The faintest quasar luminosity function at z ~ 5 from Deep Learning and Bayesian Inference

To estimate the contribution of quasars on keeping the IGM ionized, building a quasar luminosity function (LF) is necessary. Quasar LFs derived from multiple quasar surveys, however, are incompatible, especially for the faint regime, emphasizing the need for deep images. In this study, we construct quasar LF reaching M₁₄₅₀~-21.5 AB magnitude at z ~ 5, which is 1.5 mag deeper than previously reported LFs, using deep images from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP). We trained an artificial neural network (ANN) by inserting the colors as inputs to classify the quasars at z ~ 5 from the late-type stars and low-redshift galaxies. The accuracy of ANN is > 99 %. We also adopted the Bayesian information criterion to elaborate on the quasar-like objects. As a result, we recovered 5/5 confirmed quasars and remarkably minimized the contamination rate of high-redshift galaxies by up to six times compared to the selection using color selection alone. The constructed quasar parametric LF shows a flatter faint-end slope α=-127^+0.16_-0.15 similar to the recent LFs. The number of faint quasars (M₁₄₅₀ < -23.5) is too few to be the main contributor to IGM ionizing photons.