Application of the FRADO model of BLR formation to the Seyfert galaxy NGC 5548 and the first step toward determining the Hubble constant

TL;DR

This study develops a comprehensive model of the Broad Line Region in NGC 5548, successfully reproducing observed spectral features and time delays, and proposes a novel method for estimating the Hubble constant using continuum time delays.

Contribution

The paper introduces a combined accretion disk and BLR model that accurately reproduces observed delays and spectra, enabling direct Hubble constant estimation from continuum delays.

Findings

Model reproduces broadband spectrum and Hβ delay

Estimated Hubble constant H₀ = 66.9 km s⁻¹ Mpc⁻¹

Supports the BLR formation model and its role in delay measurements

Abstract

The dynamical and geometric structures of the Broad Line Region (BLR), along with the origins of continuum time delays in active galaxies, remain topics of ongoing debate. In this study, we aim to reproduce the observed broadband spectrum, the H$\beta$ line delay, and the continuum time delays using our newly developed model for the source NGC 5548. We adopt the standard accretion disk model, with the option of an inner hot flow, and employ the lamp-post model to account for disk irradiation. Additionally, we model the BLR structure based on radiation pressure acting on dust. The model is parameterized by the black hole mass, $M_{\text{BH}}$ (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 radiation by the BLR. Our model reasonably reproduces the observed broad-band continuum, the H$\beta$ time delay, and the 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, $H_0$ = $66.9^{+10.6}_{-2.1}$ km s$^{-1}$ Mpc$^{-1}$, represents a significant improvement over previously reported values derived from continuum time delays in the literature. 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 effectively using inter-band continuum time delays as a method for determining the Hubble constant. Additionally, the findings provide strong support for the adopted model for the formation of the H$\beta$ line.