The optical luminosity function of LOFAR radio-selected quasars at 1.4 ≤ z ≤ 5.0 in the NDWFS-Bootes field

We present an estimate of the optical luminosity function (OLF) of LOFAR radio-selected quasars (RSQs) at 1.4< z< 5.0 in the 9.3 deg(2) NOAO Deep Wide-field survey (NDWFS) of the Bootes field. The selection was based on optical and mid-infrared photometry used to train three different machine learning (ML) algorithms (Random forest, SVM, Bootstrap aggregation). Objects taken as quasars by the ML algorithms are required to be detected at >= 5 sigma significance in deep radio maps to be classified as candidate quasars. The optical imaging came from the Sloan Digital Sky Survey and the Pan-STARRS1 3 pi survey; mid-infrared photometry was taken from the Spitzer Deep, Wide-Field Survey; and radio data was obtained from deep LOFAR imaging of the NDWFS-Bootes field. The requirement of a 5 sigma LOFAR detection allowed us to reduce the stellar contamination in our sample by two orders of magnitude. The sample comprises 130 objects, including both photometrically selected candidate quasars (47) and spectroscopically confirmed quasars (83). The spectral energy distributions calculated using deep photometry available for the NDWFS-Bootes field confirm the validity of the photometrically selected quasars using the ML algorithms as robust candidate quasars. The depth of our LOFAR observations allowed us to detect the radio-emission of quasars that would be otherwise classified as radio-quiet. Around 65% of the quasars in the sample are fainter than M-1450=-24.0, a regime where the OLF of quasars selected through their radio emission, has not been investigated in detail. It has been demonstrated that in cases where mid-infrared wedge-based AGN selection is not possible due to a lack of appropriate data, the selection of quasars using ML algorithms trained with optical and infrared photometry in combination with LOFAR data provides an excellent approach for obtaining samples of quasars. The OLF of RSQs can be described by pure luminosity evolution at z< 2.4, and a combined luminosity and density evolution at z> 2.4. The faint-end slope, alpha, becomes steeper with increasing redshift. This trend is consistent with previous studies of faint quasars (M-1450 <= -22.0). We demonstrate that RSQs show an evolution that is very similar to that exhibited by faint quasars. By comparing the spatial density of RSQs with that of the total (radio-detected plus radio-undetected) faint quasar population at similar redshifts, we find that RSQs may compose up to similar to 20% of the whole faint quasar population. This fraction, within uncertainties, is constant with redshift. Finally, we discuss how the compactness of the RSQs radio-morphologies and their steep spectral indices could provide valuable insights into how quasar and radio activity are triggered in these systems.