pith. sign in

arxiv: 2606.12543 · v1 · pith:7S36CEZInew · submitted 2026-06-10 · 🌌 astro-ph.HE

Spectral analysis of magnetized advective accretion flows around rotating black holes

Mayank Pathak (IISc) , Shubhrangshu Ghosh (SRMUS) , Banibrata Mukhopadhyay (IISc) This is my paper

Pith reviewed 2026-06-27 08:24 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords black hole accretionMHD simulationsspectraSANEMADmagnetic fieldsrotating black holesluminosity
0
0 comments X

The pith

Spectra of magnetized accretion flows around rotating black holes show distinct features between SANE and MAD magnetic configurations that allow identification of field characteristics.

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

The paper uses numerical steady-state MHD solutions to show that spectra from accretion flows around black holes vary strongly with black hole spin, accretion rate, magnetic field strength, and electron temperature, affecting emission peaks and total luminosity. It then validates these trends against GRMHD simulations employing SANE and MAD vector potentials for two spin values. The resulting comparison reveals large differences in bolometric luminosities, peak locations, and the ratio of synchrotron to synchrotron self-Compton peaks. A reader would care because these differences supply observables that can reveal the magnetic state of real systems from their spectra.

Core claim

Numerical steady state MHD solutions of magnetized accretion flows around black holes show strong dependence of the spectrum on the spin of the black hole, accretion rate, magnetic field and the electron temperature of the flow. Validation with GRMHD simulations using SANE and MAD vector potentials for spins a=0.5 and a=0.9375 finds large differences in bolometric luminosities and emission peak locations between the two states, along with drastically distinct ratios of synchrotron radiation to synchrotron self-Comptonization peaks. The overall luminosity combined with such metrics can distinguish the magnetic field characteristics in astrophysical systems.

What carries the argument

Spectral comparison between SANE and MAD vector potentials in GRMHD simulations of magnetized advective flows around rotating black holes.

If this is right

  • The spectrum exhibits strong dependence on the spin of the black hole, accretion rate, magnetic field and the electron temperature of the flow.
  • Variations in these quantities influence the emission peaks and overall luminosity.
  • There is a large difference in the bolometric luminosities and the location of the emission peaks between SANE and MAD flows.
  • The ratio of synchrotron radiation to synchrotron self-Comptonization peaks shows drastically distinct features in SANE and MAD.

Where Pith is reading between the lines

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

  • If the luminosity and ratio distinctions persist, they could be applied to classify the magnetic states of observed X-ray binaries or active galactic nuclei from existing spectral data.
  • The approach might be extended to time-variable flows to test whether the same metrics remain stable under realistic accretion fluctuations.
  • Polarization measurements could be combined with these spectral ratios to provide an independent check on the inferred magnetic configurations.

Load-bearing premise

The chosen steady-state MHD solutions and the specific SANE/MAD vector potentials in the GRMHD runs represent the dominant physics in real magnetized accretion flows around rotating black holes.

What would settle it

High-quality multi-wavelength spectra from a rotating black hole accretion system that exhibit similar bolometric luminosities and synchrotron-to-SSC peak ratios under conditions expected to produce SANE versus MAD states would falsify the distinguishing power of these metrics.

Figures

Figures reproduced from arXiv: 2606.12543 by Banibrata Mukhopadhyay (IISc), Mayank Pathak (IISc), Shubhrangshu Ghosh (SRMUS).

Figure 1
Figure 1. Figure 1: Schematic diagram of the model accretion system and radiation mechanisms operating in each part of the flow. The outer two-component region consists of the Keplerian (middle pink) and sub-Keplerian (enveloping sky-blue) disks and inner (quasi-spherical sky-blue) region is the pure sub-Keplerian disk. The non-thermal emission generated from the inner sub-Keplerian region and thermal emission from the Kepler… view at source ↗
Figure 2
Figure 2. Figure 2: Flow profiles of (a) radial velocity and sound speed, (b) density, (c) magnetic field strength magnitude, and (d) ion and electron temperatures, for an accretion flow with M˙ = 10−3 , α = 0.01, M = 10M⊙, a = 0.998, xf = 0.5 and xfm = 0.9. ing sub-Keplerian flows, our flow density is ∼ 10−9 − 10−10gm/cm3 . Fig. 2c shows the total magnetic field profile (B) with all the components. In this case our magnetic … view at source ↗
Figure 3
Figure 3. Figure 3: Spectra of (a) stellar mass (M = 10M⊙), and (b) supermassive (M = 108M⊙) black holes with M˙ = 10−3 , α = 0.01, a = 0.998, xf = 0.5 and xfm = 0.1. Note the difference in the peak luminosities of the stellar mass and the supermassive cases. a M˙ (M˙ Edd) rc(rg) λc(rgc) Tec(µempc 2 /kb) α xf xfm disk size (rg) mi βmc 0.0 10−3 5.8 3.2 5.1 × 10−4 0.01 0.5 0.9 13.89 8 88.62 0.5 10−3 4.8 2.6 5.9 × 10−4 0.01 0.5 … view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of stellar mass (M = 10⊙) and su￾permassive (108M⊙) black hole spectra for a = 0.998. cesses. This point of transition marks the synchrotron peak in our spectra at around ν ∼ 1014Hz for SBH and around ν ∼ 1011Hz for the SMBH cases. This is because density in accretion flows scales inversely with the mass of the central black hole (from Eq. 1, ρ ∼ M /Hrv ˙ ∼ M /r ˙ 2 g c; as rg, H (in terms of rg… view at source ↗
Figure 5
Figure 5. Figure 5: Variation of overall spectra with black hole spin a for M = 10M⊙. The other parameters are same as in [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Variation of overall spectra and density profiles with accretion rate M˙ for M = 10M⊙. The other parameters are same as in [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Variation of overall spectra and magnetic field profiles with the critical point magnetic field Bc for M = 10M⊙. The other parameters are same as in [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Variation of overall spectra and Te profiles with α for M = 10M⊙. The other parameters are same as in [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Variation of overall spectra and Te profiles with critical point electron temperature Tec for M = 10M⊙. The other parameters are same as in [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Variation of overall spectra and Te profiles with xf for M = 10M⊙. The other parameters are same as in [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Variation of overall spectra and Te profiles with xfm for M = 10M⊙. The other parameters are same as in [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Time averaged radial accretion rate profiles for SANE and MAD simulations with the inflow-outflow equilibrium boundary marked by the red dashed line. These quantities (q) are calculated over one disk scale height defined by: h r = R √ −gρ|θ − π/2|dθdϕ R √ −gρdθdϕ , (21) and then density averaged using, < q >disk= R q √ −gρdθdϕ R √ −gρdθdϕ [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Radial Mach number profiles for all the simula￾tions in the LNRF frame. a MAD SANE 0.5 3.2748 × 10−4 3.5 × 10−4 0.9375 5.5017 × 10−4 3.5 × 10−4 [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Radial magnetic field and temperature profiles for MAD and SANE simulations for a = 0.5 and a = 0.9375 ratio of synchrotron to SSC luminosity is also less in the MAD case as compared to SANEs. This ratio turns out to be ∼ 13.6 and ∼ 2.5 for SANE and MAD for a = 0.9375, respectively, and ∼ 2.45×103 and ∼ 0.83 for SANE and MAD for a = 0.5, respectively. For a = 0.5 the SSC peak is slightly higher than the s… view at source ↗
Figure 15
Figure 15. Figure 15: Components of spectra for MAD and SANE simulations for a = 0.9375, M = 10M⊙ and M˙ = 10−3M˙ Edd. (a) a = 0.5 (b) a = 0.9375 [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Comparison of MAD and SANE spectra for a = 0.5 and a = 0.9375. Other disk parameters are same as in [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
read the original abstract

The spectra of an accretion disk around black holes are the basic diagnostic tool to enlighten the underlying flows and then black holes. Accretion flows around black holes, however, are controlled by parameters like the magnetic field, spin of the black hole, accretion rate and temperature of the flow. These quantities affect the (magneto)hydrodynamics of the flow thus consequently lead to variations in the spectrum. We first consider numerical steady state magnetohydrodynamic (MHD) solutions of magnetized accretion flows around black holes to study the dependence of the spectra on these disk properties. The spectrum exhibits strong dependence on the spin of the black hole, accretion rate, magnetic field and the electron temperature of the flow. Variations in these quantities influence the emission peaks and overall luminosity, which can be a tell-tale sign to extract physics of observed spectra. We further validate our results with general relativistic MHD (GRMHD) simulations using the standard and normal evolution (SANE) and magnetically arrested disk (MAD) vector potentials. We consider two black hole spins ($a=0.5$ and $a=0.9375$) to model the magnetic field configurations and study the resulting spectra by comparing MAD and SANE results. We find a large difference in the bolometric luminosities and the location of the emission peaks between SANE and MAD flows. Certain properties of the spectra, like, the ratio of synchrotron radiation to synchrotron self-Comptonization peaks in SANE and MAD, show drastically distinct features. The overall luminosity combined with such metrics can distinguish the magnetic field characteristics in astrophysical systems.

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 / 1 minor

Summary. The paper claims that spectra of magnetized advective accretion flows around rotating black holes depend strongly on black hole spin, accretion rate, magnetic field strength, and electron temperature, as shown via numerical steady-state MHD solutions. It further validates this with GRMHD simulations using standard SANE and MAD vector potentials at spins a=0.5 and a=0.9375, reporting large differences in bolometric luminosity, emission peak locations, and the synchrotron-to-SSC peak ratio that together serve as diagnostics to distinguish magnetic field characteristics in astrophysical systems.

Significance. If the reported spectral distinctions between SANE and MAD configurations prove robust, the work would provide a potentially useful observational diagnostic for inferring magnetic field properties from black hole accretion spectra, aiding interpretation of high-energy observations.

major comments (2)
  1. [GRMHD simulations] GRMHD simulations section: The claim that bolometric luminosity combined with emission peak ratios and synchrotron-to-SSC ratios can distinguish magnetic field characteristics rests on the representativeness of the standard SANE and MAD vector potentials; only two spins (a=0.5 and a=0.9375) are tested with no sensitivity analysis to alternative initial field geometries, intermediate magnetization states, or resolution variations, which is load-bearing for the diagnostic assertion.
  2. [Results] Steady-state MHD solutions and results sections: No quantitative validation such as error bars, convergence tests, or tabulated spectral data is referenced to support the reported dependencies of luminosity and peak locations on the varied parameters, undermining assessment of the strength of the distinctions.
minor comments (1)
  1. The abstract does not specify the numerical methods, codes, or grid resolutions employed for either the steady-state MHD solutions or the GRMHD runs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and indicate the revisions planned for the manuscript.

read point-by-point responses

  1. Referee: [GRMHD simulations] GRMHD simulations section: The claim that bolometric luminosity combined with emission peak ratios and synchrotron-to-SSC ratios can distinguish magnetic field characteristics rests on the representativeness of the standard SANE and MAD vector potentials; only two spins (a=0.5 and a=0.9375) are tested with no sensitivity analysis to alternative initial field geometries, intermediate magnetization states, or resolution variations, which is load-bearing for the diagnostic assertion.

    Authors: The standard SANE and MAD vector potentials are the most widely adopted benchmarks in the GRMHD literature precisely because they bracket the range of magnetic field strengths relevant to observed systems. We selected a=0.5 and a=0.9375 to sample moderate and high-spin regimes. We agree that the diagnostic claim would be strengthened by explicit tests of alternative initial geometries or intermediate magnetization; such an expanded study lies beyond the scope of the present work. In revision we will add a dedicated limitations paragraph stating that the reported distinctions apply to these canonical configurations and that future work should explore additional setups. revision: partial

  2. Referee: [Results] Steady-state MHD solutions and results sections: No quantitative validation such as error bars, convergence tests, or tabulated spectral data is referenced to support the reported dependencies of luminosity and peak locations on the varied parameters, undermining assessment of the strength of the distinctions.

    Authors: We will insert a new table that tabulates bolometric luminosity, synchrotron and SSC peak frequencies, and their ratio for each combination of spin, accretion rate, magnetic field strength, and electron temperature explored in the steady-state MHD solutions. We will also add a short subsection describing the numerical convergence criteria (grid resolution, iteration tolerance, and residual norms) employed by the MHD solver and the typical fractional uncertainties on the derived spectral quantities. For the GRMHD runs we will reference the standard resolution and convergence practices used in the community. revision: yes

Circularity Check

0 steps flagged

No circularity; spectra computed from independent MHD/GRMHD setups

full rationale

The paper solves steady-state MHD equations for magnetized flows, then computes spectra from GRMHD runs initialized with standard SANE and MAD vector potentials at two spins. Spectral features (luminosities, peak locations, synchrotron/SSC ratios) are direct numerical outputs from these distinct input configurations. No parameters are fitted to data and renamed as predictions, no quantities are defined in terms of each other, and no self-citations or uniqueness theorems are invoked to force the result. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides insufficient detail to enumerate free parameters, axioms, or invented entities; standard MHD equations and GRMHD assumptions are presumed but not audited.

pith-pipeline@v0.9.1-grok · 5839 in / 1132 out tokens · 15602 ms · 2026-06-27T08:24:56.182757+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

45 extracted references · 41 canonical work pages · 3 internal anchors

  1. [1]

    1988, ApJ, 332, 646, doi: 10.1086/166683

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

    work page doi:10.1086/166683 1988

  2. [2]

    A., & Fragile, P

    Abramowicz, M. A., & Fragile, P. C. 2013, Living Reviews in Relativity, 16, 1, doi: 10.12942/lrr-2013-1

    work page doi:10.12942/lrr-2013-1 2013

  3. [3]

    A., & Hawley, J

    Balbus, S. A., & Hawley, J. F. 1991, ApJ, 376, 214, doi: 10.1086/170270

    work page doi:10.1086/170270 1991

  4. [4]

    M., Press, W

    Bardeen, J. M., Press, W. H., & Teukolsky, S. A. 1972, ApJ, 178, 347, doi: 10.1086/151796 20

    work page doi:10.1086/151796 1972

  5. [5]

    1997, The Astrophysical Journal Letters, 486, L43

    Bisnovatyi-Kogan, G., & Lovelace, R. 1997, The Astrophysical Journal Letters, 486, L43

    1997

  6. [6]

    S., & Lovelace, R

    Bisnovatyi-Kogan, G. S., & Lovelace, R. V. E. 1997, The Astrophysical Journal, 486, L43, doi: 10.1086/310826

    work page doi:10.1086/310826 1997

  7. [7]

    Chakrabarti, S., & Titarchuk, L. G. 1995, ApJ, 455, 623, doi: 10.1086/176610

    work page doi:10.1086/176610 1995

  8. [8]

    2015, ApJ, 799, 1, doi: 10.1088/0004-637X/799/1/1

    Chan, C.-K., Psaltis, D., Özel, F., Narayan, R., & Sądowski, A. 2015, ApJ, 799, 1, doi: 10.1088/0004-637X/799/1/1

    work page doi:10.1088/0004-637x/799/1/1 2015

  9. [9]

    1967, An Introduction to the Study Of Stellar Structure (Dover, New York)

    Chandrasekhar, S. 1967, An Introduction to the Study Of Stellar Structure (Dover, New York)

    1967

  10. [10]

    2022, ApJ, 941, 30, doi: 10.3847/1538-4357/ac9d97

    Chatterjee, K., & Narayan, R. 2022, ApJ, 941, 30, doi: 10.3847/1538-4357/ac9d97

    work page doi:10.3847/1538-4357/ac9d97 2022

  11. [11]

    , year = 1990, month = aug, volume =

    Coppi, P. S., & Blandford, R. D. 1990, MNRAS, 245, 453, doi: 10.1093/mnras/245.3.453 Fernández-Ontiveros, J. A., & Muñoz-Darias, T. 2021, MNRAS, 504, 5726, doi: 10.1093/mnras/stab1108

    work page doi:10.1093/mnras/245.3.453 1990

  12. [12]

    G., & Moncrief, V

    Fishbone, L. G., & Moncrief, V. 1976, ApJ, 207, 962, doi: 10.1086/154565

    work page doi:10.1086/154565 1976

  13. [13]

    2026, Journal of High Energy Astrophysics, 50, 100469, doi: 10.1016/j.jheap.2025.100469

    Ghosh, S., & Bhattacharyya, S. 2026, Journal of High Energy Astrophysics, 50, 100469, doi: 10.1016/j.jheap.2025.100469

    work page doi:10.1016/j.jheap.2025.100469 2026

  14. [14]

    F., & Balbus, S

    Hawley, J. F., & Balbus, S. A. 1992, ApJ, 400, 595, doi: 10.1086/172021

    work page doi:10.1086/172021 1992

  15. [15]

    The Co-Evolution of Galaxies and Supermassive Black Holes: Insights from Surveys of the Contemporary Universe

    Heckman, T. M., & Best, P. N. 2014, ARA&A, 52, 589, doi: 10.1146/annurev-astro-081913-035722 Körding, E., Falcke, H., & Corbel, S. 2006, A&A, 456, 439, doi: 10.1051/0004-6361:20054144

    work page internal anchor Pith review doi:10.1146/annurev-astro-081913-035722 2014

  16. [16]

    2014, PhRvD, 89, 024041, doi: 10.1103/PhysRevD.89.024041

    Tchekhovskoy, A., & Narayan, R. 2014, PhRvD, 89, 024041, doi: 10.1103/PhysRevD.89.024041

    work page doi:10.1103/physrevd.89.024041 2014

  17. [17]

    F., Taam, R

    Liu, B. F., Taam, R. E., Meyer-Hofmeister, E., & Meyer, F. 2007, The Astrophysical Journal, 671, 695, doi: 10.1086/522619

    work page doi:10.1086/522619 2007

  18. [18]

    Mandal, S., & Chakrabarti, S. K. 2005, A&A, 434, 839, doi: 10.1051/0004-6361:20041235

    work page doi:10.1051/0004-6361:20041235 2005

  19. [19]

    1997, The Astrophysical Journal, 489, 791, doi: 10.1086/304817

    Manmoto, T., Mineshige, S., & Kusunose, M. 1997, The Astrophysical Journal, 489, 791, doi: 10.1086/304817

    work page doi:10.1086/304817 1997

  20. [20]

    , keywords =

    Merloni, A., Heinz, S., & di Matteo, T. 2003, MNRAS, 345, 1057, doi: 10.1046/j.1365-2966.2003.07017.x

    work page doi:10.1046/j.1365-2966.2003.07017.x 2003

  21. [21]

    2020, MNRAS, 495, 350, doi: 10.1093/mnras/staa1161

    Mondal, T., & Mukhopadhyay, B. 2020, MNRAS, 495, 350, doi: 10.1093/mnras/staa1161

    work page doi:10.1093/mnras/staa1161 2020

  22. [22]

    2022, Astronomy & Astrophysics, 662, A28

    Moravec, E., Svoboda, J., Borkar, A., et al. 2022, Astronomy & Astrophysics, 662, A28

    2022

  23. [23]

    2002, ApJ, 581, 427, doi: 10.1086/344227

    Mukhopadhyay, B. 2002, ApJ, 581, 427, doi: 10.1086/344227

    work page doi:10.1086/344227 2002

  24. [24]

    2015, ApJ, 807, 43, doi: 10.1088/0004-637X/807/1/43

    Mukhopadhyay, B., & Chatterjee, K. 2015, ApJ, 807, 43, doi: 10.1088/0004-637X/807/1/43

    work page doi:10.1088/0004-637x/807/1/43 2015

  25. [25]

    2022, Monthly Notices of the Royal Astronomical Society, 511, 3795, doi: 10.1093/mnras/stac285 ¨Opik, E

    Curd, B. 2022, MNRAS, 511, 3795, doi: 10.1093/mnras/stac285

    work page doi:10.1093/mnras/stac285 2022

  26. [26]

    Advection-dominated Accretion: Underfed Black Holes and Neutron Stars.Astrophys

    Narayan, R., & Yi, I. 1995, ApJ, 452, 710, doi: 10.1086/176343

    work page doi:10.1086/176343 1995

  27. [27]

    1995, Nature, 374, 623, doi: 10.1038/374623a0

    Narayan, R., Yi, I., & Mahadevan, R. 1995, Nature, 374, 623, doi: 10.1038/374623a0

    work page doi:10.1038/374623a0 1995

  28. [28]

    2025, ApJ, 981, 162, doi: 10.3847/1538-4357/adb286

    Pathak, M., & Mukhopadhyay, B. 2025, ApJ, 981, 162, doi: 10.3847/1538-4357/adb286

    work page doi:10.3847/1538-4357/adb286 2025

  29. [29]

    Magnetic Fields of Compact Objects in Close X-Ray Binary Systems

    Piotrovich, M. Y., Gnedin, Y. N., Buliga, S. D., et al. 2015, in Astronomical Society of the Pacific Conference Series, Vol. 494, Physics and Evolution of Magnetic and Related Stars, ed. Y. Y. Balega, I. I. Romanyuk, & D. O. Kudryavtsev, 114, doi: 10.48550/arXiv.1409.2283

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1409.2283 2015

  30. [30]

    2017, Computational Astrophysics and Cosmology, 4, 1, doi: 10.1186/s40668-017-0020-2

    Porth, O., Olivares, H., Mizuno, Y., et al. 2017, Computational Astrophysics and Cosmology, 4, 1, doi: 10.1186/s40668-017-0020-2

    work page doi:10.1186/s40668-017-0020-2 2017

  31. [31]

    1999, ApJ, 520, 248, doi: 10.1086/307423

    Quataert, E., & Gruzinov, A. 1999, ApJ, 520, 248, doi: 10.1086/307423

    work page doi:10.1086/307423 1999

  32. [32]

    , archivePrefix = "arXiv", eprint =

    Rajesh, S. R., & Mukhopadhyay, B. 2010, MNRAS, 402, 961, doi: 10.1111/j.1365-2966.2009.15925.x

    work page doi:10.1111/j.1365-2966.2009.15925.x 2010

  33. [33]

    M., Tchekhovskoy, A., Quataert, E., & Gammie, C

    Ressler, S. M., Tchekhovskoy, A., Quataert, E., & Gammie, C. F. 2017, MNRAS, 467, 3604, doi: 10.1093/mnras/stx364

    work page doi:10.1093/mnras/stx364 2017

  34. [34]

    C., & Dexter, J

    Scepi, N., Begelman, M. C., & Dexter, J. 2024, MNRAS, 527, 1424, doi: 10.1093/mnras/stad3299

    work page doi:10.1093/mnras/stad3299 2024

  35. [35]

    Scepi, N., Dexter, J., & Begelman, M. C. 2022, MNRAS, 511, 3536, doi: 10.1093/mnras/stac337

    work page doi:10.1093/mnras/stac337 2022

  36. [36]

    I., & Sunyaev, R

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

    1973

  37. [37]

    , keywords =

    Shapiro, S. L., Lightman, A. P., & Eardley, D. M. 1976, ApJ, 204, 187, doi: 10.1086/154162

    work page doi:10.1086/154162 1976

  38. [38]

    W., & Stone, J

    Sharma, P., Quataert, E., Hammett, G. W., & Stone, J. M. 2007, The Astrophysical Journal, 667, 714, doi: 10.1086/520800

    work page doi:10.1086/520800 2007

  39. [39]

    Tchekhovskoy, A., Narayan, R., & McKinney, J. C. 2011, MNRAS, 418, L79, doi: 10.1111/j.1745-3933.2011.01147.x

    work page doi:10.1111/j.1745-3933.2011.01147.x 2011

  40. [40]

    , archivePrefix = "arXiv", eprint =

    Xie, F.-G., & Yuan, F. 2012, MNRAS, 427, 1580, doi: 10.1111/j.1365-2966.2012.22030.x

    work page doi:10.1111/j.1365-2966.2012.22030.x 2012

  41. [41]

    Xie, F.-G., & Zdziarski, A. A. 2019, ApJ, 887, 167, doi: 10.3847/1538-4357/ab5848

    work page doi:10.3847/1538-4357/ab5848 2019

  42. [42]

    2014, ARA&A, 52, 529, doi: 10.1146/annurev-astro-082812-141003

    Yuan, F., & Narayan, R. 2014, ARA&A, 52, 529, doi: 10.1146/annurev-astro-082812-141003

    work page internal anchor Pith review doi:10.1146/annurev-astro-082812-141003 2014

  43. [43]

    2003, ApJ, 598, 301, doi: 10.1086/378716

    Yuan, F., Quataert, E., & Narayan, R. 2003, ApJ, 598, 301, doi: 10.1086/378716

    work page doi:10.1086/378716 2003

  44. [44]

    A., Pjanka, P., Sikora, M., & Stawarz, Ł

    Zdziarski, A. A., Pjanka, P., Sikora, M., & Stawarz, Ł. 2014, MNRAS, 442, 3243, doi: 10.1093/mnras/stu1009

    work page doi:10.1093/mnras/stu1009 2014

  45. [45]

    F., Brandt, W

    Zhu, S. F., Brandt, W. N., Luo, B., et al. 2020, Mon. Not. Roy. Astron. Soc., 496, 245, doi: 10.1093/mnras/staa1411

    work page doi:10.1093/mnras/staa1411 2020