Modeling the counts of faint radio-loud quasars: Constraints on the supermassive black hole population and predictions for high redshift

We use a physically motivated semianalytic model, based on the mass function of dark matter halos, to predict the number of radio-loud quasars as a function of redshift and luminosity. Simple models in which the central black hole (BH) mass scales with the velocity dispersion of its host halo as M _BH α σ_halo⁵ have been previously found to be consistent with a number of observations, including the optical and X-ray quasar luminosity functions. We find that similar models, when augmented with an empirical prescription for radio emission, overpredict the number of faint (∼10 μJy) radio sources by 1-2 orders of magnitude. This translates into a more stringent constraint on the low-mass end of the quasar BH mass function than is available from the Hubble and Chandra Deep Fields. We interpret this discrepancy as evidence that BHs with masses ≲10 ⁷ M· either are rare or are not as radio-loud as their more massive counterparts. Models that exclude BHs with masses below 10⁷ M· are in agreement with the deepest existing radio observations but still produce a significant tail of high-redshift objects. In the 1-10 GHz bands at the sensitivity of ∼10 μJy, we find surface densities of ∼100, ∼10, and ∼0.3 deg^-2 for sources located at z > 6, 10, and 15, respectively. The discovery of these sources with instruments such as the Allen Telescope Array, Extended Very Large Array, and the Square Kilometer Array would open a new window for the study of supermassive BHs at high redshift. We also find surface densities of ∼0.1 deg^-2 at z > 6 for millijansky sources that can be used to study 21 cm absorption from the epoch of reionization. We suggest that, although they are not yet optically identified, the FIRST survey may have already detected ∼10 ³-10⁴ such sources.