FEADME: Fast Elliptical Accretion Disk Modeling Engine

Abstract

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.

Figures (7)

• Figure 1: Representative rest-frame spectra for each of the five TDEs in our sample (AT 2018hyz, AT 2018zr, AT 2020nov, AT 2020zso, and PTF09djl) showing broad, double-peaked H$\alpha$ emission consistent with disk-like kinematics. Each panel displays a single epoch selected to highlight the double-peaked structure, with the offset from peak optical brightness shown in the top-left corner. The diversity in peak separation, asymmetry, and profile shape reflects underlying differences in disk geometry, orientation, and emission structure, which we explore in detail through elliptical disk modeling in Section \ref{['sec:tde-disk-structure']}.
• Figure 2: Representative examples of the three model families used to fit the AGN spectra in this work. Each panel shows an observed AGN spectrum (grey), together with the corresponding best-fit model (black dashed line). The contribution from the elliptical accretion disk is shown in gold, while all non-disk line-emission components (narrow lines and the broad Gaussian) are shown in cyan. These examples illustrate the qualitative behavior of the disk+BLR, no BLR, and no disk model families (see Section \ref{['sec:fitting']}) and highlight the different ways in which disk and non-disk components combine to reproduce the observed H$\alpha$ line profiles.
• Figure 3: Distribution of elliptical disk model parameters across AGN clusters identified via UMAP + HDBScan clustering (see Section \ref{['sec:clustering-analysis']}), as well as for the full AGN sample (light grey) and the full TDE sample (dark grey). Each panel corresponds to one of the eight model parameters: the seven elliptical disk parameters (inclination ($i$), emissivity index ($q$), turbulent broadening ($\sigma$), inner radius ($\xi_1$), outer radius ($\xi_2$), apocenter angle ($\phi_0$), and eccentricity ($e$)), along with the FWHM of the broad Gaussian component included when preferred by the fit. Widths indicate the relative density of posterior samples aggregated across all objects in a group, while the horizontal black bar shows the medians of the distributions. The TDE sample exhibits systematically lower eccentricities and outer radii compared to the AGN cluster populations. Differences in parameter distributions highlight the diversity of disk structures present in both persistent (AGN) and transient (TDE) accretion flows.
• Figure 4: Two-dimensional projection of the 5-component UMAP embedding of the AGN disk parameter space. Colored regions indicate high-density areas associated with the four HDBScan-identified AGN clusters, while individual spectra not assigned to any cluster (i.e. transitional or ambiguous sources) are shown as grey points. The density shading reflects the concentration of objects in the reduced space, with clearer structure visible in well-populated clusters. This projection highlights the dominant morphological groups and the presence of a significant population of spectra that occupy intermediate or low-density regions of the disk parameter manifold.
• Figure 5: Median rest-frame H$\alpha$ fitted disk profiles for each of the four AGN clusters identified via UMAP + HDBScan. Solid lines represent the median spectrum within each cluster, while the shaded regions denote the 16th–84th percentile range (dark shading) and the 5th–95th percentile range (light shading) at each wavelength. Spectra were normalized and interpolated onto a common grid prior to stacking. The profiles illustrate the diversity in line shape and structure across the clusters, with some groups showing well-separated double peaks and others exhibiting more blended or asymmetric broad-line features.