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REVIEW 4 major objections 6 minor 90 references

Numerical modeling the mass feeding rates onto accretion-modified stars embedded within AGN disks

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that disk shearing with angular momentum suppresses the mass feeding rate onto stars embedded in AGN disks, and that the suppression is a broken power law depending only on the thermal-mass parameter q_th.

desk verdict A useful new fitting formula for accretion suppression in AGN disks, but the sink-particle calibration needs convergence tests before the coefficients are trusted. read the letter →

arxiv 2505.15048 v1 pith:SMLQR7WQ submitted 2025-05-21 astro-ph.GA astro-ph.HEastro-ph.SR

Yang Luo , Jian-Min Wang This is my paper · ORCID
classification astro-ph.GAastro-ph.HEastro-ph.SR
keywords accretion-modifiedstarsAGNdisksmassfeedingrateBondiaccretionshearflowthermalsinkparticlesplanet
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 asks how fast a star or compact object embedded in an active galactic nucleus disk can actually pull in gas, given that the disk shears and carries angular momentum. It argues that the naive Bondi rate overestimates the feeding rate: the shear-driven angular momentum acts as a barrier, and the feeding rate is the Bondi rate times a suppression factor that depends only on q_th, the ratio of the star's Bondi radius to the disk thickness. Using 3D shearing-box simulations with a sink particle, the authors measure steady feeding rates and fit a broken power law: f = min{0.88, 0.21 $q_th^{{-0.5}}$} for low masses and f = 0.05 $q_th^{{-1.5}}$ for q_th above about 0.3. This provides a simple formula for the early growth of accretion-modified stars and shows consistency with planet-accretion scalings at low q_th.

What carries the argument

The load-bearing mechanism is a Keplerian-shear flow in a local shearing box, with the accreting star represented by a sink particle and the feeding rate measured from the mass flux through a sphere of radius four times the minimum cell size. The key control parameter is the thermal mass q_th = r_B/H_ams = mu $h^{{-3}}$, and the measured suppression factor compares the steady-state feeding rate to the Bondi rate dot M_B ∝ $M^{2}$ rho / $c_s^{3}$. The argument works because the shearing box supplies the ambient vorticity that the Bondi model ignores, while the sink prescription measures the actual inflow rather than an assumed analytic rate.

What would settle it

A direct test is a resolution study: rerun the same models with the maximum refinement level increased by one, halving the minimum cell size and the accretion radius, and check whether the measured feeding rates and the fitted f(q_th) exponents remain unchanged. A second test is to turn off or greatly reduce the shear (setting the specific angular momentum inside the Bondi radius to zero) and verify that the measured rate approaches the Bondi rate; if the plateau stays significantly below 1, the sink prescription is absorbing angular momentum or the Bondi normalization itself is miscalibrated.

Watch

Extended reading notes

Core claim

The central claim is that the mass feeding rate onto an accretion-modified star embedded in an AGN disk is not the Bondi rate but a suppressed rate dot M = f(q_th) dot M_B, with f(q_th) measured from simulations. The paper reports that the suppression factor is a broken power law in q_th = mu $h^{{-3}}$: f_1 = min{0.88, 0.21 $q_th^{{-0.5 ± 0.08}}$} when q_th is below about 0.3, and f_2 = 0.05 $q_th^{{-1.5 ± 0.12}}$ at larger q_th. The plateau at 0.88 rather than 1 reflects a residual angular-momentum barrier even for small Bondi radii, and the steep second regime corresponds to Bondi radii approaching the disk scale height, where disk geometry and tidal effects limit the supply. The fitted formula holds across disk aspect ratios h = 0.01, 0.035, and 0.07, and the flow morphology transitions from nearly spherical Bondi-like inflow to spiral-arm patterns with a central disk as q_th increases.

Load-bearing premise

The entire fitted suppression formula is calibrated on the sink-particle accretion prescription, which counts the gas flowing inward through a sphere of radius four times the smallest grid cell; the paper does not present a resolution study showing that this measured rate has converged, and the plateau at 0.88 instead of the Bondi limit of 1.0 hints at a possible systematic offset.

Editorial extensions

If this is right

  • For q_th below about 0.3, feeding rates follow the q_th^2 scaling of planet accretion, so the early growth of accretion-modified stars matches well-studied planet-formation results.
  • For larger q_th, the feeding rate drops steeply as q_th^{-1.5}, so massive embedded stars grow more slowly than Bondi predicts, and gap-opening or tidal truncation sets in near q_th ~ 0.3–1.
  • The fitted suppression factor is independent of disk aspect ratio h, so it can be applied across AGN disk radii without rescaling.
  • Radiative and mechanical feedback are subdominant to the accretion flow momentum in the early stage, so the measured feeding rate is a good proxy for the actual accretion rate until gap opening.
  • A critical radius R_ams,crit ~ 4.5 × 10^5 R_g marks where the feeding rate balances the empirical stellar mass-loss rate; inside this radius an AMS can grow without wind termination.

Reading between the lines

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

  • The broken-power-law form, with a plateau at 0.88 and two distinct exponents, hints at an underlying two-zone structure (spherical Bondi inflow inside a centrifugal barrier plus a disk-limited envelope) that might be derived analytically rather than only fitted.
  • The dependence on q_th alone, not on mu and h separately, implies a self-similar family of flows; this suggests the shearing-box results transfer to global AGN disks with a one-parameter growth recipe for population synthesis.
  • A testable extension would be to apply the same sink prescription in planet-accretion simulations with comparable q_th; agreement or disagreement in the fitted exponents would isolate the effects of vertical structure and the AGN disk's vertical gravity.
  • The 0.88 plateau, if real, implies a universal ~12% reduction in feeding even for very small stars, which would slightly lengthen AMS growth timescales and could matter for the competition between in-situ formation and captured nuclear star clusters.
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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 / 6 minor

Summary. Using 3D local shearing-box simulations in Enzo, the authors measure the steady-state gas feeding rate onto a sink particle representing an accretion-modified star embedded in an AGN disk. They vary the disk scale height h (0.01, 0.035, 0.07) and the AMS-to-SMBH mass ratio μ/μ_crit, and express the results as Mdot = f(q_th) Mdot_B, where f(q_th) is a broken power law in the thermal mass parameter q_th (Eqs. 11–12): f1 = min{0.88, 0.21 q_th^{−0.5±0.08}} for q_th ≲ 0.3 and f2 = 0.05 q_th^{−1.5±0.12} for larger q_th. The paper also compares the result with the Krumholz et al. (2005) vorticity-suppression formula and with planet-accretion scalings, and discusses radiative/mechanical feedback and gap-opening timescales for AMS growth.

Significance. If the fitted suppression formula is correct, it provides a simple, h-independent scaling that quantifies how disk shear reduces Bondi feeding onto embedded objects, with direct applications to AMS growth and possible links to planet-formation theory. The fit is not circular: f(q_th) is measured from the simulations rather than derived from the assumed inputs. The paper has clear strengths: it uses a public AMR code (Enzo), states the numerical setup and sink accretion prescription explicitly, presents time series showing steady states, and transparently reports a least-squares broken-power-law fit. The consistency check against the Choksi et al. (2023) planet-accretion slopes is a useful cross-validation. However, the calibration rests entirely on the sink-particle mass-flux measurement, and the paper does not demonstrate convergence with resolution or extraction radius; the low-q_th plateau at 0.88 is unexplained. The quantitative formula should therefore be regarded as provisional until these numerical systematics are addressed.

major comments (4)
  1. [§2, §3; Eqs. (11)–(12)] The sink-particle accretion prescription is load-bearing: every point in Fig. 2 is the steady value of Mdot_sink = 4π r_acc^2 ρ_a v_r,a measured at r_acc = 4 Δx_min ≈ 4.8×10^{-3} r_B, and Eqs. (11)–(12) are fit to those values. No resolution study or extraction-radius study is presented; the statement that a second estimator 'eventually converge[s]' compares two estimators at the same radius and does not test convergence with grid scale or r_acc. Because a systematic offset in the mass flux would shift the normalization and slopes of the fitted formula, I request a convergence test (vary maximum refinement level and r_acc) together with error bars on the steady-state rates. The unexplained plateau at f = 0.88 in Eq. (11) is exactly the sort of offset that such a test should resolve.
  2. [§3, Eq. (11), Fig. 2] The fitted plateau f1 = 0.88 for q_th below about 6×10^{-2} is physically suspicious. As q_th → 0, Ω r_B/c_s → 0, so the specific angular momentum of gas inside the Bondi sphere becomes negligible and the flow should approach spherical Bondi accretion with f → 1. A constant 12% deficit is the signature expected if the finite extraction sphere or the mass removal at the sink perturbs the flow. The authors should either demonstrate numerically that f approaches unity at smaller q_th and/or higher resolution, or provide a concrete physical mechanism for the 0.88 plateau.
  3. [§3, Fig. 2] There is an internal inconsistency between the top and bottom panels. The text states that the measured rates in the top panel follow q_th^2 scaling for q_th < 0.2 and q_th scaling for q_th > 0.2, but Eqs. (11)–(12) give f1 ∝ q_th^{-0.5} and f2 ∝ q_th^{-1.5}. Since Mdot_B ∝ q_th^2 in the same units (as stated immediately before the top panel), the implied measured scalings are Mdot ∝ q_th^{1.5} for q_th ≳ 0.06 and Mdot ∝ q_th^{0.5} for the f2 branch, not q_th^2 and q_th. Please reconcile the two descriptions; as written, the fit and the stated power-law behavior cannot both describe the same data.
  4. [§3, Fig. 2] The parameter coverage is thin relative to the generality claimed. Only three values of h, one Toomre parameter (Q=10), one angular velocity (Ω=10^{-9} s^{-1}), and one shear parameter (q=3/2 in Eq. 8) are used, and the data points in Fig. 2 carry no error bars. The quoted uncertainties in Eqs. (11)–(12) are therefore only least-squares scatter and do not include systematic or resolution errors. The claim that the relation is independent of h and sound speed would be substantially strengthened by at least one variation of Q or Ω and by error estimates on each steady-state measurement.
minor comments (6)
  1. [§1.1, Eq. (1)] The phrase 'where M_clump is expect to the the clump total mass' should read 'where M_clump is expected to be the clump total mass'.
  2. [§1.1, Eq. (5)] The phrase 'dominated the the central mass potential' should be 'dominated by the central mass potential'.
  3. [§5, first bullet] The phrase 'The equation11 remains valuable' should be 'Equation (11) remains valuable'.
  4. [§3, Fig. 2 caption] The caption states that 'the power-law indexes of the dependence are consistent' with Choksi et al. (2023), but no quantitative comparison is given in the text; please report the fitted slopes and state explicitly how they compare with the planet-accretion values.
  5. [§2] The two sink-rate estimators are said to 'eventually converge,' but no plot or quantitative comparison is shown; a supplementary figure or table would make this claim checkable.
  6. [§4.1, Eq. (21)] The assumed values h=0.03, α_B=10, f(q_th)=0.1, Q=10, and M_agn=10^8 M⊙ are introduced only in the final estimate; please state explicitly that these are input assumptions and indicate the sensitivity of R_ams,crit to the choice f(q_th)=0.1.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the suppression factor is an empirical fit to simulation data, not derived from the model inputs.

full rationale

The paper's central product, f(q_th), is obtained by least-squares fitting to Mdot_sink/Mdot_B measured from shearing-box simulations, so it is not equivalent by construction to the assumed physics; the Bondi normalization and the definition of q_th are standard and do not encode the fitted outcome. The comparisons with Krumholz et al. (2005) and Choksi et al. (2023) use external published formulas and scalings for context, and the q_th/12 adjustment attributed to Dittmann et al. (2021) is an interpretive comparison rather than a load-bearing step in the fit. Self-citations to Wang et al. (2021a,b) supply the AMS terminology and the m_bondi ~ 1e9 estimate used in illustrative feedback calculations, but they do not determine the simulated f(q_th), so they are not load-bearing. The absence of a resolution study for the sink-particle prescription is a numerical-convergence or correctness risk, not circularity, because nothing in the fitted formula is imposed analytically by the prescription. No equation in the paper reduces to its own input, and no fitted parameter is renamed as a prediction. Therefore the derivation chain is self-contained relative to the stated numerical experiments.

Assumptions & free parameters 10 free parameters · 6 assumptions · 0 invented entities

The central fitted formula (Eqs. 11-12) is a calibration of a numerical experiment, so its validity rests on the fidelity of the shearing-box simulation and the sink accretion prescription, plus the chosen model parameters (Q=10, Omega=1e-9 s^-1, three values of h). The formula contains five fitted or chosen coefficients and slopes; the break location is guided by prior planet-formation scaling. No new physical entities are introduced; the AMS concept and the <l> scaling come from prior work.

free parameters (10)
  • f1 plateau value = 0.88
    Fitted to simulated steady-state feeding rates at low q_th; unexplained 12% deviation from expected Bondi limit of 1.0.
  • f1 coefficient = 0.21
    Least-squares fit to simulated suppression in the intermediate-q_th branch (Eq. 11).
  • f1 power-law index = -0.5 +/- 0.08
    Fitted slope of the first branch (Eq. 11), quoted with 1-sigma error.
  • f2 coefficient = 0.05
    Fitted normalization of the high-q_th branch (Eq. 12).
  • f2 power-law index = -1.5 +/- 0.12
    Fitted slope of the high-q_th branch (Eq. 12), quoted with 1-sigma error.
  • break location = q_th about 0.3 (mu/mu_crit about 0.5)
    Chosen break point motivated by observed deviation from q_th^2 scaling and by Choksi et al. (2023); not independently fitted.
  • Toomre Q = 10
    Chosen by hand as representative AGN disk condition; not varied, so universality claim untested.
  • angular velocity Omega = 1e-9 s^-1
    Chosen by hand, corresponding to R about 1e4 R_g for a 1e8 M_sun SMBH; not varied.
  • alpha_B in critical-radius estimate = 10
    Assumed Bondi coefficient in Eq. 21, not fitted.
  • typical suppression factor in Eq. 21 = 0.1
    Assumed f(q_th) value for the critical-radius estimate, not fitted.
assumptions (6)
  • domain assumption The local shearing box with Keplerian shear (q=3/2) faithfully represents the gas flow around an AMS embedded in a global AGN disk.
    Invoked in Section 2; global radial gradients in density, temperature, and shear are neglected.
  • domain assumption The gas is isothermal (gamma=1) and the sink particle is static with constant mass.
    Section 2.1; accreted mass is not added to the sink, so the simulation covers only the early growth phase.
  • domain assumption The initial vertical density profile follows an exponential disk in hydrostatic equilibrium with the SMBH gravity, with scale height H_ams = c_s/Omega.
    Eq. 9-10; the disk is assumed to be vertically stratified, and the domain extends only about +/-5 r_B in z.
  • domain assumption The average specific angular momentum inside the Bondi radius scales as <l> about r_B^2 Omega/12 (Dittmann et al. 2021), used to map q_th to q_th/12 when comparing with Krumholz.
    Section 3; this scaling is taken from a prior paper and not derived or tested here.
  • domain assumption The sink particle accretion radius (4 times the minimum cell size) and the flux formula give the converged physical feeding rate.
    Section 2; no resolution convergence study is presented, and the low-q_th plateau of 0.88 versus Bondi 1.0 raises a systematic-offset concern.
  • domain assumption Relative motion between the AMS and disk gas is subsonic, so the Hoyle-Lyttleton-Bondi correction is negligible.
    Section 1.1 after Eq. 4, citing Wang et al. (2021a).

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Pith. "Pith review of Numerical modeling the mass feeding rates onto accretion-modified stars embedded within AGN disks." pith.science (2026). https://pith.science/paper/SMLQR7WQ

@misc{pith2026250515048,
  author       = {Pith},
  title        = {Pith review of: Numerical modeling the mass feeding rates onto accretion-modified stars embedded within AGN disks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SMLQR7WQ}},
  note         = {Machine review of arXiv:2505.15048}
}
abstract

Accretion disks surrounding supermassive black holes can potentially form stars within the self-gravitating region. These stars undergo high accretion rates because of the dense environment of the active galactic nuclei (AGN) accretion disk. The vorticity of the AGN disk may influence the ultimate mass feeding rate toward the star. In our study, we simulate mass feeding rates onto stars at different AGN disk thicknesses through 3D numerical models to explore the relationship between feeding rates and the thermal mass of the star ($q_{\rm th}$), defined as the ratio of the star's Bondi radius to the AGN disk thickness. Our findings indicate that disk shearing with angular momentum can notably decrease the feeding rate, and we provide an approximate formula that links the feeding rate based on the angular momentum of the surrounding gas and the thermal mass $q_{\rm th}$. Lastly, we examine the potential feedback of the rapidly accreting stars on the AGN disk and their subsequent evolution.

Figures

Figures reproduced from arXiv: 2505.15048 by the authors.

Figure 1
Figure 1. The mass feeding rate on the AMS in units of Bondi rate is plotted as a function of time. Different colors are used to distinguish lines for various values of 𝜇/𝜇crit. Results for models with ℎ = 0.035 are shown here. 𝜌0 = Ω2 √ 2𝜋𝜋𝐺𝑄 . (10) We adopt the equation of state as isothermal with a specific heat ratio of 𝛾 = 1.0. In our simulations, we choose 𝑄 = 10 and Ω = 10−9 s −1 , corresponding to the radius 𝑅ams = (𝐺… view at source ↗
Figure 2
Figure 2. Top panel: The accretion rate, measured in units of 𝜌𝑅3Ω, is plotted against the thermal mass 𝑞th. Data points are obtained from various AGN disk thickness ratio ℎ. The power-law indexes of the dependence are consistent with the results obtained in the planetary accretion models (e.g., Choksi et al. 2023). Bottom panel: The dependence of mass feeding rate on the parameter 𝑞th is plotted. A solid line represents a fi… view at source ↗
Figure 3
Figure 3. Slices of gas over-density viewed face-on (top panels) and edge on (middle panels), on scale of the the Bondi radius. Here 𝛿𝜌 is defined as the ratio of the gas density to the initial midplane density 𝜌0. Plots are taken from snapshots at the end of the simulation, with the center located on the sink particle. Results for models with ℎ = 0.035 are shown here. nearly constant at around 0.88. At 𝜇/𝜇crit ∼ 0.6, there i… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: The radial profiles of disk surface density Σ and density 𝜌 for various values of 𝜇, after the disk has reached a steady state. Results for models with ℎ = 0.035 are shown here. To obtain the AMS radius, by assuming a zero-age main sequence star with solar metallicity,…

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.