BEAGLE-AGN SED Modeling Tool

• BEAGLE-AGN is a Bayesian tool that models galaxy SEDs by combining stellar population synthesis, nebular emission, and AGN photoionization physics.
• It employs MCMC sampling to jointly recover key parameters such as stellar mass, ionization state, AGN accretion-disk luminosity, and dust attenuation from both broadband and line data.
• The framework is validated against local and high-redshift observations, showing robust performance in disentangling mixed emission contributions, though it requires high S/N data for optimal accuracy.

The BEAGLE-AGN tool is a Bayesian framework for modeling and interpreting the spectral energy distributions (SEDs) of galaxies with both star formation and active galactic nucleus (AGN) components, designed to disentangle the physical properties of nebular gas in H II regions and narrow-line regions (NLR) associated with AGN. BEAGLE-AGN combines self-consistent stellar population synthesis, nebular emission physics, and AGN photoionization grids within a modular architecture, permitting simultaneous fitting of broadband photometry and emission-line spectra to recover stellar, interstellar, and nuclear parameters.

1. Physical Model and Architecture

BEAGLE-AGN extends the base BEAGLE SED tool by incorporating the physics of obscured AGN and their impact on the emission-line spectra of galaxies. The total rest-frame SED is computed as: $$L_\lambda = L_\lambda^{\star} + L_\lambda^{\rm neb} + L_\lambda^{\rm AGN}$$ where $L_\lambda^{\star}$ is the stellar continuum, $L_\lambda^{\rm neb}$ the nebular emission from H II regions, and $L_\lambda^{\rm AGN}$ the AGN contributions (disk, lines, dusty torus). Key physical components are:

• Stellar Emission: Based on Bruzual & Charlot (2003), with metallicity, age, and star-formation-history parameters.
• Nebular Emission (H II and NLR): H II emission from Gutkin et al. (2016) models (CLOUDY c13.03); AGN NLR emission from the Feltre et al. (2016) grid, with incident AGN continuum parameterized by a broken or single power law (slope α, typically −1.2 to −2.0).
• AGN Component: Encapsulates (i) accretion-disk continuum, (ii) nebular emission via AGN ionization (lines such as [Ne IV] 2426, [O III] 5007), and (iii) dusty torus reprocessing, commonly modeled with CLUMPY or Fritz et al. radiative transfer templates.

All emission passes through host-galaxy ISM and, for high-redshift sources, intergalactic (IGM) absorption modules.

2. Parameterization and Key Physical Quantities

The model includes a suite of free and fixed parameters, each sampled or fixed according to empirical constraints and physical degeneracies:

Parameter	Typical Range	Component
$\log\,M_\star$	$[7,13]$	Stellar
$\log\,U$ (ionization)	$[-4.0,-1.5]$	H II/NLR
$\xi_d$ (dust/metal)	$[0.1,0.5]$	H II/NLR
$\log\,Z/Z_\odot$	$[-2.2,+0.3]$	H II/NLR
$\tau_V$ (dust optical)	$[0,4]$	ISM
$\mu$ (ISM dust fraction)	$[0,1]$	ISM
$\log\,L_{\rm disk}$	$[42,48]$ (erg/s)	AGN
$\alpha$ (AGN slope)	$[-1.2,-2.0]$	AGN
$n_{\rm H}$ (density)	fixed; $10^2-10^3$ cm⁻³	H II/NLR

The dimensionless ionization parameter,

$$U = \frac{Q(\mathrm{H})}{4\pi R^2 n_{\mathrm{H}} c}$$

is evaluated either at the Strömgren radius for H II regions or at the inner edge of the NLR for AGN models. Metallicity is specified as $12++\log(\mathrm{O/H})$ for direct comparison to observations. Dust attenuation follows the two-component Charlot & Fall (2000) prescription.

For AGN, the accretion-disk luminosity $L_{\rm acc}$ is a core fitted parameter, directly connected to the AGN ionizing output and, in some settings, used to infer black hole masses when paired with an assumed Eddington ratio.

3. Bayesian Inference Strategy

BEAGLE-AGN employs Bayesian inference via Markov Chain Monte Carlo (MCMC) to jointly sample the full posterior of all free parameters, utilizing simultaneous fits to both photometric SEDs and emission-line fluxes/ratios. The likelihood for a vector of observables $D$ relative to the model (parameterized by $\theta$) is: $$P(\theta\mid D) \propto \mathcal{L}(\theta)\ \pi(\theta)$$ For emission line ratios $R = X/Y$ with Gaussian errors,

$$\sigma^2_R = \frac{\mu_X^2}{\mu_Y^2}\left(\frac{\sigma_X^2}{\mu_X^2}+\frac{\sigma_Y^2}{\mu_Y^2}\right)$$

Ratios are defined so $X$ is the lower S/N line.

Three canonical fitting schemes are used to probe degeneracies:

• All parameters free (maximal exploration)
• $\xi_d$, $\mu$ fixed; fit $U$, $\alpha$ (tests impact of ISM/NLR dust)
• $\alpha$, $\xi_d$ fixed; fit $U$, $L_{\rm disk}$ (recommended for degenerate cases)

Key degeneracies include ($\xi_d \leftrightarrow U$ in NLR; $\alpha \leftrightarrow L_{\rm disk}$; $U \leftrightarrow \xi_d$ in H II regions). To minimize biases, $\alpha$ and $\xi_d$ are usually fixed at representative values (e.g., $\alpha = -1.7$, $\xi_d = 0.3$).

Proper data quality is required for unbiased retrievals:

• $S/N(\rm H\beta)\gtrsim10$ to detect NLR contributions $>10\%$ in H$\alpha$
• $S/N(\rm H\beta)\gtrsim20-30$ for accurate separation of star-forming and AGN emission in mixed or AGN-dominated spectra

4. Validation, Model Comparison, and Observational Requirements

Validation is performed using mock spectra at $z=0$ and $z=2$, with controlled NLR/H II ratios, spanning AGN-dominated, mixed, and star-formation-dominated regimes. Parameter covariance and posterior bias are evaluated for each. BEAGLE-AGN outputs are compared to:

• Other photoionization models: Feltre et al. (2016) grids, NebularBayes, Hii-Chi-mistry, showing agreement in the coverage of line-ratio diagnostics for Seyfert samples and resolving known ambiguities (e.g., double-valued solutions in $U$).
• Empirical strong-line calibrations: E.g., the Storchi-Bergmann et al. (1998) formulae and Dors et al. (2021) $R_{23}$–$P$ calibration. BEAGLE-AGN models with $12+\log(O/H)\lesssim8.5$ align with empirical planes but exhibit a curvature at high metallicity consistent with observed AGN populations and divergent from one-dimensional empirical fits.

Comprehensive broadband and emission-line spectra—covering [O II]$\lambda\lambda$3726,3729 through [S II]$\lambda\lambda$6716, 6731, plus high ionization lines (e.g. He II $\lambda$4686, [Ne IV])—are necessary for robust constraints, especially for high-redshift and mixed NLR/H II systems.

5. Applications to High-Redshift and Multi-component Systems

BEAGLE-AGN has been applied to both local galaxy surveys and high-redshift systems, including JWST-detected AGN in low-mass galaxies and the z = 12.34 galaxy GHZ2. Its salient application features include:

• Simultaneous modeling of photometry and lines, enabling self-consistent recovery of stellar mass, dust attenuation, star-formation history (SFH), and gas properties.
• Disentangling emission from H II and NLR: For each emission line, BEAGLE-AGN computes the probabilistic fractional contribution from AGN and star formation, based on the observed spectrum and the physical parameter grids.
• Leverage of high-ionization diagnostics: The presence of lines such as [Ne IV] 2426 (ionization potential ∼63 eV), which cannot arise from massive stars even at extreme parameters, provides a direct anchor for the AGN contribution, enabling stringent constraints on the NLR parameters and the separation from star-formation dominated emission. In the absence of such anchors, H II/NLR degeneracies remain high.

Recent applications include quantifying the AGN contribution to C IV$\lambda$1548 and C III]$\lambda$1908 in GHZ2 (54$^{+1}_{-1}$% and 26$^{+4}_{-2}$%, respectively), and inferring NLR metallicities and accretion-disk luminosities in $z\sim7.66$ SMACS S06355, demonstrating the tool’s relevance for studies of early black hole growth and AGN feedback (Ortiz et al., 4 Nov 2025, Silcock et al., 23 Oct 2024).

6. Strengths, Limitations, and Best Practices

BEAGLE-AGN’s principal strengths are its joint and fully Bayesian treatment of both stellar and AGN-driven ionized gas physics, flexibility to fit mixed systems, and consistency across continuum and line constraints. MCMC sampling enables full posterior exploration, including joint uncertainties and the impact of degeneracies.

Limitations are set primarily by data quality and the physics encoded in the grids:

• Degeneracies: At low S/N or with incomplete line coverage, AGN/star-formation contributions can remain poorly separated unless high-ionization lines are present.
• Fixed abundance ratios: Assumptions such as solar Ne/O or C/O can bias inferred NLR metallicity if violated at high $z$.
• Dust treatment: NLR attenuation is generally tied to host ISM curves, which may differ from the true dust geometry; allowing a separate NLR dust parameter is unconstrained without spatially resolved or multi-aperture data.
• Bolometric conversions: At subsolar $Z$ or extreme $U$, the relation between line luminosities and AGN $L_{\rm acc}$ can differ by up to 1 dex from empirical calibrations, limiting direct comparison of BEAGLE-AGN outputs to local AGN bolometric luminosities.

For best practices, line lists should cover the classical optical diagnostics, at least one unambiguous high-ionization AGN line, and be paired with photometry extending across rest-frame UV to near-IR. Fixed values of AGN slope and dust-to-metal ratio are preferred unless high S/N and a wide range of line diagnostics are available.

7. Current and Future Developments

BEAGLE-AGN is applied extensively to data from large spectroscopic surveys (SDSS, DESI, 4MOST), as well as JWST high-$z$ follow-ups, for mapping the co-evolution of black holes and galaxies. Planned enhancements include the relaxation of fixed elemental abundance ratios, improved treatment of dust geometry and attenuation, and full integration of spatially resolved spectroscopy to address aperture-dependent biases.

Ongoing validation against local and high-redshift AGN samples continues to refine the accuracy and reliability of parameter retrieval, particularly for systems with unusual chemical abundances or ISM conditions. A plausible implication is that as richer datasets and expanded model grids become available, BEAGLE-AGN’s capacity to robustly chart black hole accretion and feedback across cosmic time will be further strengthened (Vidal-García et al., 2022, Silcock et al., 23 Oct 2024, Chevallard et al., 2016).