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Low Angular Momentum Black Hole Accretion: First GRMHD Evidence of Standing Shocks

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that low-angular-momentum, weakly magnetized accretion onto a rotating black hole produces two quasi-steady standing shocks, the first time standing shocks have been reproduced in full GRMHD simulations.

desk verdict Plausible first GRMHD standing shocks, but the headline claim rides on 2.5D runs taken after MRI decayed, and the 3D validation skips the exact parameters used for the strongest shocks. read the letter →

arxiv 2507.22506 v1 pith:REWW5IP7 submitted 2025-07-30 astro-ph.HE

Jirong Mao , Indu K. Dihingia , Yosuke Mizuno , Shigehiro Nagataki This is my paper · ORCID
classification astro-ph.HE
keywords accretionblackholesGRMHDsimulationsstandingshockslowangularmomentumSANEregimequasi-periodicoscillations
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 aims to show that standing shocks, abrupt jumps in pressure and velocity where infalling gas slows from supersonic to subsonic, are genuine features of magnetized, turbulent black hole accretion, not artifacts of idealized hydrodynamic or semi-analytic treatments. Using 2.5D axisymmetric GRMHD simulations of low-angular-momentum flows in the weakly magnetized SANE regime, the authors report two quasi-steady shocks at roughly 4 to 5 gravitational radii and 40 to 50 gravitational radii when the inflow is strongly concentrated toward the equatorial plane, with the outer shock moving outward as the black hole spin increases. A 3D run at a lower inclination parameter shows an oscillating shock at about 37 gravitational radii, lending support to the 2.5D picture. If correct, this connects several decades of shock theory to state-of-the-art GRMHD simulations and offers a concrete physical mechanism for observed variability such as quasi-periodic oscillations and flares.

What carries the argument

The central control parameter is the inclination parameter $\alpha$, which concentrates the Fishbone-Moncrief torus density toward the equatorial plane via rho proportional to exp[-($\alpha$ cos $\theta$)^2], combined with a reduced angular momentum fraction F = 0.4 and a weak poloidal magnetic field. These choices establish a pressure balance between centrifugal force (amplified by frame dragging near a spinning black hole) and the ram pressure of the infalling gas; when $\alpha$ is large this balance supports two standing shocks, at roughly 4-5 rg and 40-50 rg, with increasing spin pushing the outer shock outward.

What would settle it

Run a high-resolution 3D GRMHD simulation of the alpha = 50, a* = 0.94 case for at least 15,000 tg and check the equatorial radial profiles of pressure and radial velocity: if the two sharp jumps at about 4-5 rg and 40-50 rg do not form or do not persist over several thousand tg, the claim of standing shocks in GRMHD SANE low-angular-momentum flows would be contradicted.

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Extended reading notes

Core claim

The authors report the first GRMHD evidence of standing shocks in low-angular-momentum accretion flows. In the weakly magnetized SANE regime, when the initial torus is confined near the equatorial plane (inclination parameter alpha = 50), two standing shocks form at r approximately 4-5 rg and r approximately 40-50 rg, and the outer shock shifts outward for higher black hole spin because frame dragging strengthens centrifugal support. The shock locations remain quasi-steady between 14,000 and 15,000 tg, and a 3D validation run at alpha = 10 shows a quasi-steady, gently oscillating shock at about 37 rg. This demonstrates that such structures are not limited to idealized hydrodynamics but arise naturally in turbulent, weakly magnetized GRMHD flows around a rotating black hole.

Load-bearing premise

The main results come from 2.5D axisymmetric simulations that the authors acknowledge cannot sustain MRI growth of magnetic fields after about 10,000 gravitational times, and the single 3D validation was run at the lower inclination parameter alpha = 10 rather than the alpha = 50 cases where the two-shock structure is strongest; if full 3D turbulence at high alpha destroys or prevents the shocks, the central claim fails.

Editorial extensions

If this is right

  • Standing shocks are not artifacts of 1.5D idealized flows: they can persist in turbulent magnetized GRMHD simulations, so shock-based analytic models gain a firmer footing.
  • The outer shock location depends on black hole spin through frame dragging, so measuring shock positions in observations could offer a spin diagnostic.
  • The hot, dense post-shock region acts as a post-shock corona that can up-scatter soft photons, linking these simulations to the hard X-ray tails of black hole X-ray binaries.
  • Quasi-steady radial oscillation of the shock front (seen in the 3D run) provides a plausible source of low-frequency quasi-periodic oscillations and flares such as those observed in Sgr A* and X-ray binaries.
  • If confirmed in full 3D at high alpha, the shock structures give a concrete target for general relativistic radiative transfer calculations that would predict direct observational signatures.

Reading between the lines

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

  • The 2.5D runs may underestimate how full 3D turbulence disrupts the shocks; a 3D run at alpha = 50 and high spin would be the decisive test of whether the strong two-shock structure survives.
  • The finding suggests that earlier GRMHD studies that saw no standing shocks may have used initial conditions that were too close to Keplerian or insufficiently concentrated toward the equatorial plane, with alpha as the key control.
  • If standing shocks require the weakly magnetized SANE regime, shock presence could serve as an observational discriminant between SANE and magnetically arrested (MAD) accretion states.
  • The connection between shock radius and spin implies that correlated timing and spectral observations of quasi-periodic oscillations might be used to infer both the accretion geometry and the black hole spin in a single source.
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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 / 4 minor

Summary. The paper presents 2.5D axisymmetric and one 3D GRMHD simulations, performed with BHAC, of low-angular-momentum accretion onto Kerr black holes. A sub-Keplerian parameter F=0.4 and an inclination parameter α (5, 10, 30, 50) are used, with black hole spins a*=0.8, 0.9, and 0.94. The central claim is that quasi-steady standing shocks form in the weakly magnetized SANE regime—specifically a two-shock structure around r≈4–5 rg and r≈40–50 rg for α=50—and that this is the first GRMHD demonstration of such standing shocks. The outer shock location is reported to move outward with increasing spin, and a 3D run at α=10 is presented as validation, showing an oscillating shock at r≈37±5 rg.

Significance. If the claim is correct, the paper would be a significant advance: it would show that standing shocks, previously obtained in idealized 1.5D/2D hydrodynamic and semi-analytic models, can survive in a genuinely multi-dimensional, magnetized GRMHD flow, with direct consequences for interpreting Sgr A* flares and QPOs in X-ray binaries. The paper has notable strengths: it uses the public BHAC code rather than a purpose-built solver, no free parameters are fitted to the claimed shock location, the SANE regime is checked via normalized magnetic flux, and the parameter study spans several spins and inclination parameters. The 3D validation, although limited, is an honest attempt to go beyond axisymmetry. However, the advertised strength of the claim currently exceeds what the presented diagnostics establish.

major comments (3)
  1. [Section 3 and Section 4] Section 3 states that after t≳10,000 tg the MRI cannot continuously grow the magnetic fields due to the 2D nature of the simulations, yet the shock analysis in Section 4 is time-averaged over t=12,000–15,000 tg and Figure 7 uses t=14,000–15,000 tg. This means the shocks are identified inside a window where the flow is explicitly described as having decaying MRI, so the repeated characterization of the flow as 'turbulent, weakly magnetized' in Section 4.1 is not supported for the analyzed epoch. Please provide turbulence diagnostics (e.g., Maxwell stress, magnetic energy evolution, α-viscosity parameter) over the averaging window, or identify the shocks in an earlier epoch where MRI is active, or explicitly restrict the claim to a quasi-steady but non-turbulent regime.
  2. [Section 5] The 3D validation is performed for α=10 at resolution 256×80×64, while the headline two-shock result is obtained in 2.5D for α=50 (and partially α=30) at an effective resolution of 1024×512. The α=10 3D run therefore does not validate the α=50 case, and the statement 'we expect to see a similar shock structure for higher values' is an extrapolation. To support the central claim, either run a 3D simulation with α=50 (even at reduced resolution), or provide a concrete physical argument, backed by diagnostics, for why the α=10 3D result transfers to α=50.
  3. [Section 4.1, Figure 6 and Figure 7] The identification of features as shocks rests entirely on visual discontinuities in the radial velocity and pressure along the equatorial plane at a single time (Figure 6) and in ten slices over 14,000–15,000 tg (Figure 7). No Rankine-Hugoniot jump conditions, Mach-number or magnetosonic-Mach-number checks, compression-ratio tests, or comparison with the sonic-point location are provided. Without such verification, the discontinuities could be, for example, centrifugal pressure-balance layers or numerical artifacts. Please add a quantitative shock test, at minimum an upstream Mach number greater than unity and consistency with the expected density/temperature jumps, and ideally a resolution study showing the jump sharpens or converges with resolution.
minor comments (4)
  1. [Throughout] The paper interchangeably uses '2D', '2.5D', and 'axisymmetric (2.5D)'; please define the terminology once and use it consistently, since 2.5D usually implies axisymmetry with phi derivatives retained, whereas 2D can be ambiguous.
  2. [Section 5 and Figure 9] The text says the 3D snapshots are at ts=8000, 9000, and 10,000, while the following paragraph describes t=10,000–12,000 tg and Figure 9 mentions t=10000 and 12000; the time ranges are inconsistent and should be reconciled.
  3. [Section 3 and Figure 3] The text uses a*=0.94, while Figure 3's caption and panels label a*=0.9375; please use one value throughout or explain the difference.
  4. [Section 4.1] There is a typo and spacing issue in 'aroundr = 40−50 rg' and the phrase 'by (Nakayama 1994)' should read 'by Nakayama (1994)'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the standing-shock claim is a numerical output, not a refitted input.

full rationale

The paper's central claim is that standing shocks form in low-angular-momentum GRMHD accretion flows, identified from density, radial-velocity, and pressure profiles produced by the BHAC code (Porth et al. 2017; Olivares et al. 2019). No parameter is fitted to the shock location, and no equation defining the shock is constructed from the claimed result. The inclination parameter alpha and angular-momentum fraction F are chosen to select a regime motivated by earlier semi-analytic and hydrodynamic shock studies, but the shock itself emerges from the time integration of the GRMHD equations, so this is a genuine numerical test rather than a definitional identity. Self-citations to Dihingia and Mizuno (2024, 2025) are used for setup choices and for stating that the alpha = 0 case lacks shocks; these citations support the choice of initial conditions and provide context, but they do not by themselves force the alpha = 50 two-shock structure or the spin-dependent shock locations reported here. The most serious concern raised by the manuscript is internal validity, not circularity: Section 3 states that MRI cannot continuously grow magnetic fields after t greater than about 10,000 t_g due to the 2D nature of the simulations, while the time averaging in Section 4 covers 12,000-15,000 t_g, and the 3D validation is performed only for alpha = 10 at lower resolution. These are correctness and robustness issues about whether the flow is genuinely turbulent in the analyzed window and whether the alpha = 50 result survives in 3D; they do not amount to the derivation reducing to its inputs. Accordingly, no circular step can be exhibited, and the paper should not receive a circularity penalty.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on several modeling choices: a modified sub-Keplerian Fishbone-Moncreif torus, an ad hoc equatorial focusing parameter alpha, and axisymmetric 2.5D evolution with one 3D check. No new physical entities are introduced. The shock finding is conditional on these choices, particularly alpha=50 in 2.5D.

free parameters (3)
  • sub-Keplerian fraction F = 0.40
    Fixed fraction of the Fishbone-Moncreif angular velocity, setting angular momentum below the marginally stable value. Central to producing low angular momentum flow and shock formation; inherited from Dihingia and Mizuno (2024), not scanned.
  • inclination parameter alpha = 5, 10, 30, 50 in 2.5D; 10 in 3D
    Introduced ad hoc via density factor exp[-(alpha cos theta)^2] to focus inflow near the equator. Standing shocks only appear for alpha=50 in 2.5D and alpha=10 in 3D, so the discovery is conditional on this tuning.
  • initial torus inner edge and density maximum = rin=5 rg, rmax=18.5 rg
    Chosen to provide enough mass for a quasi-steady low angular momentum flow within the computational time; not independently motivated by shock physics.
assumptions (4)
  • domain assumption Ideal single-fluid GRMHD with adiabatic index Gamma=4/3 describes the accretion plasma.
    Collisionless, radiatively inefficient plasma is modeled as an ideal gas; no radiation or kinetic effects are included (Section 2).
  • domain assumption Axisymmetric (2.5D) evolution is representative of 3D shock behavior for the main alpha=50 cases.
    Main standing shock claims come from 2.5D runs; authors note MRI stalls in 2D after ~10,000 tg but still use 2.5D results as primary evidence (Sections 3 and 5).
  • domain assumption The modified sub-Keplerian Fishbone-Moncreif torus is a valid initial condition for quasi-steady low angular momentum accretion.
    No relaxation or inflow equilibrium calculation is shown; early-time transients are large (Section 3).
  • domain assumption The flow remains in the SANE regime and magnetic pressure does not disrupt the shocks.
    Authors assert Phi/sqrt(Mdot) ~ 1 below MAD limits and exclude MAD flows by construction (Section 3).

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Pith. "Pith review of Low Angular Momentum Black Hole Accretion: First GRMHD Evidence of Standing Shocks." pith.science (2026). https://pith.science/paper/REWW5IP7

@misc{pith2026250722506,
  author       = {Pith},
  title        = {Pith review of: Low Angular Momentum Black Hole Accretion: First GRMHD Evidence of Standing Shocks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/REWW5IP7}},
  note         = {Machine review of arXiv:2507.22506}
}
abstract

Understanding the dynamics of low angular momentum accretion flow around black holes (BHs) is essential for probing extreme plasma behavior in strong gravity, where shock formation can naturally produce variability signatures. In this paper, we perform general relativistic magnetohydrodynamic (GRMHD) simulations of low angular momentum accretion flows onto a BH with different BH spins to investigate the accretion dynamics near the central BH region. The simulation results show the standard and normal evolution (SANE) regime in all cases. In particular, we report the formation and persistence of standing shocks in low-angular-momentum accretion flows using multi (two and three)-dimensional GRMHD simulations for the first time. Previous studies did not detect such stable standing shock structures, making our findings a significant advancement in this field. The finding of shock dynamics can be further associated with some radiation features, such as flares observed in Sgr~A$^\ast$ and quasi-periodic oscillation (QPO) signals detected in some XRBs and AGNs.

Figures

Figures reproduced from arXiv: 2507.22506 by the authors.

Figure 1
Figure 1. Time evolution of (a) accretion rate (M˙ ) and (b) normalized magnetic flux (Φ/ p M˙ ) at BH horizon. Left panels show variation for different α in the case of a∗ = 0.94, whereas the right panels show variations for different values of a∗ in the case of α = 50. the centrifugal support in the inner regions becomes stronger, which can help sustain more matter closer to the BH for a longer time by delaying the rapid in… view at source ↗
Figure 2
Figure 2. Distribution of logarithmic density (upper) and mass accretion rate (lower) for different inclination parameter α = 5 (panel a), 10 (panel b), 30 (panel c), and 50 (panel d), respectively. We keep the BH spin to be a∗ = 0.94. The black contour indicates the boundary where the accretion rate is equal to zero [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Same as [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Same as [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 7
Figure 7. Figure 7: The standing shock identified in the case of α=50 and a∗ = 0.9. The evolution time has the range of 14, 000 − 15, 000 tg with the time interval of 1,000 tg (The lines are from bottom to top with the time increasing in each panel). Upper panel: radial velocity v r as a …
Figure 6
Figure 6. Figure 6: The radial velocity v r and the pressure P as a function of r at the time of t = 15, 000 tg for the standing shock identification. Upper panel: the case of a∗ = 0.9375; Lower panel: the case of α = 50. From the distribution of the density in low angular momentum simula…
Figure 8
Figure 8. Figure 8: Left: Density (ρ) and Right: Temperature (p/ρ) distribution on the poloidal plane ϕ = 0 for 3D GRMHD simulations at different simulation times marked on each panel. The inset displays the distributions on the equatorial plane [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 9
Figure 9. Figure 9: Radial logarithmic density profile (log10 ρ) on the equatorial plane around the shock location for different simulation time. to perform proper general-relativistic radiative transfer (GRRT) calculations to show this radiative signature explicitly. 6. CONCLUSIONS AND D…

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Works this paper leans on

88 extracted references · 15 canonical work pages

  1. [1]

    A., & Zurek, W

    Abramowicz, M. A., & Zurek, W. H. 1981, ApJ, 246, 314, doi: 10.1086/158924

    doi:10.1086/158924 1981

  2. [2]

    2015, MNRAS, 453, 3414, doi: 10.1093/mnras/stv1874

    Aktar, R., Das, S., & Nandi, A. 2015, MNRAS, 453, 3414, doi: 10.1093/mnras/stv1874

    work page doi:10.1093/mnras/stv1874 2015

  3. [3]

    2017, MNRAS, 471, 4806, doi: 10.1093/mnras/stx1893

    Aktar, R., Das, S., Nandi, A., & Sreehari, H. 2017, MNRAS, 471, 4806, doi: 10.1093/mnras/stx1893

    doi:10.1093/mnras/stx1893 2017

  4. [4]

    2025, ApJ, 980, 251, doi: 10.3847/1538-4357/ada7f9

    Alabarta, K., M´ endez, M., Garc ´ ıa, F., et al. 2025, ApJ, 980, 251, doi: 10.3847/1538-4357/ada7f9

    doi:10.3847/1538-4357/ada7f9 2025

  5. [5]

    A., & Hawley, J

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

    doi:10.1086/170270 1991

  6. [6]

    Belloni, T. M. 2010, in Lecture Notes in Physics, Berlin Springer Verlag, ed. T. Belloni, Vol. 794, 53, doi: 10.1007/978-3-540-76937-8 3

    doi:10.1007/978-3-540-76937-8 2010

  7. [7]

    M., & Motta, S

    Belloni, T. M., & Motta, S. E. 2016, Transient Black Hole Binaries, ed. C. Bambi, Vol. 440, 61, doi: 10.1007/978-3-662-52859-4 2

    doi:10.1007/978-3-662-52859-4 2016

  8. [8]

    1952, MNRAS, 112, 195, doi: 10.1093/mnras/112.2.195

    Bondi, H. 1952, MNRAS, 112, 195, doi: 10.1093/mnras/112.2.195

    doi:10.1093/mnras/112.2.195 1952

Show all 88 references
  1. [9]

    Chakrabarti, S. K. 1989a, ApJ, 347, 365, doi: 10.1086/168125 —. 1989b, PASJ, 41, 1145 —. 1989c, MNRAS, 240, 7, doi: 10.1093/mnras/240.1.7 —. 1996a, MNRAS, 283, 325, doi: 10.1093/mnras/283.1.325 —. 1996b, ApJ, 471, 237, doi: 10.1086/177965

    doi

  2. [10]

    K., Acharyya, K., & Molteni, D

    Chakrabarti, S. K., Acharyya, K., & Molteni, D. 2004, A&A, 421, 1, doi: 10.1051/0004-6361:20034523

    2004 doi

  3. [11]

    2016, MNRAS, 459, 3792, doi: 10.1093/mnras/stw876

    Chattopadhyay, I., & Kumar, R. 2016, MNRAS, 459, 3792, doi: 10.1093/mnras/stw876

    2016 doi

  4. [12]

    Chen, X., & Taam, R. E. 1993, ApJ, 412, 254, doi: 10.1086/172916

    1993 doi

  5. [13]

    2007, MNRAS, 376, 1659, doi: 10.1111/j.1365-2966.2007.11501.x

    Das, S. 2007, MNRAS, 376, 1659, doi: 10.1111/j.1365-2966.2007.11501.x

    2007

  6. [15]

    Das, S., Chattopadhyay, I., & Chakrabarti, S. K. 2001a, ApJ, 557, 983, doi: 10.1086/321692

    doi

  7. [16]

    Das, S., Chattopadhyay, I., Nandi, A., & Chakrabarti, S. K. 2001b, A&A, 379, 683, doi: 10.1051/0004-6361:20011307

    doi

  8. [17]

    2014, Mon

    Das, S., Chattopadhyay, I., Nandi, A., & Molteni, D. 2014, Mon. Not. Roy. Astron. Soc., 442, 251, doi: 10.1093/mnras/stu864

    2014 doi

  9. [18]

    K., & Czerny, B

    Das, T. K., & Czerny, B. 2012, NewA, 17, 254, doi: 10.1016/j.newast.2011.08.002

    2012 doi

  10. [19]

    Debnath, S., Chattopadhyay, I., & Joshi, R. K. 2024, MNRAS, 528, 3964, doi: 10.1093/mnras/stae181

    2024 doi

  11. [20]

    K., Das, S., Maity, D., & Chakrabarti, S

    Dihingia, I. K., Das, S., Maity, D., & Chakrabarti, S. 2018a, PhRvD, 98, 083004, doi: 10.1103/PhysRevD.98.083004

    doi

  12. [21]

    K., Das, S., & Mandal, S

    Dihingia, I. K., Das, S., & Mandal, S. 2018b, MNRAS, 475, 2164, doi: 10.1093/mnras/stx3269

    doi

  13. [22]

    K., Das, S., & Nandi, A

    Dihingia, I. K., Das, S., & Nandi, A. 2019, Mon. Not. Roy. Astron. Soc., 484, 3209, doi: 10.1093/mnras/stz168

    2019 doi

  14. [23]

    K., Das, S., Prabhakar, G., & Mandal, S

    Dihingia, I. K., Das, S., Prabhakar, G., & Mandal, S. 2020a, MNRAS, 496, 3043, doi: 10.1093/mnras/staa1687

    doi

  15. [24]

    K., & Fendt, C

    Dihingia, I. K., & Fendt, C. 2024, arXiv e-prints, arXiv:2404.06140, doi: 10.48550/arXiv.2404.06140

    2024 doi arXiv

  16. [25]

    K., Maity, D., Chakrabarti, S., & Das, S

    Dihingia, I. K., Maity, D., Chakrabarti, S., & Das, S. 2020b, PhRvD, 102, 023012, doi: 10.1103/PhysRevD.102.023012

    doi

  17. [26]

    K., & Mizuno, Y

    Dihingia, I. K., & Mizuno, Y. 2024, ApJ, 967, 4, doi: 10.3847/1538-4357/ad391a —. 2025, ApJL, 982, L21, doi: 10.3847/2041-8213/adbc6d

    2024 doi

  18. [27]

    K., Vaidya, B., & Fendt, C

    Dihingia, I. K., Vaidya, B., & Fendt, C. 2021, MNRAS, 505, 3596, doi: 10.1093/mnras/stab1512

    2021 doi

  19. [28]

    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

    2007 doi

  20. [29]

    P., Belloni, T

    Fender, R. P., Belloni, T. M., & Gallo, E. 2004, MNRAS, 355, 1105, doi: 10.1111/j.1365-2966.2004.08384.x

    2004

  21. [30]

    G., & Moncrief, V

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

    1976 doi

  22. [31]

    2002, ACCRETION DISCS IN ACTIVE GALACTIC NUCLEI (Cambridge University Press), 244266

    Frank, J., King, A., & Raine, D. 2002, ACCRETION DISCS IN ACTIVE GALACTIC NUCLEI (Cambridge University Press), 244266

    2002

  23. [32]

    1987, PASJ, 39, 309 Standing Shock in Low-Angular-Momentum Accretion 11

    Fukue, J. 1987, PASJ, 39, 309 Standing Shock in Low-Angular-Momentum Accretion 11

    1987

  24. [33]

    F., & Popham, R

    Gammie, C. F., & Popham, R. 1998, ApJ, 498, 313, doi: 10.1086/305521

    1998 doi

  25. [34]

    K., Samanta, M

    Giri, K., Chakrabarti, S. K., Samanta, M. M., & Ryu, D. 2010, MNRAS, 403, 516, doi: 10.1111/j.1365-2966.2009.16147.x

    2010

  26. [35]

    2003, A&A, 409, 1, doi: 10.1051/0004-6361:20031080

    Gu, W.-M., & Foglizzo, T. 2003, A&A, 409, 1, doi: 10.1051/0004-6361:20031080

    2003 doi

  27. [36]

    W., Vasil, G

    Hester, E. W., Vasil, G. M., & Wechselberger, M. 2022, MNRAS, 512, 5771, doi: 10.1093/mnras/stac731

    2022 doi

  28. [37]

    Huang, J.-X., & Singh, C. B. 2025, Research in Astronomy and Astrophysics, 25, 025013, doi: 10.1088/1674-4527/ada2e8

    2025 doi

  29. [38]

    2023, MNRAS, 525, 4515, doi: 10.1093/mnras/stad2481

    Husain, N., Garg, A., Misra, R., & Sen, S. 2023, MNRAS, 525, 4515, doi: 10.1093/mnras/stad2481

    2023 doi

  30. [39]

    R., & Motta, S

    Ingram, A. R., & Motta, S. E. 2019, NewAR, 85, 101524, doi: 10.1016/j.newar.2020.101524

    2019

  31. [40]

    2015, ApJ, 807, 108, doi: 10.1088/0004-637X/807/1/108

    Iyer, N., Nandi, A., & Mandal, S. 2015, ApJ, 807, 108, doi: 10.1088/0004-637X/807/1/108

    2015 doi

  32. [41]

    2024, JCAP, 2024, 075, doi: 10.1088/1475-7516/2024/07/075

    Jana, C., & Das, S. 2024, JCAP, 2024, 075, doi: 10.1088/1475-7516/2024/07/075

    2024 doi

  33. [42]

    2009, ApJ, 705, 1503, doi: 10.1088/0004-637X/705/2/1503

    Janiuk, A., Sznajder, M., Mo´ scibrodzka, M., & Proga, D. 2009, ApJ, 705, 1503, doi: 10.1088/0004-637X/705/2/1503

    2009 doi

  34. [43]

    Kaaz, N., Murguia-Berthier, A., Chatterjee, K., Liska, M. T. P., & Tchekhovskoy, A. 2023, ApJ, 950, 31, doi: 10.3847/1538-4357/acc7a1

    2023 doi

  35. [44]

    K., Balsara, D

    Kim, J., Garain, S. K., Balsara, D. S., & Chakrabarti, S. K. 2017, MNRAS, 472, 542, doi: 10.1093/mnras/stx1986

    2017 doi

  36. [45]

    K., Chakrabarti, S

    Kim, J., Garain, S. K., Chakrabarti, S. K., & Balsara, D. S. 2019, MNRAS, 482, 3636, doi: 10.1093/mnras/sty2953

    2019 doi

  37. [46]

    M., Dai, L., & Tchekhovskoy, A

    Kwan, T. M., Dai, L., & Tchekhovskoy, A. 2023, ApJL, 946, L42, doi: 10.3847/2041-8213/acc334

    2023 doi

  38. [47]

    Lanzafame, G., Molteni, D., & Chakrabarti, S. K. 1998, MNRAS, 299, 799, doi: 10.1046/j.1365-8711.1998.01816.x

    1998

  39. [48]

    S., Wolff, M

    Le, T., Wood, K. S., Wolff, M. T., Becker, P. A., & Putney, J. 2016, ApJ, 819, 112, doi: 10.3847/0004-637X/819/2/112

    2016 doi

  40. [49]

    Liang, E. P. T., & Thompson, K. A. 1980, ApJ, 240, 271, doi: 10.1086/158231

    1980 doi

  41. [50]

    F., Yu, K

    Lu, J. F., Yu, K. N., Yuan, F., & Young, E. C. M. 1997, A&A, 321, 665

    1997

  42. [52]

    2024, ApJ, 971, 28, doi: 10.3847/1538-4357/ad55cb

    Mitra, S., & Das, S. 2024, ApJ, 971, 28, doi: 10.3847/1538-4357/ad55cb

    2024 doi

  43. [53]

    M., Mosallanezhad, A., Abbassi, S., & Das, S

    Mitra, S., Ghoreyshi, S. M., Mosallanezhad, A., Abbassi, S., & Das, S. 2023, MNRAS, 523, 4431, doi: 10.1093/mnras/stad1682

    2023 doi

  44. [54]

    Molteni, D., Lanzafame, G., & Chakrabarti, S. K. 1994, ApJ, 425, 161, doi: 10.1086/173972

    1994 doi

  45. [55]

    Molteni, D., Ryu, D., & Chakrabarti, S. K. 1996a, ApJ, 470, 460, doi: 10.1086/177877

    doi

  46. [56]

    Molteni, D., Sponholz, H., & Chakrabarti, S. K. 1996b, ApJ, 457, 805, doi: 10.1086/176775

    doi

  47. [57]

    2020, MNRAS, 497, 2119, doi: 10.1093/mnras/staa2035

    Mondal, S., & Basu, P. 2020, MNRAS, 497, 2119, doi: 10.1093/mnras/staa2035

    2020 doi

  48. [58]

    2008, ApJ, 689, 391, doi: 10.1086/590325 —

    Nagakura, H., & Yamada, S. 2008, ApJ, 689, 391, doi: 10.1086/590325 —. 2009, ApJ, 696, 2026, doi: 10.1088/0004-637X/696/2/2026

    2008 doi

  49. [59]

    1992, MNRAS, 259, 259, doi: 10.1093/mnras/259.2.259 —

    Nakayama, K. 1992, MNRAS, 259, 259, doi: 10.1093/mnras/259.2.259 —. 1993, PASJ, 45, 167 —. 1994, MNRAS, 270, 871, doi: 10.1093/mnras/270.4.871

    1992 doi

  50. [60]

    Nandi, A., Debnath, D., Mandal, S., & Chakrabarti, S. K. 2012, A&A, 542, A56, doi: 10.1051/0004-6361/201117844

    2012 doi

  51. [61]

    V., & Abramowicz, M

    Narayan, R., Igumenshchev, I. V., & Abramowicz, M. A. 2003, PASJ, 55, L69, doi: 10.1093/pasj/55.6.L69

    2003 doi

  52. [63]

    2014, MNRAS, 441, 2354, doi: 10.1093/mnras/stu738

    Okuda, T. 2014, MNRAS, 441, 2354, doi: 10.1093/mnras/stu738

    2014 doi

  53. [64]

    2015, MNRAS, 453, 147, doi: 10.1093/mnras/stv1626

    Okuda, T., & Das, S. 2015, MNRAS, 453, 147, doi: 10.1093/mnras/stv1626

    2015 doi

  54. [66]

    B., & Aktar, R

    Okuda, T., Singh, C. B., & Aktar, R. 2022, MNRAS, 514, 5074, doi: 10.1093/mnras/stac1630

    2022 doi

  55. [67]

    B., Das, S., et al

    Okuda, T., Singh, C. B., Das, S., et al. 2019, PASJ, 71, 49, doi: 10.1093/pasj/psz021

    2019 doi

  56. [68]

    2019, A&A, 629, A61, doi: 10.1051/0004-6361/201935559

    Olivares, H., Porth, O., Davelaar, J., et al. 2019, A&A, 629, A61, doi: 10.1051/0004-6361/201935559

    2019 doi

  57. [69]

    R., Mo´ scibrodzka, M

    Olivares, H. R., Mo´ scibrodzka, M. A., & Porth, O. 2023, A&A, 678, A141, doi: 10.1051/0004-6361/202346010

    2023 doi

  58. [70]

    2019, MNRAS, 487, 755, doi: 10.1093/mnras/stz1296

    Palit, I., Janiuk, A., & Sukova, P. 2019, MNRAS, 487, 755, doi: 10.1093/mnras/stz1296

    2019 doi

  59. [71]

    R., & Das, S

    Patra, S., Majhi, B. R., & Das, S. 2022, Physics of the Dark Universe, 37, 101120, doi: 10.1016/j.dark.2022.101120 —. 2024, Journal of High Energy Astrophysics, 44, 371, doi: 10.1016/j.jheap.2024.10.012

    2022

  60. [72]

    Popham, R., & Gammie, C. F. 1998, ApJ, 504, 419, doi: 10.1086/306054

    1998 doi

  61. [73]

    Porth, O., Mizuno, Y., Younsi, Z., & Fromm, C. M. 2021, MNRAS, 502, 2023, doi: 10.1093/mnras/stab163

    2021 doi

  62. [74]

    2017, Computational Astrophysics and Cosmology, 4, 1, doi: 10.1186/s40668-017-0020-2 12 Mao et al

    Porth, O., Olivares, H., Mizuno, Y., et al. 2017, Computational Astrophysics and Cosmology, 4, 1, doi: 10.1186/s40668-017-0020-2 12 Mao et al

    2017 doi

  63. [75]

    Proga, D., & Begelman, M. C. 2003, ApJ, 592, 767, doi: 10.1086/375773

    2003 doi

  64. [76]

    A., & McClintock, J

    Remillard, R. A., & McClintock, J. E. 2006, ARA&A, 44, 49, doi: 10.1146/annurev.astro.44.051905.092532

    2006 arXiv

  65. [77]

    M., Quataert, E., & Stone, J

    Ressler, S. M., Quataert, E., & Stone, J. M. 2018, MNRAS, 478, 3544, doi: 10.1093/mnras/sty1146

    2018 doi

  66. [78]

    L., Ostriker, J

    Ryu, D., Brown, G. L., Ostriker, J. P., & Loeb, A. 1995, ApJ, 452, 364, doi: 10.1086/176308

    1995 doi

  67. [79]

    2018, MNRAS, 473, 2415, doi: 10.1093/mnras/stx2505

    Sarkar, B., Das, S., & Mandal, S. 2018, MNRAS, 473, 2415, doi: 10.1093/mnras/stx2505

    2018 doi

  68. [80]

    K., & Misra, R

    Sarkar, B., Dihingia, I. K., & Misra, R. 2025, NewA, 118, 102377, doi: 10.1016/j.newast.2025.102377

    2025

  69. [81]

    2023, MNRAS, 522, 3735, doi: 10.1093/mnras/stad1064

    Sarkar, S., Singh, K., Chattopadhyay, I., & Laurent, P. 2023, MNRAS, 522, 3735, doi: 10.1093/mnras/stad1064

    2023 doi

  70. [82]

    2022, JCAP, 2022, 048, doi: 10.1088/1475-7516/2022/08/048

    Sen, G., Maity, D., & Das, S. 2022, JCAP, 2022, 048, doi: 10.1088/1475-7516/2022/08/048

    2022 doi

  71. [83]

    I., & Sunyaev, R

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

    1973

  72. [84]

    B., & Chakrabarti, S

    Singh, C. B., & Chakrabarti, S. K. 2012, MNRAS, 421, 1666, doi: 10.1111/j.1365-2966.2012.20426.x

    2012

  73. [85]

    B., Okuda, T., & Aktar, R

    Singh, C. B., Okuda, T., & Aktar, R. 2021, arXiv e-prints, arXiv:2101.05474. https://arxiv.org/abs/2101.05474

    2021 arXiv

  74. [86]

    2024, Ap&SS, 369, 1, doi: 10.1007/s10509-023-04263-6 Sukov´ a, P., Charzy´ nski, S., & Janiuk, A

    Singh, M., & Das, S. 2024, Ap&SS, 369, 1, doi: 10.1007/s10509-023-04263-6 Sukov´ a, P., Charzy´ nski, S., & Janiuk, A. 2017a, MNRAS, 472, 4327, doi: 10.1093/mnras/stx2254 —. 2017b, MNRAS, 472, 4327, doi: 10.1093/mnras/stx2254

    2024 doi

  75. [87]

    2006, ApJ, 645, 1408, doi: 10.1086/500107

    Tsuruta, S. 2006, ApJ, 645, 1408, doi: 10.1086/500107

    2006 doi

  76. [88]

    2002, ApJ, 572, 950, doi: 10.1086/340380

    Takahashi, M., Rilett, D., Fukumura, K., & Tsuruta, S. 2002, ApJ, 572, 950, doi: 10.1086/340380

    2002 doi

  77. [89]

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

    2011

  78. [90]

    2024a, Physics of the Dark Universe, 44, 101429, doi: 10.1016/j.dark.2024.101429

    Uniyal, A., Chakrabarti, S., & Das, S. 2024a, Physics of the Dark Universe, 44, 101429, doi: 10.1016/j.dark.2024.101429

    2024

  79. [91]

    K., & Mizuno, Y

    Uniyal, A., Dihingia, I. K., & Mizuno, Y. 2024b, ApJ, 970, 172, doi: 10.3847/1538-4357/ad5b5b

    doi

  80. [92]

    2025, arXiv e-prints, arXiv:2503.04011, doi: 10.48550/arXiv.2503.04011

    Wang, W., Chen, J., Tian, P., et al. 2025, arXiv e-prints, arXiv:2503.04011, doi: 10.48550/arXiv.2503.04011

    2025 doi arXiv

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