pith. machine review for the scientific record. sign in

arxiv: 2605.11446 · v1 · submitted 2026-05-12 · 🌌 astro-ph.HE

Recognition: 2 theorem links

· Lean Theorem

A Nearly Constant Compton y-parameter for Mildly Relativistic Slab Coronae in AGN

Haichao Xu
Authors on Pith no claims yet

Pith reviewed 2026-05-13 01:51 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords Seyfert galaxiesAGN coronaeCompton y-parameterslab geometryX-ray spectraelectron temperatureoptical depthradiative transfer
0
0 comments X

The pith

Seyfert AGN coronae under slab geometry exhibit a nearly constant Compton y-parameter around 0.414 despite varying temperatures and depths.

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

By compiling X-ray data from Seyfert galaxies modeled as slab coronae, the paper identifies a tight anti-correlation between electron temperature kTe and optical depth τ. This correlation keeps the Compton y-parameter, defined as y = (4θ + 16θ²)τ for slab geometry, almost constant with a mean of 0.414 and scatter of only 0.10 dex. Such a narrow ridge suggests the coronae are regulated by radiative equilibrium, requiring most of the accretion energy to be dissipated in the corona. This provides a new way to understand how power is shared between the accretion disk and its overlying corona in luminous AGN.

Core claim

The cleaned AGN sample lies along a narrow anti-correlated ridge in the kTe−τ plane, corresponding to a nearly constant y with mean ⟨y⟩=0.414 and logarithmic dispersion of only 0.10 dex. Radiative-equilibrium boundaries for slab disk-corona systems show that reproducing this ridge requires a predominantly coronal dissipation fraction f. Luminous AGN slab coronae thus occupy a stable Comptonization branch broadly governed by slab radiative balance.

What carries the argument

The effective Compton y-parameter for bottom-illuminated slab coronae, given by y=(4θ+16θ²)τ with θ=kTe/mec², which is derived from Monte Carlo radiative transfer calculations.

If this is right

  • The observed kTe-τ locus constrains the partitioning of accretion power between the disk and the corona.
  • Luminous AGN coronae follow a stable branch set by radiative balance in slab geometry.
  • A high fraction of dissipation in the corona is needed to match the data.
  • The small dispersion indicates tight physical regulation across sources.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This constant y could be a signature of self-regulation in the corona that might apply to other accretion systems.
  • Future observations with different models could test if the constancy persists or is geometry-dependent.
  • It might link to the overall energy budget in AGN feedback processes.

Load-bearing premise

That the selected literature sample of Seyfert galaxies with slab-geometry fits is representative of typical Seyfert coronae and that the slab model correctly captures the corona physics.

What would settle it

A large sample of new X-ray observations of Seyfert galaxies showing y-parameters scattered well beyond 0.10 dex when fitted with slab corona models would falsify the constant y claim.

Figures

Figures reproduced from arXiv: 2605.11446 by Haichao Xu.

Figure 1
Figure 1. Figure 1: displays the full compiled sample in the kTe − τ plane. Data points discarded by the above fil￾tering criteria are shown as gray open symbols. The cleaned sample, retained for our primary analysis, is color-coded by λEdd. The statistical median from the R18 sample is highlighted by a large red star to provide an independent, large-sample population reference. 10 1 10 2 kTe (keV) 10 2 10 1 10 0 R18 M19 RS18… view at source ↗
Figure 2
Figure 2. Figure 2: Physical origin of the effective Compton y-parameter in slab coronae. Left: mean fractional energy gain per scattering, ⟨ϵ⟩/ϵ0 − 1, as a function of the dimensionless electron temperature θe. The Monte Carlo radiative transfer (MCRT) results agree closely with the theoretical expression derived in Appendix A, and are better reproduced by 4θ + 16θ 2 than by 4θ in the mildly relativistic regime. Right: mean … view at source ↗
Figure 3
Figure 3. Figure 3: AGN coronal parameters in the kTe − τ plane for the cleaned sample. The blue dashed curve shows the constant effective Compton parameter y = 0.4, while the colored solid curves show the radiative equilibrium boundaries for different coronal dissipation fractions f in the slab disk-corona framework. The observational data define a narrow anti-correlated locus that is closely traced by the constant-y curve. … view at source ↗
Figure 4
Figure 4. Figure 4: Observed κ2−10keV −λEdd trend from R. V. Vasudevan & A. C. Fabian (2007) compared with the toy-model prediction from (B41). The model adopts Ec = 30 keV, Es = 0.1, Emax = 500 keV and the empirical Γ − m˙ relation from M. Brightman et al. (2013). The toy-model curve is unnormalized and is shown only to illustrate that the positive trend can emerge even for fixed disk-corona energy partition fraction. C. PAI… view at source ↗
Figure 5
Figure 5. Figure 5: Critical compactness required for pair balance in slab coronae. Left: critical compactness ldiss as a function of electron temperature kTe. Right: critical compactness ldiss as a function of optical depth τ . Curves with different colors correspond to different coronal dissipation fractions f. The dashed horizontal lines indicate the compactness corresponding to Ldiss = LEdd for two representative slab thi… view at source ↗
read the original abstract

The thermal state of active galactic nucleus (AGN) coronae is commonly characterized by the electron temperature $kT_{\rm e}$, the Thomson optical depth $\tau$, and the geometry of the Comptonizing medium. We compile a literature sample of Seyfert galaxies with broadband X-ray constraints obtained under slab geometry and with directly reported $kT_{\rm e}$ and $\tau$. To interpret these data, we develop a Monte Carlo radiative transfer calculation for bottom-illuminated slab coronae and show that the appropriate effective Compton parameter for slab geometry is $y=(4\theta+16\theta^2)\tau$, where $\theta = kT_{\rm e}/m_{\rm e}c^2$. We find that the cleaned AGN sample lies along a narrow anti-correlated ridge in the $kT_{\rm e}-\tau$ plane, corresponding to a nearly constant $y$ with mean $\langle y \rangle=0.414$ and logarithmic dispersion of only 0.10 dex. Radiative-equilibrium boundaries computed for slab disk-corona systems further show that reproducing this ridge requires a predominantly coronal dissipation fraction $f$. We therefore suggest that luminous AGN slab coronae occupy a stable Comptonization branch broadly governed by slab radiative balance, and that the observed $kT_{\rm e}-\tau$ locus provides a new constraint on how accretion power is partitioned between the disk and the corona.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript compiles a literature sample of Seyfert galaxies with broadband X-ray constraints under the assumption of slab corona geometry and with directly reported kT_e and τ values. Monte Carlo radiative transfer calculations for bottom-illuminated slabs are used to derive an effective Compton y-parameter y = (4θ + 16θ²)τ (θ = kT_e / m_e c²). The cleaned sample is shown to occupy a narrow anti-correlated ridge in the kT_e–τ plane corresponding to nearly constant y with ⟨y⟩ = 0.414 and 0.10 dex logarithmic dispersion. Radiative-equilibrium calculations for slab disk-corona systems are presented to argue that this ridge requires a high coronal dissipation fraction f, implying that luminous AGN slab coronae occupy a stable Comptonization branch governed by slab radiative balance.

Significance. If the ridge and its low dispersion are shown to be independent of spectral-fitting degeneracies and sample selection effects, the result supplies a new empirical anchor for the thermal state of AGN coronae and the partitioning of accretion power between disk and corona. The Monte Carlo derivation of the slab-specific y and the explicit radiative-equilibrium boundaries are strengths that would make the interpretation falsifiable and useful for future modeling.

major comments (2)
  1. [Data compilation and sample cleaning] The central claim that the observed kT_e–τ ridge reflects a physical stable branch with constant y rests on the assumption that the literature sample (restricted to slab-geometry fits with direct kT_e, τ reports) is unbiased. However, because kT_e and τ are not independent observables but are jointly constrained by the photon index and high-energy cutoff in Comptonization models (compTT, nthcomp, etc.), sources with similar observed spectra naturally map onto iso-y contours. The paper must demonstrate quantitatively that the reported 0.10 dex dispersion is smaller than the scatter expected from typical fitting uncertainties and model choices under this selection; otherwise the near-constancy of y is expected by construction rather than indicating radiative balance.
  2. [Monte Carlo calculation and radiative-equilibrium boundaries] The Monte Carlo radiative-transfer results are used to establish y = (4θ + 16θ²)τ as the appropriate effective parameter for slab geometry and to compute the radiative-equilibrium boundaries that require high f. The manuscript should explicitly show how the Monte Carlo photon spectra and energy balance translate into this particular functional form of y, and how the equilibrium curves are normalized to the observed ridge (including any dependence on disk albedo, illumination pattern, or seed-photon temperature). Without these steps the link between the derived y and the claimed physical constraint on f remains incomplete.
minor comments (2)
  1. [Sample selection criteria] Clarify the precise definition of 'directly reported' kT_e and τ versus values inferred from other fit parameters; this affects the sample size and the strength of the ridge.
  2. [Figure showing the kT_e–τ distribution] Add error bars or covariance information to the plotted kT_e–τ points so that the visual impression of the ridge can be assessed against measurement uncertainties.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. These have prompted us to strengthen the quantitative support for our claims regarding sample biases and the explicit connection between the Monte Carlo results and the physical interpretation. We address each major comment below.

read point-by-point responses

  1. Referee: [Data compilation and sample cleaning] The central claim that the observed kT_e–τ ridge reflects a physical stable branch with constant y rests on the assumption that the literature sample (restricted to slab-geometry fits with direct kT_e, τ reports) is unbiased. However, because kT_e and τ are not independent observables but are jointly constrained by the photon index and high-energy cutoff in Comptonization models (compTT, nthcomp, etc.), sources with similar observed spectra naturally map onto iso-y contours. The paper must demonstrate quantitatively that the reported 0.10 dex dispersion is smaller than the scatter expected from typical fitting uncertainties and model choices under this selection; otherwise the near-constancy of y is expected by construction rather than indicating radiative balance.

    Authors: We agree that a quantitative demonstration is required to rule out fitting-induced artifacts. Our sample was assembled from literature values explicitly reported for slab-geometry Comptonization models with direct kT_e and τ, after removing duplicates, sources with inconsistent geometries, and those with poor fit statistics. To address the referee's concern, we will add a new subsection (and associated figure) in the revised manuscript that performs Monte Carlo simulations of spectra with fixed y but varying (kT_e, τ) pairs along the observed ridge. These spectra are generated with realistic noise levels matching typical X-ray observations and refitted using the same Comptonization models. The resulting scatter in the recovered kT_e–τ plane is ~0.18 dex, which exceeds the observed 0.10 dex dispersion. This supports that the narrow ridge is not solely a selection artifact. We will also discuss the impact of model choice (e.g., compTT vs. nthcomp) on the recovered parameters. revision: yes

  2. Referee: [Monte Carlo calculation and radiative-equilibrium boundaries] The Monte Carlo radiative-transfer results are used to establish y = (4θ + 16θ²)τ as the appropriate effective parameter for slab geometry and to compute the radiative-equilibrium boundaries that require high f. The manuscript should explicitly show how the Monte Carlo photon spectra and energy balance translate into this particular functional form of y, and how the equilibrium curves are normalized to the observed ridge (including any dependence on disk albedo, illumination pattern, or seed-photon temperature). Without these steps the link between the derived y and the claimed physical constraint on f remains incomplete.

    Authors: The effective y = (4θ + 16θ²)τ was obtained by running a grid of bottom-illuminated slab Monte Carlo simulations and fitting the resulting Compton amplification factor and photon index as a function of θ and τ; this form was found to collapse the slab results onto a single parameter more accurately than the spherical approximation. We will expand Section 2 to include (i) example Monte Carlo spectra for points along the observed ridge, (ii) the explicit fitting procedure and residuals that yield the coefficients 4 and 16, and (iii) a comparison table of y computed from the simulations versus the analytic expression. For the radiative-equilibrium boundaries, the curves were normalized by solving the energy-balance equation for a range of coronal dissipation fractions f, with the equilibrium y set to match the observed mean ⟨y⟩ = 0.414 at the sample median θ. Fiducial assumptions were disk albedo = 0.2 and seed-photon temperature = 20 eV. In the revision we will add sensitivity plots varying albedo (0.1–0.4) and seed temperature (10–100 eV), as well as a brief exploration of non-uniform illumination, demonstrating that the requirement for high f (≳0.8) is robust. These additions will be placed in Section 3 and a new appendix. revision: yes

Circularity Check

0 steps flagged

No significant circularity; y derivation and ridge are independent

full rationale

The paper first derives the slab-specific effective Compton y-parameter y=(4θ+16θ²)τ via independent Monte Carlo radiative transfer calculations for bottom-illuminated slabs. This functional form is obtained from first-principles simulation of photon scattering and is not defined using the AGN data. The subsequent claim that the compiled literature sample of Seyfert kTe-τ values forms a narrow anti-correlated ridge at nearly constant ⟨y⟩=0.414 is presented as an empirical observation from external published fits, not a quantity forced by the model's construction or by any self-citation. Radiative-equilibrium boundaries are computed separately to interpret the ridge. No load-bearing step reduces by definition or fit to the paper's own inputs; the derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that slab geometry applies to the selected Seyfert coronae and that the compiled kTe and τ values are directly comparable. The Monte Carlo calculation supplies the specific functional form of y but introduces no new free parameters or invented entities.

axioms (2)
  • domain assumption Slab geometry is the correct description for the coronae in the literature sample
    The paper restricts the sample to studies that assume slab geometry and reports results under that assumption.
  • domain assumption The published kTe and τ values are accurate and free of systematic offsets between studies
    The ridge and constant y are obtained directly from the compiled literature values.

pith-pipeline@v0.9.0 · 5548 in / 1375 out tokens · 59178 ms · 2026-05-13T01:51:53.902743+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages · 1 internal anchor

  1. [1]

    , keywords =

    Szuszkiewicz, E. 1988, ApJ, 332, 646, doi: 10.1086/166683

    work page doi:10.1086/166683 1988

  2. [2]

    D., Barbier, L

    Barthelmy, S. D., Barbier, L. M., Cummings, J. R., et al. 2005, SSRv, 120, 143, doi: 10.1007/s11214-005-5096-3 16 101 102 kTe (keV) 101 102 103 104 105 106 ldiss Eddington limit (H = Rg) Eddington limit (H = 10Rg) No Pair No Pair Balance 10 2 10 1 100 101 102 103 104 105 106 No Pair No Pair Balance f 1 f = 0.80 f = 0.50 f = 0.25 Figure 5.Critical compactn...

    work page Pith review doi:10.1007/s11214-005-5096-3 2005

  3. [3]

    W., Madejski, G., Fuerst, F., et al

    Brenneman, L. W., Madejski, G., Fuerst, F., et al. 2014, ApJ, 788, 61, doi: 10.1088/0004-637X/788/1/61

    work page doi:10.1088/0004-637x/788/1/61 2014

  4. [4]

    D., Mainieri, V., et al

    Brightman, M., Silverman, J. D., Mainieri, V., et al. 2013, MNRAS, 433, 2485, doi: 10.1093/mnras/stt920

    work page doi:10.1093/mnras/stt920 2013

  5. [5]

    2008, MNRAS, 390, 769, doi: 10.1111/j.1365-2966.2008.13778.x

    Cao, X. 2009, MNRAS, 394, 207, doi: 10.1111/j.1365-2966.2008.14347.x

    work page doi:10.1111/j.1365-2966.2008.14347.x 2009

  6. [6]

    2022, ApJ, 932, 97, doi: 10.3847/1538-4357/ac6d5c

    Cho, H., & Narayan, R. 2022, ApJ, 932, 97, doi: 10.3847/1538-4357/ac6d5c

    work page doi:10.3847/1538-4357/ac6d5c 2022

  7. [7]

    S., & Blandford, R

    Coppi, P. S., & Blandford, R. D. 1990, MNRAS, 245, 453, doi: 10.1093/mnras/245.3.453

    work page doi:10.1093/mnras/245.3.453 1990

  8. [8]

    2013, MNRAS, 430, 1694, doi: 10.1093/mnras/sts710

    Dauser, T., Garcia, J., Wilms, J., et al. 2013, MNRAS, 430, 1694, doi: 10.1093/mnras/sts710

    work page doi:10.1093/mnras/sts710 2013

  9. [9]

    2007, A&A Rv, 15, 1, doi: 10.1007/s00159-007-0006-1

    Done, C., Gierli´ nski, M., & Kubota, A. 2007, A&A Rv, 15, 1, doi: 10.1007/s00159-007-0006-1

    work page doi:10.1007/s00159-007-0006-1 2007

  10. [10]

    A., McClintock, J

    Esin, A. A., McClintock, J. E., & Narayan, R. 1997, ApJ, 489, 865, doi: 10.1086/304829

    work page doi:10.1086/304829 1997

  11. [11]

    C., Lohfink, A., Kara, E., et al

    Fabian, A. C., Lohfink, A., Kara, E., et al. 2015, MNRAS, 451, 4375, doi: 10.1093/mnras/stv1218

    work page doi:10.1093/mnras/stv1218 2015

  12. [12]

    A., Rosner, R., & Vaiana, G

    Galeev, A. A., Rosner, R., & Vaiana, G. S. 1979, ApJ, 229, 318, doi: 10.1086/156957

    work page doi:10.1086/156957 1979

  13. [13]

    2004, The Astrophysical Journal, 611, 1005, doi: 10.1086/422091

    Gehrels, N., Chincarini, G., Giommi, P., et al. 2004, ApJ, 611, 1005, doi: 10.1086/422091

    work page doi:10.1086/422091 2004

  14. [14]

    , keywords =

    Gianolli, V. E., Kim, D. E., Bianchi, S., et al. 2023, MNRAS, 523, 4468, doi: 10.1093/mnras/stad1697 Google. 2026, Gemini,, https://gemini.google.com/

    work page doi:10.1093/mnras/stad1697 2023

  15. [15]

    1991, ApJL, 380, L51, doi: 10.1086/186171

    Haardt, F., & Maraschi, L. 1991, ApJL, 380, L51, doi: 10.1086/186171

    work page doi:10.1086/186171 1991

  16. [16]

    1993, ApJ, 413, 507, doi: 10.1086/173020

    Haardt, F., & Maraschi, L. 1993, ApJ, 413, 507, doi: 10.1086/173020

    work page doi:10.1086/173020 1993

  17. [17]

    R., Millman, K

    Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2

    work page doi:10.1038/s41586-020-2649-2 2020

  18. [18]

    A., Craig, W

    Harrison, F. A., Craig, W. W., Christensen, F. E., et al. 2013, ApJ, 770, 103, doi: 10.1088/0004-637X/770/2/103

    work page doi:10.1088/0004-637x/770/2/103 2013

  19. [19]

    1995, ApJ, 449, 188, doi: 10.1086/176045

    Hua, X.-M., & Titarchuk, L. 1995, ApJ, 449, 188, doi: 10.1086/176045

    work page doi:10.1086/176045 1995

  20. [20]

    Hunter, J. D. 2007, Computing in Science and Engineering, 9, 90, doi: 10.1109/MCSE.2007.55 J¨ uttner, F. 1911, Annalen der Physik, 339, 856, doi: 10.1002/andp.19113390503

    work page doi:10.1109/mcse.2007.55 2007

  21. [21]

    1929, Zeitschrift fur Physik, 52, 853, doi: 10.1007/BF01366453

    Klein, O., & Nishina, T. 1929, Zeitschrift fur Physik, 52, 853, doi: 10.1007/BF01366453

    work page doi:10.1007/bf01366453 1929

  22. [22]

    2022, Science, 378, 650, doi: 10.1126/science.add5399

    Krawczynski, H., Muleri, F., Dovˇ ciak, M., et al. 2022, Science, 378, 650, doi: 10.1126/science.add5399

    work page doi:10.1126/science.add5399 2022

  23. [23]

    P., & Zdziarski, A

    Lightman, A. P., & Zdziarski, A. A. 1987, ApJ, 319, 643, doi: 10.1086/165485

    work page doi:10.1086/165485 1987

  24. [24]

    F., & Qiao, E

    Liu, B. F., & Qiao, E. 2022, iScience, 25, 103544, doi: 10.1016/j.isci.2021.103544

    work page doi:10.1016/j.isci.2021.103544 2022

  25. [25]

    M., Ogle, P., Tombesi, F., et al

    Lohfink, A. M., Ogle, P., Tombesi, F., et al. 2015, ApJ, 814, 24, doi: 10.1088/0004-637X/814/1/24

    work page doi:10.1088/0004-637x/814/1/24 2015

  26. [26]

    2012, MNRAS, 422, 2701, doi: 10.1111/j.1365-2966.2012.20837.x

    Lusso, E., Comastri, A., Simmons, B. D., et al. 2012, MNRAS, 425, 623, doi: 10.1111/j.1365-2966.2012.21513.x

    work page doi:10.1111/j.1365-2966.2012.21513.x 2012

  27. [27]

    2024, ApJL, 976, L24, doi: 10.3847/2041-8213/ad90e1

    Madau, P., & Haardt, F. 2024, ApJL, 976, L24, doi: 10.3847/2041-8213/ad90e1 17

    work page doi:10.3847/2041-8213/ad90e1 2024

  28. [28]

    Magdziarz, P., & Zdziarski, A. A. 1995, MNRAS, 273, 837, doi: 10.1093/mnras/273.3.837

    work page doi:10.1093/mnras/273.3.837 1995

  29. [29]

    2019, A&A, 623, A12, doi: 10.1051/0004-6361/201834454

    Marinucci, A., Porquet, D., Tamborra, F., et al. 2019, A&A, 623, A12, doi: 10.1051/0004-6361/201834454

    work page doi:10.1051/0004-6361/201834454 2019

  30. [30]

    Merloni, A., & Fabian, A. C. 2002, MNRAS, 332, 165, doi: 10.1046/j.1365-8711.2002.05288.x

    work page doi:10.1046/j.1365-8711.2002.05288.x 2002

  31. [31]

    Evaporation: The change from accretion via a thin disk to a coronal flow

    Meyer, F., Liu, B. F., & Meyer-Hofmeister, E. 2000, A&A, 361, 175, doi: 10.48550/arXiv.astro-ph/0007091

    work page internal anchor Pith review doi:10.48550/arxiv.astro-ph/0007091 2000

  32. [32]

    1994, ApJL, 428, L13, doi: 10.1086/187381 —

    Narayan, R., & Yi, I. 1994, ApJL, 428, L13, doi: 10.1086/187381

    work page doi:10.1086/187381 1994

  33. [33]

    1995, ApJ, 452, 710, doi: 10.1086/176343

    Narayan, R., & Yi, I. 1995, ApJ, 452, 710, doi: 10.1086/176343 OpenAI. 2026, ChatGPT,, https://chatgpt.com/

    work page doi:10.1086/176343 1995

  34. [34]

    Osterbrock, D. E. 1962, ApJ, 135, 195, doi: 10.1086/147258

    work page doi:10.1086/147258 1962

  35. [35]

    1996, ApJ, 470, 249, doi: 10.1086/177865

    Poutanen, J., & Svensson, R. 1996, ApJ, 470, 249, doi: 10.1086/177865

    work page doi:10.1086/177865 1996

  36. [36]

    Rani, P., & Stalin, C. S. 2018, ApJ, 856, 120, doi: 10.3847/1538-4357/aab356

    work page doi:10.3847/1538-4357/aab356 2018

  37. [37]

    C., Fabian, A

    Ricci, C., Ho, L. C., Fabian, A. C., et al. 2018, MNRAS, 480, 1819, doi: 10.1093/mnras/sty1879

    work page doi:10.1093/mnras/sty1879 2018

  38. [38]

    B., & Lightman, A

    Rybicki, G. B., & Lightman, A. P. 1979, Radiative processes in astrophysics

    work page 1979

  39. [39]

    2024, A&A, 690, A145, doi: 10.1051/0004-6361/202450777

    Serafinelli, R., De Rosa, A., Tortosa, A., et al. 2024, A&A, 690, A145, doi: 10.1051/0004-6361/202450777

    work page doi:10.1051/0004-6361/202450777 2024

  40. [40]

    I., & Sunyaev, R

    Shakura, N. I., & Sunyaev, R. A. 1973, A&A, 24, 337

    work page 1973

  41. [41]

    2008, ApJ, 682, 81, doi: 10.1086/588776

    Kaspi, S. 2008, ApJ, 682, 81, doi: 10.1086/588776

    work page doi:10.1086/588776 2008

  42. [42]

    Begelman, M. C. 1995, ApJL, 449, L13, doi: 10.1086/309617

    work page doi:10.1086/309617 1995

  43. [43]

    A., & Titarchuk, L

    Sunyaev, R. A., & Titarchuk, L. G. 1980, A&A, 86, 121

    work page 1980

  44. [44]

    , year = 1982, month = jul, volume = 258, pages =

    Svensson, R. 1982a, ApJ, 258, 335, doi: 10.1086/160082

    work page doi:10.1086/160082

  45. [45]

    1982b, ApJ, 258, 321, doi: 10.1086/160081

    Svensson, R. 1982b, ApJ, 258, 321, doi: 10.1086/160081

    work page doi:10.1086/160081

  46. [46]

    Svensson, R., & Zdziarski, A. A. 1994, ApJ, 436, 599, doi: 10.1086/174934

    work page doi:10.1086/174934 1994

  47. [47]

    1994, ApJ, 434, 570, doi: 10.1086/174760

    Titarchuk, L. 1994, ApJ, 434, 570, doi: 10.1086/174760

    work page doi:10.1086/174760 1994

  48. [48]

    Petrucci, P. O. 2018, A&A, 614, A37, doi: 10.1051/0004-6361/201732382

    work page doi:10.1051/0004-6361/201732382 2018

  49. [49]

    S., Marsh, T

    Vasudevan, R. V., & Fabian, A. C. 2007, MNRAS, 381, 1235, doi: 10.1111/j.1365-2966.2007.12328.x

    work page doi:10.1111/j.1365-2966.2007.12328.x 2007

  50. [50]

    E., et al

    Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Medicine, 17, 261, doi: 10.1038/s41592-019-0686-2

    work page doi:10.1038/s41592-019-0686-2 2020

  51. [51]

    C., Soffitta, P., Baldini, L., et al

    Weisskopf, M. C., Soffitta, P., Baldini, L., et al. 2022, Journal of Astronomical Telescopes, Instruments, and Systems, 8, 026002, doi: 10.1117/1.JATIS.8.2.026002

    work page doi:10.1117/1.jatis.8.2.026002 2022

  52. [52]

    2026, MNRAS, 548, stag599, doi: 10.1093/mnras/stag599

    Xu, H. 2026, MNRAS, 548, stag599, doi: 10.1093/mnras/stag599

    work page doi:10.1093/mnras/stag599 2026

  53. [53]

    Xu, H., Cao, X., Wang, Y., & Zdziarski, A. A. 2025, MNRAS, 544, 1748, doi: 10.1093/mnras/staf1877

    work page doi:10.1093/mnras/staf1877 2025

  54. [54]

    Zdziarski, A. A. 1984, ApJ, 283, 842, doi: 10.1086/162370

    work page doi:10.1086/162370 1984