Hβ line shape and radius-luminosity relation in 2.5D FRADO

¹ Institut d’Astrophysique et de Géophysique, Université de Liège, Allée du six août 19c, B-4000 Liège (Sart-Tilman), Belgium
² Astronomy Department, Universidad de Concepción, Barrio Universitario S/N, Concepción, 4030000 Chile
³ Millennium Nucleus on Transversal Research and Technology to Explore Supermassive Black Holes (TITANs), Concepción, Chile
⁴ Millennium Institute of Astrophysics (MAS), Nuncio Monseñor Sótero Sanz 100, Providencia, Santiago, Chile
⁵ Astronomical Observatory Belgrade, Volgina 7, 11060 Belgrade, Serbia
⁶ Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland

^⋆ Corresponding author: mh.naddaf@uliege.be

Received: 1 June 2025
Accepted: 13 August 2025

Abstract

Context. Galaxies with active galactic nuclei (AGNs) exhibit broad emission lines as a key spectral feature. The shape of the emission-line profiles depends on the complex dynamics of discrete clouds within a spatially extended region known as the broad line region (BLR). The distribution of cloud positions within the BLR (or the de facto geometry of BLR) is directly linked to measurements of BLR time lags.

Aims. In this work, we convolved a large grid of physically based simulations of cloud distributions in BLR with photon-flux weighted emissivity of BLR clouds to investigate the generic shape of spectral line profiles. More importantly, we were able to extract the time-delay histograms of corresponding models to calculate the size of BLR.

Methods. Our physical model is based on the assumption that the clouds are launched by the radiation pressure acting on dust in the atmosphere of the outer disk. It has very few global parameters. The model is appropriate for the low-ionization part of the BLR, as seen in earlier model tests. It uses a non-hydrodynamical single-cloud approach to the BLR dynamics, which enables us to simulate the distribution of positions and velocities of the clouds.

Results. We found that the line profile width broadens with increasing black hole mass (or with viewing angle) and narrows with increasing accretion rate. The blue wing of the emission line profiles becomes more pronounced with increasing black hole mass and accretion rate, consistent with the formation and intensification of an outflow structure. We also found that the peak time delays offer a better representation of the observational trend and the scatter in the radius-luminosity (R–L) relation, compared to averaged delay values.