Deep VLA observations of an optically selected sample of intermediate redshift QSOs and the optical luminosity function of the radio loud QSOs

We present deep VLA observations of a complete sample of 23 optically selected QSOs with B < 19.4 at intermediate redshift (0.8 < z < 3.4). The observations were carried out at 5 and 1.4 GHz in the C array configuration. 4 of our 23 QSOs were detected (2 radio loud and 2 radio quiet), confirming the decrease of the radio loud (α_ro_ > 0.19) fraction of QSOs with increasing redshift. Stronger constraints are obtained for the radio luminosity of the radio quiet population at 2 < z < 3 with L_5 GHz_ < 10^24.2^ W Hz^-1^. Combining our observations with other existing radio data on optically selected samples (a total of 357 QSOs), we derive the evolutionary functional form of the optical luminosity function of the radio loud QSOs in the redshift range 0 < z < 2.9. The data are consistent with a radio loud optical luminosity function having lower densities but a similar shape with respect to the total (radio quiet plus radio loud) population, i.e., {PHI}(L) is proportional to Lgamma^ with -3.5 > γ > -4.1 at bright luminosities, and -1.7 > γ > -2.4 at faint luminosities. The evolution is slower (2.7< k < 3.1), and the "break magnitude" is brighter (24 > M_B_^*^ > -25 at z = 0) than in the parent total optical luminosity function. It results that the differential evolution between the radio loud and radio quiet QSOs population could account for the recent claims of a steepening with redshift of the total QSO luminosity function.