Application of the FRADO model of broad line region formation to Seyfert galaxy NGC 5548 and a first step toward determining the Hubble constant

¹ Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
² Department of Physics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
³ Department of Physics and Astronomy, University of Utah, Salt Lake City, UT 84112, USA
⁴ Institut d’Astrophysique et de Géophysique, Université de Liège, Allée du six Août 19c, B-4000 Liège (Sart-Tilman), Belgium
⁵ International Gemini Observatory/NSF NOIRLab, Casilla 603, La Serena, Chile
⁶ Astroinformatics, Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany

^⋆ Corresponding author: vkj@cft.edu.pl

Received: 4 October 2024
Accepted: 12 August 2025

Abstract

Context. The dynamical and geometric structures of broad line region (BLRs) and the origins of continuum time delays in active galaxies remain topics of ongoing debate.

Aims. In this study, we aim to reproduce the observed broadband spectrum, the Hβ line delay, and the continuum time delays using our newly developed model for the source NGC 5548.

Methods. We adopted the standard accretion disk model, with the option of an inner hot flow, and employed the lamp-post model to account for disk irradiation. Additionally, we modeled the BLR structure based on radiation pressure acting on dust. The model is parameterized by the black hole mass, M_BH (which is fixed), the accretion rate, the viewing angle, the height of the lamp-post, the cloud density, and the cloud covering factor. The resulting continuum time delays arise from a combination of disk reprocessing and the reprocessing of a fraction of the radiation by the BLR.

Results. Our model can reasonably reproduce the observed broadband continuum, Hβ time delay, and continuum inter-band time delays measured during the observational campaign. When the accretion rate is not constrained by the known distance to the source, our approach allows for a direct estimation of the distance. The resulting Hubble constant, H₀ = 66.9^+10.6_−2.1 km s⁻¹ Mpc⁻¹, represents a significant improvement over previously reported values derived from continuum time delays in the literature.

Conclusions. This pilot study demonstrates that with sufficient data coverage, it is possible to disentangle the time delays originating from the accretion disk and the BLR. This paves the way for efficient applications of inter-band continuum time delays as a method for determining the Hubble constant. Additionally, these findings provide strong support for the adopted model for the formation of the Hβ line.