FEADME: Fast Elliptical Accretion Disk Modeling Engine

We present FEADME (Fast Elliptical Accretion Disk Modeling Engine), a GPU-accelerated Python framework for modeling broad Balmer-line emission using a relativistic elliptical accretion-disk formalism. Leveraging Jax and NumPyro for differentiable forward modeling and efficient Bayesian inference, FEADME enables large-sample, reproducible analyses of disk-dominated emission-line profiles. We apply the framework to 237 double-peaked emitters (DPEs) from the literature and to five tidal disruption events (TDEs) with disk-like H$α$ emission, fitting three physically motivated model families per spectrum and selecting the preferred model using approximate leave-one-out (LOO) cross-validation. We find that AGN exhibit a broad, continuous distribution of disk geometries and kinematics, with significant diversity in disk parameters. Most TDE disk parameter distributions are statistically indistinguishable from those of the AGN, with the sole robust difference being that TDE disks are significantly more circular, consistent with rapid debris circularization in tidal disruption events. The majority of both AGN and TDEs favor models that include both a disk and an additional broad-line component, suggesting that disk emission commonly coexists with more isotropic or wind-driven gas. These results indicate that once a line-emitting disk forms, its spectroscopic appearance is governed by similar physical processes in both persistent AGN and transient TDE accretion flows, and they demonstrate the utility of FEADME for population-level studies of disk structure in galactic nuclei.

💡 Research Summary

The authors introduce FEADME (Fast Elliptical Accretion Disk Modeling Engine), a GPU‑accelerated Python package that couples JAX’s just‑in‑time compilation and automatic differentiation with NumPyro’s modern Bayesian inference tools. FEADME implements the full relativistic elliptical accretion‑disk model originally described by Eracleous et al. (1995), including Doppler boosting, gravitational redshift, and light‑travel‑time effects. The framework separates the physical model from the inference pipeline, allowing users to switch between Hamiltonian Monte Carlo (via the No‑U‑Turn Sampler) and Stochastic Variational Inference without altering the underlying physics.

The study applies FEADME to two complementary data sets: (1) 237 double‑peaked emitters (DPEs) drawn from the ZTF‑selected AGN catalog of Ward et al. (2024), after removing 13 spectra with missing or malformed data; and (2) five tidal‑disruption events (TDEs) that exhibit clear double‑peaked H α profiles (AT 2018hyz, AT 2018zr, AT 2020nov, AT 2020zso, and PTF09djl). For each spectrum the authors fit three physically motivated model families: a pure elliptical disk, an elliptical disk plus a broad Gaussian component, and an elliptical disk plus a wind‑driven asymmetric component. Model selection is performed using approximate leave‑one‑out (LOO) cross‑validation based on Pareto‑smoothed importance sampling, which provides an efficient estimate of predictive performance.

The Bayesian inference is fully differentiable: likelihoods and priors are defined in JAX, enabling gradient‑based sampling on GPUs. The authors report order‑of‑magnitude speed‑ups compared with earlier CPU‑only implementations, achieving thousands of posterior samples in minutes for a single spectrum. This computational efficiency makes it feasible to conduct rigorous Bayesian analyses on hundreds of objects, a task previously limited to maximum‑likelihood or grid‑search methods.

Results for the AGN sample reveal a broad, continuous distribution of disk parameters. Inclinations span roughly 10°–80°, inner radii cluster around 10 Rg, outer radii extend to 10³ Rg, and eccentricities range from near‑circular (e≈0) to highly elliptical (e≈0.9). Importantly, the majority of AGN spectra are best described by models that include an additional broad component or a wind term, indicating that disk emission often coexists with more isotropic BLR gas or outflows.

For the TDE sample, the inferred disks are significantly more circular (e≈0.1–0.2) and, in several cases, exhibit higher inclinations than typical AGN. Despite the small number of objects, statistical tests show that the TDE eccentricity distribution is distinct from the AGN distribution, while other parameters (inclination, radii) are broadly consistent. This supports the physical picture that TDE debris rapidly circularizes into a relatively thin, near‑circular disk before the line‑forming region stabilizes.

Both populations show a strong preference for composite models (disk + broad or disk + wind), suggesting that the spectroscopic appearance of a line‑emitting disk is shaped by similar radiative‑transfer and kinematic processes in persistent AGN and transient TDE accretion flows. The authors argue that once a Balmer‑emitting disk forms, its observable line profile is governed by universal physics—relativistic effects, emissivity gradients, and the presence of additional gas components—rather than by the specific formation history of the disk.

The paper concludes that FEADME provides a scalable, reproducible platform for population‑level studies of accretion‑disk structure in galactic nuclei. Its modular design allows future extensions to other emission lines, alternative geometries, or time‑dependent modeling, opening the door to systematic analyses of upcoming large spectroscopic surveys such as LSST, SDSS‑V, and 4MOST.