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REVIEW 4 major objections 5 minor 2 cited by

Bridging Scales in Black Hole Accretion and Feedback: Relativistic Jet linking the Horizon to the Host Galaxy

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper argues that a rapidly spinning black hole's jet feedback efficiency stays near 30% across a wide range of galactic gas-supply radii, while the accretion rate falls as the inverse square root of the Bondi radius.

desk verdict Strong method paper whose headline claim—constant ~30% jet efficiency across Bondi radii—is plausible but rests on unvalidated time-averaging of an intermittent jet at large R_B. read the letter →

arxiv 2507.17818 v1 pith:DUDQFKNN submitted 2025-07-23 astro-ph.HE astro-ph.GA

Hyerin Cho , Ben S. Prather , Ramesh Narayan , Kung-Yi Su , Priyamvada Natarajan This is my paper
classification astro-ph.HEastro-ph.GA
keywords blackholeaccretionrelativisticjetsGRMHDsimulationsmultizonemethodjetfeedbackefficiencyBondiradiusmagneticallyarresteddisksupermassive
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 extends a scale-bridging simulation method to black holes with spin $a_*=0.9$ and asks what sets how much of the inflowing gas energy a relativistic jet returns to the host galaxy. It claims that once magnetically arrested accretion reaches its final state, the time-averaged jet feedback efficiency is about 30% of the accreted rest-mass energy, and that this value is independent of the Bondi radius $R_B$ over three decades, from $400\,r_g$ to $2\times10^5\,r_g$. The accretion rate onto the hole is suppressed relative to the Bondi rate as $\dot{M}/\dot{M}_B \propto R_B^{-1/2}$. The payoff is a parameter-free subgrid formula for galaxy and cosmological simulations, $\dot{E}_{\rm fb} = 2\times10^{-3}\,[R_B/(2\times10^5\,r_g)]^{-1/2}\,\dot{M}_B c^2$ for $a_*=0.9$. If correct, this means black hole spin, not galactic gas properties, governs feedback efficiency in hot accretion flows.

What carries the argument

The carrying tool is the multizone V-cycle method, in which the simulation domain is divided into spherical annuli, each zone is evolved for a while while the others are frozen, and the active zone sweeps inward and then outward repeatedly so that every scale relaxes on its own characteristic timescale instead of being limited by the tiny horizon timestep. For spinning black holes the paper fixes all zone outer radii to a common outer boundary, uses an internal magnetic boundary treatment that lets field lines slide coherently so Poynting flux survives across zone boundaries, and applies static mesh refinement that coarsens the azimuthal grid near the poles to resolve the jet without crippling timesteps. These modifications let the simulations reach Bondi radii as large as $2\times10^5\,r_g$ while preserving the jet power that a frozen-field boundary would otherwise kill.

What would settle it

Run a one-zone or otherwise independent GRMHD simulation at a Bondi radius large enough to matter, ideally $R_B \approx 2\times10^5\,r_g$, with the same spin and magnetization, and measure the time-averaged feedback efficiency at $r \lesssim R_B$; if it comes out near a few percent rather than about 30%, or if changing the V-cycle zone schedule changes $\eta$ by a large factor, the claim of Bondi-radius independence would fail. A more practical falsifier is a head-to-head multizone versus cyclic-zoom run at $R_B \approx 2\times10^4\,r_g$, where both methods are still feasible and a clear disagreement would indicate a numerical bias in one of the two.

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Extended reading notes

Core claim

For a spinning black hole ($a_*=0.9$) embedded in a strongly magnetized, Bondi-like hot accretion flow, the time-averaged feedback efficiency is $\eta \sim 30\%$, with little to no dependence on the Bondi radius. The paper also shows that prograde and retrograde torus-like initial conditions, which initially produce efficiencies near 100% and 10%, converge to the same intermediate value when evolved long enough, because accumulated magnetic fields strip the gas of coherent rotation and push the flow into alternating corotating and counter-rotating states. The accretion suppression $\dot{M}/\dot{M}_B \propto R_B^{-1/2}$ combines with the $\eta \simeq 30\%$ floor to give a direct feedback prescription. The central claim is that black hole spin sets the feedback efficiency, while the galactic-scale Bondi radius sets the gas supply rate.

Load-bearing premise

The load-bearing premise is that the multizone V-cycle method, which is validated only at a small Bondi radius against conventional one-zone GRMHD, correctly captures the time-averaged jet efficiency at a realistic Bondi radius of about $2\times10^5\,r_g$, where no ground-truth simulation exists and an independent cyclic-zoom method finds a much lower efficiency.

Editorial extensions

If this is right

  • Galaxy and cosmological simulations can replace ad hoc feedback constants with the derived formula $\dot{E}_{\rm fb} = 2\times10^{-3}\,[R_B/(2\times10^5\,r_g)]^{-1/2}\,\dot{M}_B c^2$ for $a_*=0.9$.
  • The predicted feedback power at a realistic Bondi radius is roughly $2\times10^{-3}\,\dot{M}_B c^2$, comparable to the levels adopted in some large-scale simulations and one to two orders of magnitude below others, implying that if the stronger prescriptions are right, real supermassive black holes are likely rapidly spinning.
  • The jet in the largest simulation propagates beyond several Bondi radii, depositing energy on scales relevant to the host galaxy rather than only near the horizon.
  • The simulated density slope is steeper along the jet ($\rho \propto r^{-1.3}$) than in the midplane ($\rho \propto r^{-1.1}$), a signature that X-ray observations of jet and disk regions could test.
  • Because different initial conditions converge to the same final efficiency, future simulations can reach the steady state faster by initializing with strong magnetic fields rather than rotating tori.

Reading between the lines

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

  • If the Bondi-radius independence of feedback efficiency holds, hot-accretion feedback in cosmological simulations can be modeled with a spin-dependent efficiency, but the $R_B^{-1/2}$ accretion suppression still has to be included or gas supply will be overestimated.
  • The disagreement at large $R_B$ with an independent cyclic-zoom method, which reports a decreasing efficiency at realistic Bondi radii, could be settled by a matched comparison run at an intermediate radius where both methods are thought to be reliable; such a run would test whether the frozen-zone boundary in the multizone method biases the time-averaged jet power.
  • The $R_B^{-1/2}$ suppression, if general, predicts that black holes in hotter galactic nuclei, which have smaller Bondi radii, grow more slowly than simple Bondi scaling would suggest.
  • The authors' rough scaling of the feedback coefficient with $a_*^2$ via the Blandford-Znajek relation could be turned into a full $\dot{E}_{\rm fb}(R_B, a_*)$ prescription by running the multizone method at intermediate spins such as $a_*=0.5$ and $0.7$.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This paper extends the multizone GRMHD method of Cho et al. (2023, 2024) to spinning black holes with a*=0.9, where relativistic jets are launched. The method is first validated at a small Bondi radius, R_B~400 r_g, against conventional one-zone GRMHD simulations for three initial conditions (strongly magnetized Bondi-like B, prograde torus-like T+, and retrograde torus-like T-). The validated method is then applied to R_B~400, 2e3, 2e4, and 2e5 r_g. The paper reports that the horizon accretion rate scales as Mdot/Mdot_B ~ R_B^{-1/2}, while the time-averaged feedback efficiency is eta~30%, independent of R_B, leading to a subgrid feedback prescription for cosmological simulations in Equation (10).

Significance. If the central claim holds, this is an important contribution: it provides a first-principles, parameter-free subgrid prescription for jet feedback in galaxy and cosmological simulations, with efficiency set by BH spin rather than by the galactic Bondi radius. The paper has genuine strengths: the small-scale validation against one-zone GRMHD for three initial conditions (Figure 2) is convincing; the bflux-const magnetic boundary condition is physically motivated and demonstrably preserves Poynting flux across internal boundaries (Section 3.4); the resolution study in Appendix D supports the fiducial grid; and the comparison with M84 density slopes (Section 4.2) is a falsifiable observational test. However, the large-R_B extrapolation is the load-bearing premise of the paper, and the supporting evidence at R_B=2e4-2e5 r_g is weaker than the presentation suggests, for the reasons detailed below.

major comments (4)
  1. [§4.1, Table 3] The claim of R_B-independent efficiency rests on exactly four simulations, one per Bondi radius, with time-averaged efficiencies eta(R_B/3)=0.25, 0.29, 0.29, and 0.24. No statistical uncertainties or convergence measures are reported, and the largest-R_B value is the lowest of the four. Because Figure 9 shows that the amplitude of eta fluctuations increases with R_B, the observed scatter is equally consistent with a constant efficiency or with a mild decline at large R_B. Please report the number of V-cycles contributing to the last-20% average for each run and demonstrate that the mean has converged with respect to the number of sampled jet states.
  2. [§2.5, §5.1] The central methodological premise is that the stitched V-cycle time average equals the physical time average of a strongly intermittent jet, but this is not validated at large R_B. Section 5.1 explicitly states that the multizone method is not designed to study time variability, and Figure 9 shows eta(5 r_g) fluctuating by an order of magnitude at R_B=2e5 r_g. Each V-cycle samples zone-0 only briefly while interior zones are frozen, so the stitched profile averages over a small number of jet states rather than a continuous physical time average. A concrete test would be to run zone-0 continuously for a comparable physical time at an intermediate R_B (e.g., 2e4 r_g) and compare the resulting mean efficiency with the V-cycle estimate; this would directly test the load-bearing assumption.
  3. [§5.2] The disagreement with Guo et al. (2025), who find eta~3% at large R_B, is not resolved. The authors attribute the difference to cyclic zoom's de-refinement of magnetic fields, but they do not quantify any bias in the multizone V-cycle schedule for an intermittent jet. Since no one-zone ground truth exists at R_B~2e5 r_g, the two methods currently give competing results, and the paper has not shown that its own averaging procedure is unbiased in this regime. I suggest a targeted cross-method comparison at an intermediate R_B (e.g., 2e4 r_g) that compares not only the mean eta but also its distribution and the dependence on the number of V-cycles.
  4. [§3.1, Table 3] All large-R_B runs use the strongly magnetized, non-rotating B initial condition, whose initial plasma beta~1 is a free parameter of the model. The claimed initial-condition independence of the final state is only demonstrated at R_B=400 r_g (mz+long and mz-long runs in Figure 2). Given that the paper's central message is that galactic properties (encoded in R_B) do not affect eta, the robustness of this result should be checked with at least one alternative initial condition at an intermediate Bondi radius, such as a weakly magnetized torus-like IC evolved long enough to reach the proposed final state.
minor comments (5)
  1. [Figure 5] The caption contains a typo: "prescriptionss" should be "prescriptions".
  2. [§5.2] The text contains "disgreements" and should read "disagreements".
  3. [§6] The summary section contains "accrretion" and should read "accretion".
  4. [Table 2] For one-zone runs, the column n is listed as "-"; consider using a footnote to clarify that these runs have no internal zones, rather than relying on an unlabeled dash.
  5. [§2.5] The description of the time-averaging procedure would be easier to reproduce if the paper stated how many V-cycles fall within the last 20% of the total runtime for each model.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: measured simulation outputs are combined into Eq. 10, and self-citations are corroborated by in-paper validation.

full rationale

The paper's central results are direct measurements from GRMHD simulations, not quantities derived from assumptions that already contain them. The claimed scaling Mdot/Mdot_B ∝ R_B^{-1/2} and efficiency η ∼ 0.3 are read out from the simulations in Section 4 (Figures 7 and 9), with the multizone method validated against one-zone ground-truth runs at R_B ≈ 400 r_g (Section 3, Figure 2). Equation 10 is a restatement of the measured efficiency and accretion suppression, combined through the definitional relation eta_B = eta (Mdot/Mdot_B) in Equation 9; it is a summary of simulated outputs rather than an independent prediction that could reduce to its inputs by construction. The paper's self-citations to Cho et al. (2023, 2024) for the multizone method and to Cho & Narayan (2025) for the idea that different initial conditions converge are tested within the paper itself (e.g., the mz+long and mz-long runs in Section 3.2, and the new code's reproduction of earlier non-spinning results to within a factor of 2 in Section 2.4), so these are not load-bearing unverified self-citations. The acknowledged lack of ground truth at large R_B and the sparse V-cycle time sampling (Section 5.1) are legitimate methodological and robustness concerns, and the disagreement with Guo et al. (2025) is a scientific dispute over the two methods' treatment of magnetic fields, not a circular derivation. No step in the paper exhibits an equation or fitted parameter that is equivalent by construction to the claimed prediction, so the circularity score is 0.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claims depend on the validity of the multizone approximation at large R_B (not directly testable), the representativeness of the strongly magnetized IC (partially tested), and the bflux-const boundary condition. These are numerical/domain assumptions rather than fitted parameters; no free parameters are fitted to target data.

free parameters (3)
  • Initial plasma beta of B IC = ~1
    Strongly magnetized Bondi-like initial condition chosen to accelerate convergence to the claimed final state; the paper argues the final state is independent of this choice via T+/T- long runs.
  • Zone runtime per active zone = 8000 delta t (zone-0: 80000 delta t)
    Numerical hyperparameter replacing the previous characteristic-timescale prescription; validated against one-zone runs at R_B=400 r_g.
  • Zone base spacing b = 8
    Logarithmic spacing of zone inner radii; tested in prior work (Cho et al. 2024) and cited as insensitive.
assumptions (5)
  • standard math Ideal GRMHD equations in Kerr spacetime accurately model the accretion flow and jet launching.
    Used throughout; the paper relies on the standard HARM-like scheme (Gammie et al. 2003) and BZ mechanism.
  • domain assumption The multizone V-cycle approximation, in which only one spherical annulus evolves while the rest are frozen, reproduces the time-averaged steady state of a fully coupled domain.
    Validated against one-zone runs only at R_B ≈ 400 r_g (Section 3); the large-R_B runs have no ground truth, so the method's validity at R_B > 10^5 r_g is an assumption (Section 5.2).
  • domain assumption The strongly magnetized Bondi initial condition (plasma beta ~ 1) is representative of the late-time attractor state reached by all initial conditions.
    Supported by the long multizone runs mz+long and mz-long, but these runs inherit the multizone approximation; Guo et al. (2025) do not see this convergence at large R_B.
  • domain assumption The bflux-const magnetic boundary condition at internal Dirichlet radii preserves physical jet power propagation.
    Demonstrated for R_B ≈ 400 r_g against bflux0 (Section 3.4), but the behavior at large R_B is not directly verifiable against ground truth.
  • domain assumption The external medium is a spherically symmetric, non-rotating Bondi flow without galactic gravitational potential or radiative cooling.
    IC and outer boundary setup (Section 2.3); the paper notes in Section 4.2 that extending beyond R_B will require the galaxy potential.

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Cite this review

Pith. "Pith review of Bridging Scales in Black Hole Accretion and Feedback: Relativistic Jet linking the Horizon to the Host Galaxy." pith.science (2026). https://pith.science/paper/DUDQFKNN

@misc{pith2026250717818,
  author       = {Pith},
  title        = {Pith review of: Bridging Scales in Black Hole Accretion and Feedback: Relativistic Jet linking the Horizon to the Host Galaxy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DUDQFKNN}},
  note         = {Machine review of arXiv:2507.17818}
}
abstract

Simulating black hole (BH) accretion and feedback from the horizon to galactic scales is extremely challenging, as it involves a vast range of scales. Recently, our multizone method has successfully achieved global dynamical steady-states of hot accretion flows in three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulations by tracking the bidirectional interaction between a non-spinning BH and its host galaxy. In this paper, we present technical improvements to the method and apply it to spin $a_*=0.9$ BHs, which power relativistic jets. We first test the new multizone set-up with a smaller Bondi radius, $R_B\approx400\,r_g$, where $r_g$ is the gravitational radius. The strongly magnetized accretion launches a relativistic jet with an intermediate feedback efficiency $\eta\sim30\,\%$, in between that of a prograde ($\eta\sim100\,\%$) and retrograde ($\eta\sim 10\,\%$) torus. Interestingly, both prograde and retrograde simulations also eventually converge to the same intermediate efficiency when evolved long enough, as accumulated magnetic fields remove gas rotation. We then extend strongly magnetized simulations to larger Bondi radii, $R_B\approx 2\times10^3,~2\times 10^4,~2\times 10^5\,r_g$. We find that the BH accretion rate $\dot{M}$ is suppressed with respect to the Bondi rate $\dot{M}_B$ as $\dot{M}/\dot{M}_B\propto R_B^{-1/2}$. However, despite some variability, the time-averaged feedback efficiency is $\eta\sim30\,\%$, independent of $R_B$. This suggests that BH feedback efficiency in hot accretion flows is mainly governed by the BH spin ($a_*$) rather than by the galactic properties ($R_B$). From these first-principles simulations, we provide a feedback subgrid prescription for cosmological simulations: $\dot{E}_{\rm fb}=2\times10^{-3}[R_B/(2\times10^5\,r_g)]^{-1/2}\dot{M}_Bc^2$ for BH spin $a_*=0.9$.

Figures

Figures reproduced from arXiv: 2507.17818 by the authors.

Figure 1
Figure 1. Schematics of the multizone method for spinning BH runs with a Bondi radius RB ≈ 2 × 105 rg. The x-axis shows runtime (not to scale) and the y-axis shows radius. Each black box’s vertical extent marks the range of active radii for that zone. Changing colors in the horizontal direc￾tion within boxes represent time evolution, while fixed colors outside boxes represent the frozen state of the zone while it is inactive.… view at source ↗
Figure 2
Figure 2. Time-averaged radial profiles of the feedback ef￾ficiency η(r) in small-scale simulations (Section 3) with a Bondi radius RB ≈ 400 rg. Runs with different initial con￾ditions are labeled as in [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Correlation plot of the efficiency η against the shell-averaged angular velocity ⟨Ω⟩ measured at r = 5 rg. The data correspond to the strongly magnetized one-zone run with B ICs (model oz), and cover one rotation flip episode in the simulation. The color of the dots traces time t divided by the Bondi time tB. respect to the BH spin), the efficiency is similar to that of a retrograde torus with η ∼ 0.1 − 0.2. On the … view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: The total feedback efficiency η (solid lines) and the electromagnetic feedback efficiency ηEM (dashed lines) for different coordinate systems. The black and blue lines (oz+ and mz+) correspond to the uniform polar grid EKS and the green lines (mz+jks) correspond to the…
Figure 5
Figure 5. Figure 5: Snapshots of the electromagnetic energy flux T r t,EM√ −g at the end of running zone-0 (left) and zone-1 (right) when using the bflux0 (top) and bflux-const (bot￾tom) prescriptionss. bflux-const preserves the electromag￾netic power of the jet across the internal bounda…
Figure 6
Figure 6. Figure 6: Snapshot of the BH spin a∗ = 0.9 simulation with Bondi radius RB ≈ 2 × 105 rg (model 2e5 in [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: Dependence of the time-averaged accretion rate M˙ in units of the Bondi rate M˙ B measured at the BH hori￾zon rH, and the feedback efficiency η measured at RB/3, as a function of the Bondi radius RB for simulations with BH spin a∗ = 0.9 (filled circles). The accretion …
Figure 8
Figure 8. Figure 8: Time-averaged radial profiles of (left) the feedback efficiency η, and (right) the shell-averaged temperature ⟨T⟩, for magnetized Bondi accretion with Bondi radii of RB ≈ 400 rg (yellow), ≈ 2000 rg (red), ≈ 2 × 104 rg (purple), and ≈ 2 × 105 rg (black). The vertical da…
Figure 9
Figure 9. Figure 9: Time evolution of the accretion rate M˙ (rH) in units of the Bondi accretion rate M˙ B, the feedback efficiency η(5 rg), and the dimensionless magnetic flux parameter ϕb(rH), for four magnetized Bondi simulations with Bondi radii of RB ≈ 400 rg (yellow curves), 2000 rg…
Figure 10
Figure 10. Figure 10: Density profiles averaged over three ranges of the polar angle θ for the 2e5 run with Bondi radius RB ≈ 2×105 rg (vertical gray line): north pole (N, red), θ = 0−30◦ ; south pole (S, blue), θ = 150 − 180◦ ; midplane (M, black), θ = 75 − 105◦ . The jet regions (N, S) h…
Figure 11
Figure 11. Figure 11: A 2D schematic of the magnetic boundary conditions (bflux0 and bflux-const) similar to Cho et al. (2024) but for face-centered magnetic fields. In 2D, the face-centered magnetic fields are evolved following the induction equation (Balsara & Spicer 1999) B x,n+1 i+1/2,…
Figure 12
Figure 12. Figure 12: Cell indices of the first physical layer neighboring the ghost cells when the highest level of de-refinement is n = 1. ISMR for the case of only one level of de-refinement n = 1 is described first and is generalized below. The coarse cell is comprised of two fine cell…
Figure 13
Figure 13. Figure 13: Comparison of the EKS and JKS coordinate systems. While the θ−grid is uniform at all radius for EKS, θ−grid collimates near the poles at large radius for JKS. The code coordinates x r , x θ , x φ are spaced evenly in the range x r ∈ [0, log (rout)], x θ ∈ [0, 1], x φ …
Figure 14
Figure 14. Figure 14: Time-averaged profiles of accretion rate M˙ , feedback efficiency η, and shell-averaged angular velocity ⟨Ω⟩ of torus simulations for different resolutions and BH spins. The runs with lower resolutions (dashed lines) show similar radial profiles as the higher resoluti…

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