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 work tests the FRADO model for BLR formation in the Seyfert galaxy NGC 5548 by integrating a lamp-post irradiated disk, a warm/cold disk structure, and a FRADO-based BLR with CLOUDY emissivity calculations. By fitting both the broadband SED and inter-band continuum time delays, and treating the luminosity distance as a free parameter, the authors obtain a Hubble constant of $H_0 = 66.9^{+10.6}_{-2.1}$ km s$^{-1}$ Mpc$^{-1}$, demonstrating the potential of continuum inter-band delays as a cosmological probe. The study highlights the importance of disentangling disk and BLR delays and supports the FRADO scenario for Hβ line formation, while acknowledging systematic uncertainties from dust temperature, fixed parameters, and relativistic effects. As a pilot, it lays the groundwork for applying this approach to a broader AGN sample and for leveraging upcoming time-domain surveys to constrain cosmic distances with AGN reverberation data.

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$β$ 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$β$ 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$β$ line.

Figures (12)

• Figure 1: Upper panel: 3-D plot of cloud positions from FRADO model for NGC 5548 with $M_{BH}=5 \times 10^7 M_{\odot}$, $L/L_{Edd} = 0.02$, metallicity Z = 5 in solar units. The axes are in units of $r_g$. Bottom panel: a cross-section of cloud positions for $y>-300 \, r_g$ and $y<300 \, r_g$. The black line indicates the thickness of the Keplerian disk. Clouds form a geometrically thin complex layer above the disk.
• Figure 2: Upper panel: Velocity–delay map of NGC 5548 constructed from FRADO model with inclination angle $i = 40$ degrees. Color coding represents the number density of BLR clouds in each velocity-delay bin. The white dashed line shows the virial envelope corresponding to Keplerian disk-like rotation for $v^2 \times \tau$ = constant with $M_{\mathrm{BH}} = 5 \times 10^7 \,M_{\odot}$. Bottom panel: BLR response function generated using the cloud positions from the model shown in Figure \ref{['fig:cloud']}, assuming an inclination angle of $i = 40$ degrees.
• Figure 3: Line profile generated by the FRADO model using the parameters from Figure \ref{['fig:cloud']}.
• Figure 4: Emissivity profile (ratio of the reprocessed to the incident continuum) of a BLR cloud for the adopted parameters: $\log n_H~[\text{cm}^{-3}] = 11$, $\log L~[\text{erg}~\text{s}^{-1}] = 44$, and the BLR distance of $10^{16}$ cm.
• Figure 5: Upper panel: Response functions of the disk at different wavelengths. Bottom panel: Combined response functions of the disk and BLR across the same wavelengths. These representative response functions are obtained for Model C. Parameters used: $M_{\text{BH}}$ = $5.0 \times10^{7}M_{\odot}$, Eddington ratio = 0.015, $L_X = 9.68 \times10^{43}$ erg s$^{-1}$, height: $h = 48.29 r_g$, $R_{in} = 94.87 r_g$, $R_{out} = 10000 r_g$, and viewing angle: $i = 40$ degrees.