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About the accuracy of the relxill/relxill_nk models in view of the next generation of X-ray missions

T0 review · 4 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper shows that relxill and relxill_nk recover input black-hole parameters in simulated next-generation X-ray observations, but steep disk emissivity profiles expose numerical inaccuracies that are fixed by tripling the…

desk verdict Useful and honest accuracy study of relxill/relxill_nk for Athena/X-IFU and LAD, but the paper's own chi2 values undermine the claim that NFRAD=3000 fixes the residuals. read the letter →

arxiv 2412.00349 v1 pith:ALPCFRYO submitted 2024-11-30 astro-ph.HE gr-qc

Honghui Liu , Askar B. Abdikamalov , Temurbek Mirzaev , Cosimo Bambi , Thomas Dauser , Javier A. Garcia , Zuobin Zhang This is my paper · ORCID
classification astro-ph.HEgr-qc
keywords X-rayreflectionspectroscopyrelxillrelxill_nkraytracingblackholespinaccretiondiskemissivityAthena/X-IFUtransferfunction
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

X-ray reflection spectroscopy is the main tool for measuring black hole spin and testing General Relativity in strong gravity, and the next generation of X-ray observatories will deliver much higher-quality data than current ones. This paper asks whether the standard reflection models relxill and relxill_nk can handle that data quality. Simulating Athena/X-IFU and LAD observations of bright Galactic black holes with a precise ray-tracing code, fitting with relline and relline_nk, the paper finds the input spin, inclination, and deformation parameters are always recovered, but steep emissivity profiles ($q=5$) leave residuals that disappear only when the number of disk interpolation points $\mathrm{NFRAD}$ is raised from 1000 to 3000. For full reflection spectra, the paper finds that the convolution energy resolution must be raised to $\mathrm{NENER\_CONV}=524288$, and that with the physically correct, radius-dependent emission angle neither model fits ($\chi^2/\nu > 50$). The conclusion is that the relativistic calculations are basically sound but need these numerical upgrades, plus a proper emission-angle treatment, for the coming high-quality data.

What carries the argument

The central object is the Cunningham transfer function $f(g_*, r_e, i)$, which maps the emission integral over the observer's image plane into an integral over disk radius and the relative redshift factor $g_*$. relxill and relxill_nk precompute and tabulate this function, then integrate it numerically; the paper shows that the number of radial interpolation points in that integration, $\mathrm{NFRAD}$, must be raised from 1000 to 3000 to capture steep emissivity profiles, and that the number of energy bins in the convolution, $\mathrm{NENER\_CONV}$, must be raised from 4096 to 524288 for full reflection spectra. The second mechanism is the disk emission angle $\theta_e$: correct angle-dependent reflection requires using the angle-resolved reflection table per emission site rather than averaging the emission angle over radial zones.

What would settle it

Recompute the same simulated iron-line and full-reflection spectra with an independent ray-tracing code, or against analytic line shapes for a Schwarzschild black hole, and compare channel by channel; if the two reference calculations differ by as much as the residuals that $\mathrm{NFRAD}=3000$ removes, then the reference standard itself is the problem. A second check is to fit real X-IFU-class observations of a bright Galactic black hole with steep emissivity and see whether residuals reappear when $\mathrm{NFRAD}$ is lowered back to 1000.

Watch

Extended reading notes

Core claim

The paper establishes that the relativistic calculations underlying relxill and relxill_nk are accurate enough for next-generation X-ray data only after specific numerical upgrades. Fitting simulated Athena/X-IFU and LAD observations of bright Galactic black holes with relline and relline_nk always recovers the input spin and inclination, but for a steep power-law emissivity $q=5$ the fits show residuals at the iron-line low-energy tail, particularly at low inclination. Raising $\mathrm{NFRAD}$ from 1000 to 3000 removes the residuals without changing the tabulated transfer function. For full reflection spectra, the convolution must use $\mathrm{NENER\_CONV}=524288$ when the emission angle equals the inclination angle; when the correct radially-varying emission angle is used, neither relxill nor relxill_nk provides an acceptable fit ($\chi^2/\nu > 50$), because relxill averages the emission angle over radial zones.

Load-bearing premise

The load-bearing premise is that the ray-tracing code used to generate the simulated "true" spectra is accurate enough to serve as the reference standard; if that code has systematic errors in photon trajectories, redshifts, or emission angles, then the residuals blamed on relxill and relxill_nk, and the proposed fixes, would be misattributed.

Editorial extensions

If this is right

  • Future X-IFU and LAD iron-line fits should adopt $\mathrm{NFRAD}=3000$ to avoid artificial residuals for steep emissivity profiles with $q>3$.
  • The tabulated transfer functions themselves do not need to be recomputed; the fix lies in the integration routine, so both relxill and relxill_nk can be updated by a code change rather than new FITS grids.
  • For full reflection spectra with $\theta_e=i$, $\mathrm{NENER\_CONV}=524288$ is needed to match X-IFU and LAD data quality, otherwise residuals appear that are unrelated to the transfer function.
  • With physically correct, radius-dependent emission angles, current angle-averaged reflection models cannot fit next-generation data at all ($\chi^2/\nu>50$), so a model that uses the actual emission angle per disk zone is required.
  • Existing measurements with current instruments remain valid, because the angle-averaging approximation has only a minor impact on parameter estimation at present data quality.

Reading between the lines

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

  • Beyond the paper, the residual pattern for $q=5$ at low inclination suggests the integration error is concentrated at small disk radii where the emissivity peaks; a finer or adaptive radial grid would likely fix the same problem for broken power-law emissivities, which the paper did not test.
  • Beyond the paper, the $\chi^2/\nu>50$ failure with correct emission angles implies that future reflection models will need angle-resolved xillver-style tables or ray-traced angle-dependent convolution, not just higher-resolution grids, and this may change inferred spin and ionization parameters in high-quality data.
  • Beyond the paper, a cheap test of the NFRAD fix is to vary the emissivity index continuously and locate the threshold $q$ where residuals appear at $\mathrm{NFRAD}=1000$; the paper only tests $q=3$ and $q=5$.
  • Beyond the paper, the same accuracy checks could be applied to the lamppost coronal geometry, where the emissivity is computed rather than prescribed as a power law, to see whether the required $\mathrm{NFRAD}$ grows worse when the illuminating flux is concentrated at the innermost stable circular orbit.
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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

4 major / 4 minor

Summary. This manuscript assesses whether the relativistic calculations in relxill and relxill_nk are accurate enough for simulated Athena/X-IFU and LAD observations. The authors use the blackray ray-tracing code to generate iron-line and full-reflection spectra for spins a*=0.5, 0.9, 0.998; inclinations i=15, 45, 75 deg; and emissivity indices q=3, 5, then fit them with relline/relline_nk or relconv*xillver/relxill in XSPEC and compare residuals and recovered parameters. They report correct parameter recovery in all cases, q=5 iron-line residuals that decrease when the number of disk interpolation points NFRAD is increased from 1000 to 3000, full-reflection residuals that require an increase of the energy-convolution parameter N_ENER_CONV to 524288, and unacceptable fits for full reflection spectra when realistic emission angles are used, leading to the recommendation that future models treat the emission angle properly.

Significance. If the quantitative claims held, the paper would provide a useful and reproducible benchmark for the community: it uses a public ray-tracing code, a systematic grid of simulations over spin, inclination, and emissivity index, and it identifies concrete numerical parameters (NFRAD, N_ENER_CONV) and the emission-angle treatment as the main sources of inaccuracy in current models. The explicit separation of transfer-function accuracy from atomic-table accuracy in xillver is also a helpful contribution. However, the central demonstration needs to be re-examined: as reported, the NFRAD=3000 fits for q=5 are not statistically acceptable at X-IFU/LAD count rates, so the paper's conclusion that the residual problem is solved and that the models are 'good enough' is not yet supported by its own numbers.

major comments (4)
  1. [Sec. 3.2 and Fig. 6] The claim that increasing NFRAD from 1000 to 3000 makes the q=5 residuals disappear is contradicted by the reported chi-square statistics. For a*=0.998, q=5, the right panels of Fig. 6 give chi^2/nu = 13072.2/9966 (i=15 deg), 13527.1/9966 (i=45 deg), and 11593.0/9966 (i=75 deg), i.e., reduced chi^2 of 1.31, 1.36, and 1.16. With nu ~ 10^4, the expected scatter is sqrt(2*nu) ~ 141, so these values lie about 22, 25, and 12 sigma above the mean. The same issue affects the relline_nk fits in Fig. 7. The residual plots can look flat while still indicating statistically significant model error at X-IFU/LAD count rates. Please replace the visual 'residuals disappear' criterion with a quantitative convergence test: report chi^2/nu for NFRAD = 3000, 6000, and 12000 (and, if needed, larger values) for the q=5 cases, and either demonstrate that chi^2 approaches nu or revise the conclusion to state that the models are not yet accurate enough for these data.
  2. [Sec. 2] The paper's accuracy statements are all relative to blackray, which is used as the ground truth, but no independent validation of blackray is presented in this manuscript. Section 2 specifies integration tolerances (10^-8 to 10^-6) and pixel sampling, but it does not compare computed photon trajectories, redshifts, or line profiles with analytic solutions or with a second, independent ray-tracing code. Since blackray is from the same collaboration as the models under test, a systematic error in blackray would be misattributed to relxill/relxill_nk in the residual analysis. Please add a validation test for blackray, such as a comparison of Kerr iron-line profiles with the analytic Cunningham transfer-function calculation or with an independent ray-tracing code, or explicitly identify where such validation was performed previously.
  3. [Sec. 3.2] The generality of the NFRAD fix is not established by the presented fits. The residual problem is reported in Sec. 3.1 for the q=5 grid, but the NFRAD=3000 demonstration is shown only for a*=0.998 (Figs. 4-6). Please show NFRAD=3000 fits for the remaining spins (a*=0.5 and 0.9) and report the best-fit chi^2 and recovered parameters for all 18 iron-line simulations, since the conclusion that the current models are good enough for next-generation detectors is a claim about the full parameter grid.
  4. [Sec. 3.4] In Case II, the conclusion that full reflection models should implement the correct emission angle rests on fitting failures with chi^2/nu > 50, but the description of the attempted improvement is incomplete. The paper states that relxill_nk uses 50 radial zones instead of relxill's one-zone approximation yet does not improve the fits, without specifying whether those 50 zones use the correct local emission angle for each zone or still average the angle within a zone. Please clarify the implementation and, if the 50-zone model is only a radial refinement, state explicitly that it does not test the emission-angle hypothesis.
minor comments (4)
  1. [Fig. 4 caption] The caption contains a typo: 'ray-traing code' should be 'ray-tracing code'.
  2. [Sec. 4] The first paragraph of the Discussion contains a duplicated article: 'between the ray-tracing code calculations and the the reflection models' should read 'and the reflection models'.
  3. [Sec. 3 and Fig. 1] The paper does not provide a table of best-fit values and uncertainties for the 18 simulations; Fig. 1 shows only dots with error bars smaller than the symbol size, which makes it difficult to verify the claim that input parameters are recovered correctly. A supplementary table of best-fit parameters and 90% confidence ranges would improve reproducibility.
  4. [Sec. 3.2] The parameters NFRAD and N_ENER_CONV are introduced with their new recommended values, but the computational cost of changing them is not quantified anywhere in the paper. Since the Discussion recommends using the more accurate settings only when necessary, please report the runtime increase for NFRAD=3000 and N_ENER_CONV=524288.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the accuracy test is a first-principles benchmark of relxill/relline against a direct ray-tracing code; self-citations are descriptive, not load-bearing.

full rationale

The paper's central comparison is between spectra generated by a direct ray-tracing code and the relxill/relline (and relxill_nk/relline_nk) models. The ray-tracing code implements Eq. (2) by integrating over the observer's image plane, while the models use the transfer-function formalism of Eq. (4). The paper correctly notes that Eq. (4) follows from Eq. (2) by a change of variables, so the comparison tests numerical accuracy and tabulation/integration choices rather than a quantity fitted to the target result. The proposed fixes (NFRAD = 3000 and N_ENER_CONV = 524288) are numerical accuracy parameters, not parameters fitted to make the test pass; they are shown to reduce residuals in Figures 4-6 and 8. Self-citations to model papers and to the ray-tracing code (Abdikamalov et al. 2019; Bambi et al. 2017; Dauser et al. 2010; Garcia et al. 2013, 2014) are descriptive and not load-bearing in the sense of importing an unverified uniqueness theorem or defining the target result into the input. The reference ray-tracing code is from the same collaboration, which is a limitation in independent validation, but it computes spectra from first principles and is not calibrated to the models under test. A separate statistical concern exists: Fig. 6 reports chi2/nu values around 1.16-1.36 with ~10^4 dof for the q=5, NFRAD=3000 fits, so the claim that residuals 'disappear' may be statistically overstated; however, this is a correctness and statistical-significance issue, not a circularity issue. No derivation step reduces by construction to its own input, so the circularity score is low.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new physical entities or fitted constants. Its central claims rest on the accuracy of the ray-tracing code (used as ground truth), the assumption that the xillver local reflection tables are correct (explicitly untested), and the standard thin-disk and spacetime assumptions. The numerical settings NFRAD and N_ENER_CONV are hand-chosen to eliminate residuals and are listed as free parameters.

free parameters (2)
  • NFRAD = 3000
    Number of interpolation points on the accretion disk in the transfer function integral, increased from 1000 to 3000 by hand to remove residuals in iron-line fits for steep emissivity (q=5). It is a numerical resolution parameter, not a physical constant.
  • N_ENER_CONV = 524288
    Number of energy bins in the reflection kernel convolution, increased from 4096 to 524288 by hand to remove residuals in full reflection spectra fits. It controls energy resolution in the convolution.
assumptions (6)
  • domain assumption Kerr metric describes the spacetime around the simulated black holes.
    Used as the background geometry for all simulations in Sections 3.1 and 3.2.
  • domain assumption Johannsen metric with deformation parameter alpha13 describes non-Kerr spacetimes.
    Used in Section 3.3 to test deviations from Kerr.
  • domain assumption The accretion disk is geometrically thin, lies in the equatorial plane, and particles follow circular prograde orbits.
    Standard assumption in reflection models; invoked in Section 2.
  • domain assumption The xillver tables provide accurate local rest-frame reflection spectra.
    Used both in the ray-tracing code and in relxill/relxill_nk; the paper explicitly says the accuracy of these atomic calculations is not tested.
  • domain assumption The ray-tracing code blackray computes photon trajectories, redshifts, and emission angles with sufficient precision to serve as ground truth.
    The entire accuracy assessment is relative to this code; if it is inaccurate, the conclusions about relxill/relxill_nk are compromised. This is the weakest premise.
  • standard math The transfer function formalism of Cunningham (1975) is a correct rewrite of the image-plane integral.
    Equations (4) and (5) in Section 3.2 rely on this change of variables.

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Cite this review

Pith. "Pith review of About the accuracy of the relxill/relxill_nk models in view of the next generation of X-ray missions." pith.science (2026). https://pith.science/paper/ALPCFRYO

@misc{pith2026241200349,
  author       = {Pith},
  title        = {Pith review of: About the accuracy of the relxill/relxill_nk models in view of the next generation of X-ray missions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ALPCFRYO}},
  note         = {Machine review of arXiv:2412.00349}
}
read the original abstract

X-ray reflection spectroscopy is a powerful tool to study the strong gravity region of black holes. The next generation of astrophysical X-ray missions promises to provide unprecedented high-quality data, which could permit us to get very precise measurements of the properties of the accretion flow and of the spacetime geometry in the strong gravity region around these objects. In this work, we test the accuracy of the relativistic calculations of the reflection model relxill and of its extension to non-Kerr spacetimes relxill_nk in view of the next generation of X-ray missions. We simulate simultaneous observations with Athena/X-IFU and LAD of bright Galactic black holes with a precise and accurate ray-tracing code and we fit the simulated data with the latest versions of relline and relline_nk. While we always recover the correct input parameters, we find residuals in the fits when the emission from the inner part of the accretion disk is higher. Such residuals disappear if we increase the number of interpolation points on the disk in the integral of the transfer function. We also simulate full reflection spectra and find that the emission angle from the accretion disk should be treated properly in this case.

Figures

Figures reproduced from arXiv: 2412.00349 by the authors.

Figure 1
Figure 1. Constraints on the spin parameter and inclination angle after fitting the simulated spectra with the current version of relline. The crosses of dashed grey lines represent the input values for the simulations and the black dots indicate the best-fit values of the two parameters. The error bars (90% CL) are smaller than the size of the dots. The left panel is for the case with emissivity index q = 3 and the right pan… view at source ↗
Figure 2
Figure 2. Residuals of fitting the simulated spectra with the model relline. Only those with a∗ = 0.998 are shown. The left panel represents the case when the emissivity index is q = 3 and the right is for q = 5. The black color represents data of Athena/X-IFU and red is for LAD [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Iron line profile generated with the ray-tracing code and best-fit model of relline (top panel) and their ratio plot (bottom panel) for the case a∗ = 0.998, i = 15 deg, and q = 5. panels of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Difference between the broad iron line from the ray-traing code and relline model for N FRAD = 1000, 2000, and 3000. Panel (a) for a∗ = 0.998, i = 15 and q = 3, (b) for a∗ = 0.998, i = 15 and q = 5, (c) for a∗ = 0.998, i = 75 and q = 3 and (d) for a∗ = 0.998, i = 75 an…
Figure 5
Figure 5. Figure 5: The same as [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Residuals of fitting the simulated spectra for a∗ = 0.998 with the relline model in which the number of interpolation points on the disk (N FRAD) is set to 3000. See the text in Section 3.2 for more details. The left panel represents the case q = 3 and the right is for…
Figure 7
Figure 7. Figure 7: Residuals of fitting the simulated spectra for a∗ = 0.998, q = 5 with the relline nk model in which the number of interpolation points on the disk (N FRAD) is set to 3000. The ∆χ 2 values represent the improvement in χ 2 compared to the case of α13 = 0. See the text in…
Figure 8
Figure 8. Figure 8: Residuals of fitting the simulated full reflection spectra for a∗ = 0.5 and q = 5, which is the case showing the largest residuals in our set of simulations. The left panel represents fittings with current models and the right is for when increasing the parameter N ENE…
Figure 9
Figure 9. Figure 9: Example of a full reflection spectrum generated with the ray-tracing code and best-fit model of relxill (top panel) and their ratio plot (bottom panel) in Case II. In this simulation, we assume a∗ = 0.998, i = 15 deg, Γ = 1.7, Ecut = 300 keV, q = 5, log ξ = 1.0, and AF…

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Impact of the returning radiation on X-ray reflection spectroscopy measurements: the case of Galactic black holes

    astro-ph.HE 2025-01 conditional novelty 6.0 of 10

    Including returning radiation in relxill does not significantly alter the best-fit parameters of three Galactic black holes.

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.