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arxiv: 2604.14708 · v1 · submitted 2026-04-16 · 🌌 astro-ph.HE

Recognition: unknown

Influence of winds on shocked magnetized viscous accretion flows around rotating black holes

Camelia Jana , Santabrata Das
Authors on Pith no claims yet

Pith reviewed 2026-05-10 10:51 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords accretion disksblack holeswindsstanding shocksviscous flowsmagnetized accretionrotating black holestransonic solutions
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The pith

Winds in black hole accretion flows reduce disk luminosity and eliminate standing shocks above a critical mass-loss strength.

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

The paper models relativistic magnetized viscous accretion onto spinning black holes while letting the accretion rate drop inward as a power law to represent mass lost in winds. Solving the coupled flow equations shows that this mass and angular momentum loss changes the global transonic structure, lowers overall radiative output, and shifts the location, compression, and strength of any standing shocks that form. The authors identify a critical wind parameter p^crit beyond which steady shocks disappear entirely, and they show that higher viscosity or stronger angular-momentum extraction by the wind lowers this critical value. The central object is therefore the coupled interplay between wind-driven mass loss, viscosity, and shock formation in the disk.

Core claim

Incorporating a radially decreasing mass-accretion rate to account for winds yields global transonic solutions in which standing shocks are possible only for wind parameters below a critical value p^crit; above that threshold no steady shocks exist, the disk luminosity drops markedly, and the remaining shock properties (radius, compression ratio, and strength) are strongly modified, with the critical threshold itself decreasing when viscosity or wind angular-momentum extraction increases.

What carries the argument

The power-law radial decline in mass-accretion rate that self-consistently removes mass and angular momentum from the flow while the governing relativistic viscous MHD equations (including toroidal fields and synchrotron cooling) are integrated for global transonic solutions.

If this is right

  • Steady standing shocks exist only for wind strengths below the critical p^crit.
  • Higher viscosity shrinks the range of wind parameters that still permit shocks.
  • Stronger angular-momentum removal by winds further lowers p^crit.
  • Disk luminosity decreases once winds are included at any appreciable level.
  • Shock radius moves outward and compression ratio and strength change as wind strength rises.

Where Pith is reading between the lines

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

  • The same wind prescription could be tested in non-relativistic or weakly magnetized disks to see whether the critical p^crit behavior persists.
  • Observed changes in X-ray luminosity or quasi-periodic oscillation frequencies might be used to constrain the wind parameter p in real sources.
  • If the power-law mass-loss assumption is replaced by a more detailed wind model, the location of p^crit could shift, offering a direct test of the simplified treatment.

Load-bearing premise

Mass loss in winds can be represented by a simple power-law drop in the local accretion rate with radius without needing to solve the wind-launching equations separately.

What would settle it

Detection of a standing shock in an accretion flow whose measured wind mass-loss index exceeds the calculated p^crit for the observed viscosity and black-hole spin would falsify the claimed disappearance of shocks.

Figures

Figures reproduced from arXiv: 2604.14708 by Camelia Jana, Santabrata Das.

Figure 1
Figure 1. Figure 1: Variation of Mach number (M) with radial dis￾tance (x) for different wind parameters (p) for flows passing through the inner critical points (xin). Here, we choose the model parameters as αB = 0.02, ak = 0.0, βin = 100.0, and m˙ in = 0.01. The left panel corresponds to l = 0.8, xin = 5.14, and λin = 3.42, while the right panel represent the case with l = 1.2, xin = 6.30, and λin = 3.46. See text for the de… view at source ↗
Figure 2
Figure 2. Figure 2: Variation of Mach number (M) with radial distance (x) for different wind parameters (p) for flow containing outer critical points (xout). The flow is injected from xedge = 103 with ˙medge = 0.1 and βedge = 104 , while αB = 0.2 and ak = 0.0 are kept fixed. In panel (a), we consider l = 0.8, Eedge = 1.95 × 10−3 , and λedge = 3.60, whereas in panel (b), l = 1.2, Eedge = 1.58 × 10−3 , and λedge = 4.65 are chos… view at source ↗
Figure 3
Figure 3. Figure 3: Radial variation of flow variables for different wind parameters p. Here, we fix l = 0.8, ak = 0.0, and αB = 0.02 and flow is injected from xedge = 1000 with Eedge = 1.95 × 10−3 , λedge = 3.60, ˙medge = 0.1, and βedge = 104 . The solid (blue), dashed (red), and dotted (green) curves correspond to p = 0.0, 0.2, and 0.4, respectively. See text for further details. that mass loss effectively cools down the di… view at source ↗
Figure 5
Figure 5. Figure 5: Variation of the disk luminosity (Ldisk) as a func￾tion of wind parameter (p) for a set of plasma-β param￾eters. Here, the flow is injected from xedge = 103 with Eedge = 1.95 × 10−3 , λedge = 3.60, ˙medge = 0.1 and we set l = 0.8, αB = 0.02 and ak = 0.0. Circles, diamonds, and asterisks connected with solid (blue), dashed (red), and dotted (green) lines correspond to βedge = 102 , 103 , and 104 , respectiv… view at source ↗
Figure 7
Figure 7. Figure 7: Plot of shock-mediated global accretion solution around non-rotating (ak = 0.0; left panels) and rapidly ro￾tating (ak = 0.95; right panels) black holes. Panels (a) and (d) present the variation of the Mach number (M), while panels (b) and (e) display the corresponding density profiles (ρ) as functions of the radial coordinate (x). The colour bars in the upper and lower panels indicate the distribu￾tion of… view at source ↗
Figure 8
Figure 8. Figure 8: Modification of shock-induced accretion solutions in the presence of wind. Here, we fix l = 1.0 and αB = 0.02. In panel (a), a non-rotating (ak = 0.0) black hole is con￾sidered, and the outer boundary is set at xedge = 1000 with input parameters Eedge = 0.00158, λedge = 4.818, βedge = 5 × 104 , and ˙medge = 0.1. The solid (blue), dashed (red), and dotted (green) curves are plotted for wind pa￾rameters p = … view at source ↗
Figure 9
Figure 9. Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Variation of the critical wind parameter p crit as a function of αB for different values of l. Here, βin = 100, m˙ in = 0.01, and ak = 0.95 are adopted. See text for the details. out this analysis for a rotating black hole with spin ak = 0.95, and choose βin = 100 and ˙min = 0.01 at the inner critical point xin. By varying the flow energy (Ein) and angular momentum (λin) at xin, we determine p crit for gi… view at source ↗
read the original abstract

We study global transonic solution for a relativistic, magnetized, viscous advective accretion flow around a rotating black hole, incorporating the effects of mass and angular momentum loss through winds. Our model considers dominant toroidal magnetic fields with synchrotron radiation as the primary cooling mechanism. To self-consistently model mass loss, the mass accretion rate is prescribed to decrease inward as a power-law with disk radius. With this, we solve the governing equations that describe the accretion flows in presence of winds and obtain the flow structure in terms of the inflow parameters (energy $\mathcal{E}$, angular momentum $\lambda$, plasma-$\beta$, accretion rate $\dot{m}$, and viscosity $\alpha_{\rm B}$), the wind parameters ($p$, governing mass loss; and $l$, governing angular momentum transport by winds), and the black hole spin ($a_{\rm k}$). Our analysis reveals that winds substantially modify the accretion flow leading to a significant decrease in disk luminosity. We specifically identify global solutions that admit standing shocks and find that winds profoundly alter shock properties, such as the shock radius ($x_{\rm s}$), compression ratio ($R$), and shock strength ($S$). Furthermore, we determine the critical wind parameter $p^{\rm crit}$ beyond which steady shock solutions cease to exist. We demonstrate that increased viscosity and strong angular momentum extraction by winds lead to reduce $p^{\rm crit}$. These findings evidently highlight a complex interplay between viscosity and winds in governing the dynamics of shock formation in accretion disks.

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

1 major / 1 minor

Summary. The manuscript develops a model for global transonic solutions of relativistic, magnetized, viscous accretion flows around rotating black holes that incorporates mass and angular momentum loss through winds. The mass accretion rate is modeled to decrease inward following a power-law dependence on radius. The authors solve for the flow structure and identify solutions with standing shocks, showing that winds reduce disk luminosity, modify shock radius, compression ratio, and strength, and that there exists a critical wind parameter p^crit above which steady shocks no longer exist. They further show that increased viscosity and angular momentum extraction by winds lower this critical value.

Significance. If the modeling assumptions hold, this work contributes to understanding the role of winds in regulating accretion dynamics and shock formation in black hole systems. The identification of p^crit and its dependence on viscosity provides a potentially useful diagnostic for when shocks can persist in the presence of outflows. The inclusion of toroidal magnetic fields and synchrotron cooling adds to the realism for applications to observed high-energy phenomena.

major comments (1)
  1. [Model setup and governing equations] The central modeling choice is the prescription that the mass accretion rate decreases inward as a power-law with disk radius (Ṁ(r) ∝ r^p) to self-consistently model mass loss through winds. This functional form is imposed rather than derived from vertical wind-launching conditions such as centrifugal barrier, magnetic torque, or thermal driving. Because the reported global transonic solutions, standing shocks, altered x_s/R/S, reduced luminosity, and the existence and value of p^crit all follow from integrating the conservation equations under this constraint, the critical boundary is tied to the specific power-law assumption. A derivation from first principles or a sensitivity study to alternative Ṁ(r) profiles is required to establish whether p^crit is a robust physical feature.
minor comments (1)
  1. [Abstract and parameter list] The abstract lists inflow parameters including plasma-β but does not specify how β is initialized or evolved in the global solutions; clarifying this in the methods would aid reproducibility.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for their constructive comments, which help clarify the scope and limitations of our modeling approach. We address the major comment point by point below.

read point-by-point responses

  1. Referee: The central modeling choice is the prescription that the mass accretion rate decreases inward as a power-law with disk radius (Ṁ(r) ∝ r^p) to self-consistently model mass loss through winds. This functional form is imposed rather than derived from vertical wind-launching conditions such as centrifugal barrier, magnetic torque, or thermal driving. Because the reported global transonic solutions, standing shocks, altered x_s/R/S, reduced luminosity, and the existence and value of p^crit all follow from integrating the conservation equations under this constraint, the critical boundary is tied to the specific power-law assumption. A derivation from first principles or a sensitivity study to alternative Ṁ(r) profiles is required to establish whether p^crit is a robust physical feature.

    Authors: We acknowledge that the power-law form Ṁ(r) ∝ r^p is a phenomenological prescription rather than derived from explicit vertical wind-launching physics. This choice follows standard practice in the literature on wind-affected accretion flows (e.g., as used in studies of mass-loss in advective disks) to enable self-consistent radial integration of the conservation equations while capturing the net effect of outflows. A first-principles derivation would require resolving the vertical structure and launching mechanisms (centrifugal, magnetic, or thermal), which necessitates at least 2D axisymmetric simulations and is beyond the scope of the present 1D radial model. We have, however, extensively varied p across a range of values to map the existence and properties of shocks, including the identification of p^crit and its dependence on viscosity and angular momentum loss. To strengthen the manuscript, we will add a dedicated paragraph in the model section discussing the rationale for the power-law assumption, its common usage in similar works, and the associated limitations, along with a brief note that future multi-dimensional extensions could test alternative profiles. revision: partial

standing simulated objections not resolved
  • A derivation of the Ṁ(r) profile from first-principles vertical wind-launching conditions (centrifugal barrier, magnetic torque, or thermal driving), as this requires multi-dimensional modeling outside the current 1D framework.

Circularity Check

0 steps flagged

No significant circularity; parametric study within explicit modeling ansatz

full rationale

The paper adopts an explicit power-law prescription for the radial decline of mass accretion rate (Ṁ(r) ∝ r^p) as the modeling choice to represent wind-driven mass loss, then integrates the conservation equations for energy, angular momentum, and magnetic flux under that fixed functional form to obtain transonic solutions, standing shocks, and the boundary value p^crit at which shocks cease to exist. This is a standard parameter-space exploration in which p is an input that is varied to map solution existence; p^crit emerges from the numerical integration and boundary conditions rather than being identical to the prescription by construction. No self-definitional loop, fitted-input-as-prediction, or load-bearing self-citation is present in the derivation chain.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

Abstract-only review yields limited visibility into assumptions; the power-law mass-loss prescription is an ad-hoc modeling choice required to close the system.

free parameters (3)
  • p
    Wind parameter controlling the radial power-law index of mass loss; central to locating p^crit.
  • l
    Wind parameter controlling angular momentum extraction; affects p^crit.
  • alpha_B
    Viscosity parameter whose increase is shown to lower p^crit.
axioms (2)
  • domain assumption Dominant toroidal magnetic fields with synchrotron radiation as the primary cooling mechanism.
    Stated as the basis for the energy equation.
  • ad hoc to paper Mass accretion rate decreases inward as a power-law with disk radius.
    Explicitly prescribed to incorporate wind mass loss.

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