Simulating Disky Broad Line Region Reverberation

Variability studies of the broad emission lines of Active Galactic Nuclei (AGNs) and quasars show stochastic radial velocity variations (i.e., fluctuations in the centroid of the line), ‘jitter’, on timescales of weeks to months. This jitter may be intrinsic as the broad-line emitting region (BLR) reverberates from the AGN continuum. There are also coordinated variations in the width of the broad emission lines and the luminosity of the central source (‘breathing’ or ‘anti-breathing’) which remain unexplained. These can be used as a tool for testing models of the BLR. We have constructed a pipeline to simulate a disk-like BLR geometry that reverberates in response to various chosen continuum light curves and produce synthetic emission line profiles. These profiles can then be characterized by measured shape parameters (centroid velocity shift, velocity dispersion, and Pearson skewness coefficient) and compared to observed time series of those same parameters. We have found that through our pipeline, we can recreate the velocity jitter at similar variations found in observations. The computational tools presented in this paper will also be applicable to case studies of quasars observed under the Sloan Digital Sky Survey V (SDSS-V) Black Hole Mapper reverberation mapping program. This paper is the first in a series of papers – in this paper, we present the model and pipeline, and in future papers, we will present applications.

💡 Research Summary

This paper presents a new computational pipeline designed to simulate the reverberation response of a disk‑like broad‑line region (BLR) in active galactic nuclei (AGN) to arbitrary continuum light curves. The authors motivate the work by noting two persistent observational phenomena: stochastic centroid velocity shifts (“jitter”) on timescales of weeks to months, and coordinated changes in line width versus continuum luminosity, commonly referred to as “breathing” or “anti‑breathing.” Both effects are poorly understood but are potentially powerful diagnostics of BLR geometry and kinematics, and they also constitute a source of false positives in spectroscopic searches for sub‑parsec supermassive black‑hole binaries.

Model Foundations
The BLR is assumed to be a geometrically thin, Keplerian disk extending outward from the central ionizing source, which is treated as a point emitter. The disk is described in cylindrical coordinates (ξ, φ), where ξ = r/rg is the radius in units of the gravitational radius rg = GM/c². The line‑emitting region occupies an annulus between inner radius ξin and outer radius ξout. The authors adopt an analytic formalism originally developed by Chen et al. (1989) and Murray et al. (1995), in which the observed flux density fν is obtained by integrating over the disk surface:

fν ∝ ∫∫ ε(ξ, φ) exp