The Steep-spectrum Radio-loud AGN Luminosity Function and Its Implications for Black Hole Growth and Star Formation

TL;DR

This study models the evolution of radio-loud AGN luminosity functions across cosmic time, revealing a unified framework that links black hole growth and star formation history, with implications for understanding galaxy evolution.

Contribution

It introduces a preferred LADE model for the radio luminosity function that unifies AGN and star-forming galaxy evolution, explaining cosmic downsizing without separate laws.

Findings

The LADE model fits the observed RLFs and source counts well.

The AGN kinetic luminosity function tracks cosmic star formation rate density.

A unified two-component model describes both AGN and star-forming galaxies.

Abstract

We study the cosmic evolution of radio-loud active galactic nuclei (AGNs) using a beaming-minimized sample of 4{,}555 steep-spectrum sources over $0<z\lesssim4$, compiled from the XXL survey, VLA-COSMOS, and other wide-field data sets. We model the rest-frame 1.4 GHz radio luminosity function (RLF) with a luminosity-and-density evolution (LADE; DE+LE) framework coupled to a flexible local LF family. Among the tested parameterizations, Model~C is statistically preferred and provides a globally consistent description of the binned RLFs while remaining compatible with local RLF measurements and Euclidean-normalized source counts. In the fiducial solution, the LE term rises toward cosmic noon ($z\sim2$--3) and then flattens or mildly declines, whereas the DE term decreases monotonically with redshift. This combined evolution naturally reproduces the observed luminosity-dependent turnover redshift $z_{\rm peak}(L)$ (often termed ``cosmic downsizing'') without imposing \emph{a priori} distinct evolutionary laws for low- and high-power sources. We further show that the same LADE functional family calibrated for star-forming galaxies also describes radio-loud AGNs when fitted independently, enabling a unified two-component (SFG+AGN) model consistent with both the local RLF and source-count statistics. Finally, converting the AGN RLF to a kinetic luminosity function yields a radio-mode black hole accretion rate density (BHAD) whose redshift dependence closely tracks the radio-based cosmic star formation rate density (after a conventional rescaling), with both histories peaking near $z\sim2$.