We present an estimate of the optical luminosity function ( OLF ) of LOFAR radio-selected quasars at 1.4 < z < 5.0 in the 9.3 \ > \textrm { deg } ^ { 2 } NOAO Deep Wide-field survey ( NDWFS ) of the Boötes 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-Boötes 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 134 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-Boötes 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 _ { \textrm { 1450 } } < -24.0 , a regime where the OLF of quasars selected through their radio emission ( radio-selected quasars , RSQs ) , 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 _ { \textrm { 1450 } } < -22.0 ) .
We demonstrate that RSQs show an evolution that is very similar to the 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 \sim 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 .