Population synthesis of active galactic nuclei based on the radiation-regulated unification model

D. Gerolymatou, S. Paltani, C. Ricci, T. T. Ananna

First listed 2026-05-17 | Last updated 2026-05-17

Abstract

X-ray surveys of active galactic nuclei (AGNs) provide direct constraints on the properties of individual AGNs, such as their emission, obscuration, and accretion rate. Previous AGN population synthesis models have not addressed such properties self-consistently. Here, we use a simulation-based inference (SBI) approach to constrain the geometrical and physical properties of the AGN population. We perform numerical simulations with our ray-tracing code, RefleX, which allows the self-consistent modelling of the X-ray emission of AGNs with flexible circumnuclear and source geometries. We create our synthetic population by sampling the intrinsic active black hole mass function (BHMF) and Eddington ratio distribution function (ERDF) of local AGNs, and we construct a geometry based on the radiation-regulated model, along with Eddington-ratio-dependent emission spectra. Using the RefleX-simulated emission of the AGN population, we aim to simultaneously reproduce the cosmic X-ray background (CXB), differential AGN number counts, and several observed absorption properties of local AGNs, such as the fraction of $N_\mathrm{H}$ in bins of log($N_\mathrm{H}$), the Compton-thick fraction as a function of limiting flux, and the number of obscured and unobscured AGNs as a function of Eddington ratio. With this approach, we test the consistency of the radiation-regulated model with a very comprehensive set of X-ray observables, while constraining the size and density of the dusty torus and the evolution of the local AGN population. We derive an intrinsic Compton-thick fraction of $40\pm3$%, and find that a simple evolutionary prescription controlling the active fraction of supermassive black holes is sufficient for our synthetic population to reproduce the CXB.

Short digest

This paper builds a self-consistent AGN population synthesis model by combining the local active black hole mass function and Eddington ratio distribution with a radiation-regulated torus geometry and Eddington-ratio-dependent X-ray spectra simulated with RefleX. Using simulation-based inference, the authors fit the cosmic X-ray background, differential number counts in the 2–10, 8–24, and 14–195 keV bands, the local N_H distribution, Compton-thick fractions versus limiting flux, and the observed obscured and unobscured AGN counts as a function of Eddington ratio. The main result is that the radiation-regulated unification picture can reproduce this broad X-ray constraint set while implying an intrinsic Compton-thick fraction of 40±3% and constraining the dusty torus size and density. It matters because the model ties obscuration, reflection, and accretion demographics together physically rather than treating AGN spectral components as independent templates.

Key figures to inspect

• Figure 1. This is the key setup figure for the whole paper because it defines the RefleX geometry that links absorption and reflection self-consistently. Use it to show how the accretion disc, BLR, torus, source height, and the reference column-density sightlines are parameterized, since the paper’s main claims about obscuration and reflected emission depend directly on this construction.
• Figure 3. This is the central evidence figure because it demonstrates that one posterior-constrained synthetic population can simultaneously match the cosmic X-ray background, number counts in three X-ray bands, the observed N_H distribution, Compton-thick fractions versus flux limit, and the obscured and unobscured AGN counts as a function of Eddington ratio. It is the clearest single figure for the paper’s headline claim that the radiation-regulated model is globally consistent with a comprehensive local X-ray dataset.
• Figure 4. This figure captures the paper’s main physical interpretation by showing the model covering factor as a function of Eddington ratio and comparing it directly to the observationally adapted trend. It matters because the radiation-regulated unification model predicts that obscuration is driven primarily by Eddington ratio rather than luminosity, so this is a conclusion-level diagnostic rather than a setup plot.
• Figure 5. This figure shows how the inferred population splits into obscured and unobscured AGNs in both BHMF and ERDF space at low redshift, and compares those predictions to the Ananna et al. 2022 constraints used to seed the model. It is important because the paper is not only fitting X-ray backgrounds and counts, but also testing whether the recovered demographic structure of the AGN population remains consistent with observed type 1 and type 2 distributions.
• Figure 6. This is the strongest self-consistency diagnostic for the spectral modelling because it links the model-predicted reflected fraction in the 14–195 keV band to line-of-sight N_H and compares that relation to stacked hard-X-ray observations. Include it to show that the same geometry used for the population synthesis also reproduces the observed reflection-obscuration correlation, which is one of the paper’s distinctive advances over template-based models.