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

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 $z\sim2$.

Figures (14)

• Figure 1: Redshift--luminosity distribution of the steep-spectrum radio-loud AGN sample used throughout this work (after excluding FSRQ sources)
• Figure 2: Panel (a): Kernel density estimate of the rest-frame 1.4 GHz luminosity distribution for the full AGN sample, highlighting the presence of three distinct components. Panel (b): Evolution of the height of the high-luminosity peak as a function of the minimum spectral index threshold $\alpha_{\rm min}$, obtained by progressively removing sources with $\alpha < \alpha_{\rm min}$. Panel (c): Best-fitting weight $B$ of the FSRQ component in the Three-Gaussian model (Equation \ref{['eq:fsrq1']}) as a function of $\alpha_{\rm min}$, with $3\sigma$ uncertainties. Panel (d): Comparison between the KDE result from KDE-diffusion and our Three-Gaussian model at $\alpha_{\rm min}=0.45$; the two distributions agree within the uncertainties.
• Figure 3: Local radio LF at 1.4 GHz of AGN from several surveys with different observed areas and sensitivities (colored data points). The colored lines show the fits to the combined data from our models.
• Figure 4: Radio LFs of AGNs in different redshift bins, compared with the nonparametric LFs obtained using the PC method (green open hexagons). The best-fitting parametric LFs for Models A, B, and C are shown as blue, orange, and green solid curves, respectively, with shaded bands indicating the corresponding $3\sigma$ confidence regions. For comparison, the grey dashed curves show the LDDE model of 2024AA...684A..19S, while the purple dash-dotted curves depict our LDDE-based fits, with their $3\sigma$ confidence intervals indicated by the purple shaded regions. The top panels display the full comparison among Models A, B, and C, whereas the bottom panels only show Model C and its $3\sigma$ confidence region together with the PC-based LFs, to highlight the agreement between our fiducial model and the nonparametric estimates. The vertical grey dash-dotted lines in the bottom panels mark the flux limits of the individual surveys contributing to each redshift bin.
• Figure 5: Comparison of our best-fit models with the Euclidean normalized $1.4$ GHz SCs for AGNs observed in the literature. The blue, orange, and green dash-dotted lines show our best-fit SCs of Models A, B, and C, respectively. The SCs from 2023MNRAS.520.2668H in the COSMOS and XMM-LSS fields are shown as brown right triangles and cyan pentagons, respectively. Also shown are the observed SCs from Smolcic2017a (brown five-pointed stars), Algera_2020 (blue squares), and Padovani2015 (red circles), with associated error bars in all cases.