to suggest more than one kind of radio source .
Extrapolating the power laws to lower luminosities predicts the remaining QSOs should be extremely radio quiet , but they are not .
Most were detected statistically on the NVSS images with median peak flux densities S _ { p } ( { mJy~ { } beam } ^ { -1 } ) \approx 0.3 and 0.05 in the low- and high-redshift samples , corresponding to spectral luminosities \log [ L _ { 1.4 GHz } ( { W~ { } Hz } ^ { -1 } ) ] \approx 22.7 and 24.1 , respectively .
We suggest that the faint radio sources are powered by star formation at rates \dot { M } \sim 20 M _ { \sun } { ~ { } yr } ^ { -1 } in the moderate luminosity ( median \langle M _ { i } \rangle \approx - 23.4 ) low-redshift QSOs and \dot { M } \sim 500 M _ { \sun } { ~ { } yr } ^ { -1 } in the very luminous ( \langle M _ { i } \rangle \approx - 27.5 ) high-redshift QSOs .
Such luminous starbursts [ \langle \log ( L _ { IR } / L _ { \sun } ) \rangle \sim 11.2 and 12.6 , respectively ] are consistent with “ quasar mode ” accretion in which cold gas flows fuel both AGN and starburst .