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A bayesian-like approach to derive chemical abundances in Type-2 Active Galactic Nuclei based on photoionization models

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read This paper claims that a Bayesian-like grid comparison of optical emission lines reproduces the oxygen and nitrogen abundances of type-2 AGN narrow-line regions found by detailed tailored photoionization models, within the errors.

desk verdict Useful public tool for AGN abundances; validation is a consistency check against the same code family, not an independent test. read the letter →

arxiv 1908.04827 v1 pith:YYIV426X submitted 2019-08-13 astro-ph.GA

E. Pérez-Montero , O. L. Dors , J. M. Vílchez , R. García-Benito , M. V. Cardaci , G. F. Hägele This is my paper · ORCID
classification astro-ph.GA
keywords activegalacticnucleitype-2Seyfertgalaxiesnarrow-lineregionchemicalabundancesphotoionizationmodelsBayesian-likemethodionizationparameterN/Oabundanceratio
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that chemical abundances in the narrow-line regions of type-2 active galactic nuclei can be derived from a handful of optical emission-line ratios by comparing them, in a Bayesian-like chi-squared-weighted way, against a large grid of photoionization models. This matters because the standard electron-temperature method applied to AGNs gives implausibly low metallicities, while building a detailed photoionization model for every object is too slow for large surveys. When the recipe is applied to 47 Seyfert 1.9/2 galaxies, it reproduces the total oxygen abundance and nitrogen-to-oxygen ratio obtained from tailored model-by-model analysis, with mean offsets within the quoted errors. The recovered values place the sample at high metallicity, with N/O consistent with secondary nitrogen production but showing large dispersion, and with ionization parameters about 1.5 dex larger than in star-forming galaxies at similar metallicity. The paper also argues that the old disagreement with the electron-temperature method is largely a missing-ionization effect: a large fraction of oxygen is more ionized than O2+ and invisible in optical lines, so models are needed to supply the ionization correction.

What carries the argument

The load-bearing mechanism is the two-stage, chi-squared-weighted Bayesian-like comparison implemented in the HCm code adapted for AGNs: first N/O is set from N2O2 and N2S2, then O/H and log U are set from RO3, N2, O3N2, R23, and O2Ne3. The comparison grid consists of 5,865 Cloudy photoionization models computed for a homogeneous gas slab with density 500 $cm^{-3}$, filling factor 0.1, and a two-component ionizing spectral energy distribution (a big blue bump peaking at 1 Ryd plus a power-law X-ray tail with alpha_ox = -0.8); all abundances are scaled to solar proportions, with nitrogen left free. The grid covers 12+log(O/H) from 6.9 to 9.1, log(N/O) from -2.0 to 0.0, and log U from -4.0 to -0.5, and the code can interpolate the model fluxes by a factor of five in each variable. The restriction to log U > -2.5 avoids the region where the [O ii]/[O iii] versus U relation is double-valued and would degenerate the ionization-parameter solution.

What would settle it

Measure the high-ionization oxygen fraction directly in a few control-sample Seyfert 2s with UV or far-infrared spectroscopy (e.g. [O IV] 25.9 microns, [Ne V] 3426 Angstroms or 14.3/24.3 microns), and compare the total O/H obtained including those ions with the code's predicted ionization-correction factor at the fitted log U; if the model-predicted missing oxygen fraction is contradicted by the observed high-ionization lines, the derived O/H values are systematically biased.

Watch

Extended reading notes

Core claim

The central discovery is that a Bayesian-like comparison between observed optical emission-line ratios and a precomputed grid of 5,865 photoionization models, run in two stages, recovers the chemical abundances of the narrow-line regions of type-2 AGNs. In the first stage the code derives the nitrogen-to-oxygen ratio from the low-excitation ratios N2O2 and N2S2, which are nearly independent of ionization parameter. In the second stage, with N/O fixed, it derives total oxygen abundance and ionization parameter from RO3, N2, O3N2, R23, and O2Ne3, discarding models with log U below -2.5 to avoid a double-valued relation between [O ii]/[O iii] and U. On the 47-object control sample the method returns O/H values in the range 12+log(O/H) = 8.37 to 9.07 and N/O values in the range log(N/O) = -1.11 to -0.04, agreeing within the errors with the tailored-model determinations of the control sample. The paper interprets the well-known underestimate from the electron-temperature method as an ionization-correction problem: in these high-metallicity, high-U NLRs a large fraction of oxygen occupies ionization stages above O2+ whose optical lines are not measured, so a model-based ionization correction factor is mandatory for total abundances from optical spectra.

Load-bearing premise

The load-bearing premise is that the narrow-line region is effectively a single homogeneous gas slab at density 500 $cm^{-3}$ with a fixed two-component ionizing spectrum, and that the oxygen missing from optical lines really is in higher, unobserved ionization stages; if that ionization correction is wrong, the total O/H values would be systematically biased even though the Bayesian fit appears internally consistent.

Editorial extensions

If this is right

  • Large optical surveys of type-2 AGNs can now be processed automatically with the same Bayesian grid code, yielding O/H, N/O, and log U with uncertainties even when the auroral line [O III] lambda4363 or the blue [O II] lambda3727 line is missing.
  • Abundances of AGN narrow-line regions and star-forming galaxies can be placed on a common model-based scale, because the same Bayesian-like code has already been applied to H II regions.
  • The electron-temperature method's systematically low AGN metallicities should be read as evidence for a large unobserved high-ionization oxygen fraction, not as a contradiction with photoionization models; metallicity- and U-dependent ionization corrections are required.
  • The sample's high O/H with N/O increasing toward high metallicity, though with large scatter, supports secondary nitrogen production in these systems and warns against calibrating metallicity from [N II] lines without an independent N/O constraint.
  • Because the derived log U values are roughly 1.5 dex higher than in star-forming galaxies at the same metallicity, ionization parameter must be treated separately when comparing AGN and star-forming samples.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the missing-ionization interpretation is correct, optical-only AGN surveys should adopt a metallicity- and U-dependent ionization-correction factor rather than a constant offset; the paper demonstrates the need in model space but does not publish a closed-form correction formula.
  • The double-valued [O ii]/[O iii] versus U relation implies that log U cannot be uniquely derived from strong-line ratios in this regime; the code's choice to keep only the upper branch (log U > -2.5) could hide a population of lower-excitation NLRs, a hypothesis testable with independent indicators such as [Ne V]/[Ne III].
  • The same grid-based Bayesian approach should extend to rest-frame UV and mid-infrared line sets, where the supposedly missing high-ionization oxygen ions become directly observable; a successful check there would turn the paper's main assumption into a verified prediction.
  • The new linear relations between log(N/O) and N2O2 or N2S2 derived for AGN NLRs could be used as quick empirical N/O estimators for large samples, though their scatter around the control-sample values (roughly 0.12-0.13 dex) sets the precision floor.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This manuscript presents an adaptation of the public Hii-Chi-mistry code (HCm) to the narrow-line regions of type-2 AGNs. The authors build a grid of 5,865 Cloudy photoionization models spanning 12+log(O/H)=6.9-9.1, log(N/O)=-2.0-0.0, and log U=-4.0 to -0.5 under fixed density (500 cm^-3), filling factor (0.1), and a two-component SED with alpha_ox=-0.8. The code first estimates N/O from the N2O2 or N2S2 ratios, then constrains O/H and U from optical ratios (RO3, N2, O3N2, R23, O2Ne3), restricting log U to > -2.5 to avoid the double-valued [O ii]/[O iii] branch. Applied to 47 Seyfert 1.9/2 galaxies from Dors et al. (2017), the method returns 12+log(O/H)=8.37-9.07, log(N/O)=-1.11 to -0.04, and log U=-2.42 to -1.27, in nominal agreement with the tailored-model abundances of Dors et al. (2017). The paper also shows that the Te-method O^+ + O^2+ ionic abundances fall roughly 0.7 dex below the model total O/H, attributes this to unobserved higher-ionization oxygen, and tests sensitivity to density and alpha_ox.

Significance. If the method is accurate, it would be a convenient, reproducible tool for abundance measurements in large AGN samples and would support the conclusion that Seyfert 2 NLRs are metal-rich, with secondary nitrogen production and high ionization parameters. Strengths of the manuscript include the public release of the code, explicit Monte Carlo uncertainty propagation, a transparent grid, and a fair discussion of the double-valued excitation diagnostics. The principal weakness is that the only quantitative validation uses Dors et al. (2017), whose tailored models share the Cloudy code, the same SED prescription, and an author with the present paper; the agreement therefore validates the numerical inversion but not the physical ionization correction factor that carries the main abundance result. The N/O residual pattern in Table 1 also needs explanation before the "agreement within errors" claim can be accepted in full. With these points addressed, the paper would be a useful methodological contribution.

major comments (3)
  1. [§4.2 / §4.4] The validation is not independent. Both the new grid and the Dors et al. (2017) control abundances are computed with Cloudy, adopt largely the same SED and homogeneous-slab geometry, and share authorship, so the reported agreement mainly checks that a grid inversion can reproduce tailored fits within the same model family. The physically important claim, that the 0.7 dex deficit of the Te-method O^+ + O^2+ abundances is an ionization correction to total O/H, is exactly the kind of model-dependent step that this comparison cannot test. I request an external validation (e.g., infrared or ultraviolet oxygen lines, X-ray constraints, or an independent photoionization code with different atomic data) or at least a quantitative exploration of matter-bounded geometries and SED variations to show that the derived O/H is not a common bias of the shared assumptions.
  2. [§3.2.1 / Table 1] The reported N/O residuals are internally inconsistent. The direct N2O2 and N2S2 calibrations against the same Dors et al. (2017) sample give mean offsets of +0.07 and +0.05 dex, but the all-lines solution in Table 1 has a mean residual of +0.23 dex with a scatter of 0.19 dex, and the residual changes non-monotonically with the line set (+0.12 for [O iii]a, [O iii]n, [N ii], [S ii]; -0.11 for [O iii]n, [N ii], [S ii]). Since the code fixes N/O from N2O2/N2S2 before deriving O/H, the origin of this roughly 0.2 dex offset should be explained; as written, it weakens the claim that the method is consistent and independent of the input line set.
  3. [§3.2.2 / Fig. 13] The decision to discard models with log U < -2.5 is implemented before comparing with the data, and Figure 13 shows that when the full grid is allowed many objects fall in the turnover region that has no models, so the restriction is effectively an assumption rather than a result. Because the abstract emphasizes that the derived log U values are much larger than in star-forming objects, the authors should demonstrate that this conclusion is robust to the branch choice, for example by testing an independent U diagnostic or by reporting how many objects would move to low-log U solutions without the restriction.
minor comments (5)
  1. [Throughout] The phrase "bayesian-like" is used throughout, but equations (1), (7), and (8) define weighted means with weights 1/chi^2 and no priors or normalization are specified; please either define the probabilistic interpretation or use a less committal term.
  2. [§3.1] The sentence stating that a density of 500 cm^-3 is "about the maximum value found by Dors et al. (2014)" is incomplete and should be reworded with the relevant reference and a brief justification for choosing the maximum value.
  3. [Abstract / §4.5] There are typographical errors that should be corrected, including "consistent wit" in the abstract, "more deepley studied" in Section 4.1, and "hte" in Section 4.2.
  4. [Fig. 14] The solid model lines for different values of U in Figure 14 are not identified in the caption; a legend or line labels are needed for the comparison with the black circles.
  5. [§4.2] The statement that there are no degeneracies between metallicity and the optical ratios for log U > -2.5 is strong; a diagnostic figure or a quantitative measure of the degeneracy would help support it.

Circularity Check

1 steps flagged · score 2.0 of 10

Abundance derivation is a self-contained grid inversion, but the validation benchmark is not fully independent: the grid SED and the Dors et al. (2017) control abundances share Cloudy, model assumptions, and authorship.

  1. self citation load bearing [Section 2 (control sample) and Section 3.1 (grid SED choice)]
    "In order to establish comparisons between the predicted abundances from our code with other model-based results in a sample of objects with the required spectral information we resorted to the objects described and analyzed in Dors et al. (2017). // This value represents the highest in the range derived in the sample of radio-intermediate and radio-loud quasars studied by Miller et al. (2011), but it is the most adequate to reproduce [O iii]/Hβ most type-2 AGNs according to Dors et al. (2017)."

    The paper's accuracy claim rests on agreement with Dors et al. (2017), which is co-authored by a present author and uses the same Cloudy photoionization code. Moreover, the grid's ionizing SED is not independently fixed: the adopted alpha_ox = -0.8 is chosen specifically because it reproduces the [O iii]/Hbeta ratio of the same type-2 AGNs according to Dors et al. (2017). Thus the validation benchmark and the tested model grid share the key physical assumptions (Cloudy, SED, density, filling factor) and are tuned to the same observed sample. A shared systematic error, such as the large unobserved high-ionization oxygen fraction discussed in Section 4.4, would not appear as a disagreement.

full rationale

I found no circular step in the central abundance derivation. The HCm-AGN method performs a Bayesian-like weighted inversion of observed optical line ratios against a grid of Cloudy photoionization models: N/O is first constrained from N2O2 or N2S2 (Eqs. 1-4), then O/H and log U are weighted means over models constrained to that N/O using RO3, N2, O3N2, R23, and related ratios (Eqs. 7-13). The linear relations in Eqs. 5-6 are fits to the model grid, not fits to the Dors et al. (2017) abundances, so they are not a fitted input renamed as a prediction. The paper is internally consistent and self-contained against observed line fluxes. The only circularity-adjacent issue is that the validation sample is not an external benchmark: Dors et al. (2017) shares authorship, uses the same Cloudy code, and the grid SED is explicitly chosen to reproduce the same objects' [O iii]/Hbeta according to that work. Consequently the agreement shown in Figures 9-11 and Table 1 is weaker evidence than a fully independent comparison would be, and the paper's own Section 4.4 acknowledges that the derived total O/H relies on a large model-dependent ionization correction. This is a legitimate concern about validation independence, but not a case where the prediction reduces to the input by construction. The paper itself flags the dependence on grid assumptions and the difficulty of the ICF, which supports a proportionate low score rather than a charge of circularity.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

No new physical particles, forces, or conserved quantities are introduced. The method relies on a grid of photoionization models with several hand-chosen input assumptions: the SED shape (including a literature-calibrated alpha_ox), gas density and filling factor, solar-scaled element abundances, and a log U branch restriction. The only fitted numerical outputs are the empirical N2O2 and N2S2 calibrations, which are fits to the same model grid.

free parameters (5)
  • alpha_ox = -0.8
    The SED power-law index between 2 keV and 2500 A was chosen as the value 'most adequate to reproduce [O iii]/H-beta most type-2 AGNs according to Dors et al. (2017)' (Section 3.1), effectively calibrating the model to the sample.
  • N2O2 calibration slope = 0.97 +/- 0.01
    Linear fit to the model grid for log(N/O) as a function of N2O2 (Eq. 5), presented as an alternative direct N/O estimator.
  • N2O2 calibration intercept = -0.50 +/- 0.01
    Constant term in the linear fit of log(N/O) versus N2O2 (Eq. 5), fitted to the same model grid.
  • N2S2 calibration slope = 0.88 +/- 0.01
    Linear fit to the model grid for log(N/O) as a function of N2S2 (Eq. 6).
  • N2S2 calibration intercept = -0.69 +/- 0.01
    Constant term in the linear fit of log(N/O) versus N2S2 (Eq. 6).
assumptions (6)
  • domain assumption Cloudy v17.01 accurately predicts the emission-line spectrum of the NLR gas around type-2 AGNs.
    The entire grid of predicted line ratios depends on the fidelity of the Cloudy photoionization code, which is treated as a given tool.
  • domain assumption The NLR gas is homogeneous, with a constant density of 500 cm^-3 and a filling factor of 0.1.
    Stated in Section 3.1 as 'typical in the NLRs around type-2 AGNs'; the robustness test only changes density to 2000 cm^-3, not filling factor or inhomogeneities.
  • ad hoc to paper The ionizing SED can be represented by a Big Blue Bump plus a power law with alpha_x = -1 and alpha_ox = -0.8.
    The SED shape is a modeling choice, and alpha_ox is explicitly selected to reproduce the observed [O iii]/H-beta of the sample rather than measured per object.
  • domain assumption All chemical abundances scale with oxygen following solar proportions from Asplund et al. (2009), except nitrogen which is free.
    This is a standard simplifying assumption for photoionization model grids, enabling a manageable parameter space.
  • ad hoc to paper For type-2 AGN NLRs, the correct branch of the double-valued [O ii]/[O iii] versus log U relation is the upper branch with log U > -2.5.
    The code discards all models with log U < -2.5 (Section 3.2.2, Figure 6) to avoid degeneracy, based on the expectation that AGNs have high log U (Dopita et al. 2014).
  • ad hoc to paper When N/O cannot be estimated from lines, the O/H-N/O relation for star-forming regions applies to AGN NLRs.
    Stated in Section 4.2 as a fallback assumption, with the caveat that strong interactions can cause deviations from this relation.

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Pith. "Pith review of A bayesian-like approach to derive chemical abundances in Type-2 Active Galactic Nuclei based on photoionization models." pith.science (2026). https://pith.science/paper/YYIV426X

@misc{pith2026190804827,
  author       = {Pith},
  title        = {Pith review of: A bayesian-like approach to derive chemical abundances in Type-2 Active Galactic Nuclei based on photoionization models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YYIV426X}},
  note         = {Machine review of arXiv:1908.04827}
}
read the original abstract

We present a new methodology for the analysis of the emission lines of the interstellar medium in the Narrow Line Regions around type-2 Active Galactic Nuclei. Our aim is to provide a recipe that can be used for large samples of objects in a consistent way using different sets of optical emission-lines that takes into the account possible variations from the (O/H)-(N/O) relation to use [N II] lines. Our approach consists of a bayesian-like comparison between certain observed emission-line ratios sensitive to total oxygen abundance, nitrogen-to-oxygen ratio and ionization parameter with the predictions from a large grid of photoionization models calculated under the most usual conditions in this environment. We applied our method to a sample of Seyfert 2 galaxies with optical emission-line fluxes and determinations of their chemical properties from detailed models in the literature. Our results agree within the errors with other results and confirm the high metallicity of the objects of the sample, with N/O values consistent wit a large secondary production of N, but with a large dispersion. The obtained ionization parameters for this sample are much larger than those for star-forming object at the same metallicity.

Figures

Figures reproduced from arXiv: 1908.04827 by the authors.

Figure 1
Figure 1. Diagnostic diagrams showing the emission-line ratio [O iii]/Hβ in relation to [N ii]/Hα (left) and to [S ii]/Hα (right) both for the control sample (black circles) and the whole grid of models (colored squares). The color bar represents the metallicity of each model. The solid line represents the curve defined by Kauffman et al (2003) to separate AGNs and star-forming regions. The dashed red line represents the line… view at source ↗
Figure 2
Figure 2. Relation between the elemental abundance ratio N/O with the emission line ratios N2O2 (upper panels) and N2S2 (lower panels) both for some of the models of the grid and for the control sample with the abundances derived by Dors et al (2017). The panels in the left column show results from the models described in the text at a fixed O/H = 8.7 and the panels at right column at a fixed log(U) = -2.0. The dashed black l… view at source ↗
Figure 3
Figure 3. Relation between the total oxygen abundance and the logarythm of the emission line ratio [O iii] λλ5007/4363 ˚A both for the abundances derived by Dors et al (2017) for the control sample, as represented with black circles, and for models, for dif￾ferent values of U, at a fixed log(N/O) value of -0.5. models by the code in the previous step described above, the [N ii] emission lines can be now used to derive oxygen … view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: Relation between the total oxygen abundance 12+log(O/H) with the emission line ratio N2 (upper panels) and O3N2 (lower panels) both for the abundances derived by Dors et al. (2017) for the control sample and from some of the models described in the text at a fixed log(…
Figure 5
Figure 5. Figure 5: Relation between the total oxygen abundance 12+log(O/H) as derived in Dors et al (2017) for the control sample with the emission line ratios R23 (left upper panel), [O ii]/[O iii] (right upper panel), O2Ne3 (left lower panel), and [O ii]/[Ne iii] (right lower panel). A…
Figure 6
Figure 6. Figure 6: Relation between the ionization parameter and the emission-line ratios [O ii]/[O iii] (at left), and O3N2 (at right) as predicted from photoionization models for different metallicities and assuming a constant N/O value at -1.0. MNRAS 000, 1–18 (2017) [PITH_FULL_IMAGE…
Figure 7
Figure 7. Figure 7: Relations between O/H and N/O (left) and U (right) for the resulting values of our method for the control sample. Grey points represent the sample of star-forming regions analyzed following a similar bayesian-like procedure by P´erez-Montero (2014). The solid black lin…
Figure 8
Figure 8. Figure 8: Comparison between chemical abundances derived using the method described in this work and those obtained assuming the ionizing spectral energy distribution of a massive young star cluster for the control sample. At left comparison of derived 12+log(O/H) and at right f…
Figure 9
Figure 9. Figure 9: Comparison between chemical abundances derived using the method described in this work and those taken from Dors et al. (2017) from tailored photoionization models. At left comparison of derived 12+log(O/H) and at right for log(N/O). The upper panels show the compariso…
Figure 10
Figure 10. Figure 10: Comparison between the chemical abundances derived from our method when only certain sets of lines are considered and the abundances derived in Dors et al (2017) for the control sample. In top row, in absence of [O ii] λ3727 ˚A; in middle row when [O ii] and [O iii] λ…
Figure 11
Figure 11. Figure 11: Comparison between the oxygen abundances derived from our method when only certain lines are considered as input and a previous derivation of N/O is not carried out but an empirical O/H-N/O relation is adopted with respect to the values presented by Dors et al (2017) …
Figure 12
Figure 12. Figure 12: Comparison between the resulting O/H (left panel) and N/O (right panel) derived by HCm using a non-interpolated and an interpolated grid of models. In both panels the red solid line represents the 1:1 relation. AGNs (e.g. Dors et al. 2015). Our results confirm that th…
Figure 13
Figure 13. Figure 13: Comparison between the resulting O/H ( upper left panel), N/O (upper right panel), and log U (left lower panel) derived by HCm using a non-restricted and a U-restricted grid of models. In all these panels the red solid line represents the 1:1 relation. The right lower…
Figure 14
Figure 14. Figure 14: Comparison between total oxygen abundance and the addition of the abundances of the two main ions observed in the optical part of the spectrum (i.e. O+ and O2+), at left, and between N/O and the corresponding ion abundance ratio N+/O+, at right. Models are represented…
Figure 15
Figure 15. Figure 15: Relations between different emission-line observables and abundances ratios used in the models as a function of different input parameters. Panels in the left column show the difference between models using an electron density of 2000 cm−3 (solid line) and 500 cm−3 (d…
Figure 16
Figure 16. Figure 16: Comparison between O/H (upper row), N/O (middle row) and log U )lower row) from our method and all input emission lines using the grid of models with an electron density of 500 cm−3 and a αOX = -0.8 and the results from the same code but changing two parameters in the…

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.