{"id":"c06e6331-4324-41d6-8fb6-aca8d48a83cd","arxiv_id":"2505.15048","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":10,"one_line_summary":"Numerical shearing-box simulations provide a broken power-law formula for the suppression of mass feeding onto stars in AGN disks, with a plateau at 88% of the Bondi rate at low thermal mass.","lead":"3D simulations of a star embedded in a black hole accretion disk show that the disk's rotation slows the gas feeding rate below the standard Bondi estimate. The slowdown is fit to a simple broken power law depending on the star's thermal mass, and the same scaling appears in planet formation theory.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Sink-particle accretion prescription is the least secure link: no resolution or extraction-radius study is presented, so the fitted normalization and slopes in Eqs. 11-12 may carry a numerical offset.","rationale":"The reader's weakest assumption identifies the same load-bearing concern: the absolute calibration of the extracted feeding rate rests on an unvalidated sink-particle prescription. The paper's strongest external check, qualitative agreement with Choksi et al. planet-formation scaling, does not constrain the absolute normalization of f(q_th), which is precisely what Eqs. 11-12 supply for AMS applications. The unexplained 0.88 plateau is a physical warning sign, and the absence of a resolution study means the fitted constants could be numerical rather than physical. This is not a rejection of the paper: the simulations are transparent, the fitting procedure is stated, and the comparison to prior work is useful. But the central formula cannot be fully accepted until the sink prescription is shown to be converged with resolution and extraction radius. Since the reader already reached CONDITIONAL and this concern supports that verdict, no adjustment is needed.","tokens_in":16628,"tokens_out":15630,"duration_ms":140307,"concrete_test":"For the h=0.035 sequence at the two extreme mu/mu_crit values (0.04 and 0.9), rerun with maximum refinement level 8 instead of 7 (halving Delta_x_min) and, in a second run, keep level 7 but set r_acc = 8*Delta_x_min. Measure the steady Mdot_sink/Mdot_B at r_acc and also as the flux through spheres of radius 2*r_acc and 4*r_acc. If the ratio changes by more than about 10% between resolutions, or differs between extraction radii, the sink prescription is not converged and Eqs. 11-12 need recalibration before the conditional can be lifted.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central product is the fitted suppression factor f(q_th) in Eqs. 11-12. Every data point entering that fit is the steady value of Mdot_sink = 4*pi*r_acc^2*rho_a*v_r,a measured at r_acc = 4*Delta_x_min ~ 4.9e-3*r_B (Section 2). No resolution study is given; the statement that a second sink-rate estimator 'eventually converges' compares two estimators at the same extraction radius and does not test convergence of the flux with r_acc or grid scale. The low-q_th plateau at 0.88 instead of 1.0 is a red flag: as q_th -> 0, the dimensionless rotation parameter Omega*r_B/c_s = q_th vanishes, so the flow should approach spherical Bondi accretion and f should approach unity. A systematic 12% deficit is the signature one would expect if mass removal or the finite extraction sphere perturbs the flow. If the plateau and power-law slopes are numerical artifacts, the claimed formula, and the subsequent analytic estimates that use it, are not calibrated.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":16776,"tokens_out":12785,"duration_ms":105904,"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":[{"comment":"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.","section":"§2, §3; Eqs. (11)–(12)"},{"comment":"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.","section":"§3, Eq. (11), Fig. 2"},{"comment":"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.","section":"§3, Fig. 2"},{"comment":"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.","section":"§3, Fig. 2"}],"minor_comments":[{"comment":"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'.","section":"§1.1, Eq. (1)"},{"comment":"The phrase 'dominated the the central mass potential' should be 'dominated by the central mass potential'.","section":"§1.1, Eq. (5)"},{"comment":"The phrase 'The equation11 remains valuable' should be 'Equation (11) remains valuable'.","section":"§5, first bullet"},{"comment":"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.","section":"§3, Fig. 2 caption"},{"comment":"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.","section":"§2"},{"comment":"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.","section":"§4.1, Eq. (21)"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely publishable after a numerical convergence study and a reconciliation of the power-law statements. I would not recommend rejection because the central idea is sound and the simulations are transparent; the requested tests are within the scope of a revision. One editorial concern is that the comparison with Krumholz et al. (2005) through the q_th/12 rescaling is presented as a direct comparison, but the rescaling is external and should be labeled as illustrative."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The new thing here is the broken power-law suppression factor f(q_th) in Eqs. 11-12, with a 0.88 plateau and exponents -0.5 and -1.5. That is not in Krumholz et al. 2005 or Dittmann et al. 2021, and the connection to planet-formation scalings (q_th^2 then q_th) is a nice bridge. The simulations are competently run with a public code, and the authors are transparent that the formula is a least-squares fit, not a derivation. The qualitative conclusion that shearing suppresses feeding more than the uniform-vorticity Krumholz formula is plausible and consistent with the higher density concentration they see.\n\nThe soft spot is the sink-particle accretion prescription, as the stress-test note says. Every fitted point is a measurement of Mdot_sink = 4π r_acc^2 ρ v_r at r_acc = 4 Δx_min. There is no resolution or extraction-radius study, and the low-q_th plateau at 0.88 instead of 1.0 is exactly the sign you would expect from a finite sink sphere perturbing the flow. The statement that a second estimator converges compares two prescriptions at the same radius; it does not test convergence with resolution. So the absolute normalization of Eqs. 11-12 could shift. That matters because the subsequent analytic estimates in Section 4 use f(q_th)=0.1 as a typical value, so an offset of tens of percent propagates into the critical radius estimate. The parameter space is also thin: three h values, one Q, one Omega. The claim that the formula holds across all h and sound speeds goes beyond the data.\n\nI am not convinced the plateau at 0.88 is fatal. The Bondi limit is recovered only in the limit of zero rotation; at finite q_th some deficit is physical, and 12% may just be the residual effect of the shearing box at the smallest q_th they ran. But without a convergence study, the fitted slopes and normalization remain hostage to the sink model. The authors should release the run table and data, add error bars, and run at least one resolution doubling before the coefficients are used as calibration.\n\nWho is this for? People modeling AMS growth, embedded BH accretion in AGN disks, and EMRI/GW source populations. They will use Eq. 11 as a practical prescription. The paper deserves a serious referee; the core product is useful and the execution is honest, but the calibration needs hardening. I would send it to review with a request for convergence tests and softened universality claims.","headline":"A useful new fitting formula for accretion suppression in AGN disks, but the sink-particle calibration needs convergence tests before the coefficients are trusted.","tokens_in":17450,"tokens_out":1647,"would_cite":true,"duration_ms":14460,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["accretion-modified stars","AGN disks","mass feeding rate","Bondi accretion","shear flow","thermal mass","sink particles","planet accretion"],"falsifier":"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.","tokens_in":16318,"feed_emoji":"🌟","tokens_out":5669,"duration_ms":46980,"temperature":0.7,"pith_summary":"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.","feed_headline":"AGN disk shear slashes stellar feeding rates","feed_subtitle":"New 3D simulations give a two-power-law suppression factor that depends only on the Bondi-radius-to-disk-thickness ratio.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Defines the spherical Bondi accretion rate dot M_B used as the normalization for all feeding-rate ratios in this paper.","marker":"Bondi 1952"},{"why":"Provides the uniform-flow suppression formula f(q_th) = min{1, 2(pi q_th)^{-1} sinh^{-1}[(2 q_th)^{1/3}]} that the paper's fitted broken power law is compared against and found to deviate from.","marker":"Krumholz et al. 2005"},{"why":"Supplies the planet-accretion scalings (dot M ∝ q_th^2 h^3 for q_th < 0.3 and dot M ∝ q_th h^3 for larger q_th) that the measured AMS accretion rates are checked against.","marker":"Choksi et al. 2023"},{"why":"Gives the estimate that the mean specific angular momentum inside the Bondi radius is <l> ~ r_B^2 Omega / 12, which motivates adjusting q_th to q_th/12 in the suppression formula.","marker":"Dittmann et al. 2021"},{"why":"Describes the sink-particle accretion algorithm and the accretion-radius prescription used to measure the mass feeding rate in the simulations.","marker":"Krumholz et al. 2004"},{"why":"Documents the adaptive-mesh-refinement cosmological hydrodynamics code that carries out the shearing-box simulations and the super-Lagrangian refinement used to resolve the Bondi radius.","marker":"Bryan et al. 2014"},{"why":"Introduces the local shearing-box approximation that the simulations use to impose the disk shear and rotation.","marker":"Goldreich & Lynden-Bell 1965"}],"fun_headline_variants":["AGN disk shear curbs star feeding by two power laws","Star feeding in AGN disks obeys broken power law","Angular momentum barrier stifles AGN star feeding","Shear limits mass supply to stars in AGN disks","Feeding rates in AGN disks get a two-power-law fix"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["AGN disk shear curbs star feeding by two power laws","Star feeding in AGN disks obeys broken power law","Angular momentum barrier stifles AGN star feeding","Shear limits mass supply to stars in AGN disks","Feeding rates in AGN disks get a two-power-law fix"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000274,"raw_usage":{"total_tokens":1644,"prompt_tokens":951,"completion_tokens":693,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":567,"completion_tokens_details":{"reasoning_tokens":610}},"tokens_in":567,"tokens_out":693,"duration_ms":7116,"temperature":1.0,"reasoning_tokens":610,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T15:25:26.001140+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}