{"id":"98718051-ba61-43f2-bcc0-29b5a3cdcf94","arxiv_id":"2411.16070","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A small black hole near an intermediate-mass black hole in an AGN disk is usually captured into a merger or ejected, and both paths yield two successive EMRI/IMRI events.","lead":"Using 3D gas simulations and a relativistic three-body code, this paper tracks the fate of a small black hole caught near a heavier intermediate-mass black hole migrating inward inside an AGN accretion disk. It predicts that such pairs produce two successive gravitational wave events for LISA instead of a single one.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The PN-phase two-event prediction rests on an untested assumption that the gas torque on the sBH remains constant as the inner disk drains; a weaker or time-varying force could decouple the sBH before the close encounter and yield only a single IMRI.","rationale":"Both the hydro and PN parts have strengths: the hydro runs include two surface densities and a no-inner-disk lower limit, and they show explicitly that gas and tidal torques together can sustain synchronized migration in a quasi-steady disk; the PN code includes 2.5PN dynamics and a 100-run phase scan. The central claim, however, is a two-stage pipeline, and the seam between the stages is the weakest point. The hydro simulations stop at radii where GW is negligible, and the PN code starts at 30 RS with a hand-calibrated gas force; no sensitivity analysis is given for the force law, and the constant-force assumption is justified by one cited simulation rather than by a test. The viscous depletion argument makes the concern concrete: at 20–30 RS the disk drains on a timescale of years, comparable to the simulated GW inspiral, so 'the surface density does not change a lot' is not self-evident. We agree with the reader's weakest_assumption. A decisive test is easy because the PN code is fast: rescale the gas force and repeat the phase scan. Until such a test is done, the paper should remain conditional.","tokens_in":21794,"tokens_out":11319,"duration_ms":105391,"concrete_test":"Rerun the 100-phase-angle PN suite of Section 5.4 with the gas drag amplitude reduced by an order of magnitude and with the force multiplied by exp(-t/3 yr), approximating the viscous depletion of the inner disk at ~20 RS; if the fraction of runs producing two successive GW events falls below 50%, the central claim is conditional on the constant-gas-force assumption. A complementary control with amplitude increased by 3x would bracket the sensitivity.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that two successive GW events are produced in most cases depends on the sBH remaining in the mHz band (≈5–10 RS) when the IMBH catches up. In Section 5.1, the authors introduce a fictitious gas drag in the PN code calibrated on the hydro runs at ~100 RS and then hold it fixed, citing Cerioli et al. (2016) for the claim that disk squeezing is negligible until ~5 RS. This is the single most load-bearing assumption. The hydro simulations themselves show the inner disk surface density dropping by ~0.5 dex over 200 P0 (Figure 7), and for the adopted disk parameters (h/r=0.02, α=0.02) the viscous depletion timescale at 20–30 RS is only ~5–10 yr, comparable to the ~8 yr duration of the PN inspiral shown in Figures 10–12. If the gas torque on the sBH fades as the inner disk drains, or if the calibrated force is miscalibrated, the sBH will decouple from the IMBH earlier; the IMBH will then catch it at ~20 RS, ejecting it without a prior temporary EMRI, so only a single IMRI is detectable. The paper presents no sensitivity study over the gas-force amplitude or the disk depletion timescale, so the ~96% two-event fraction is not robust. The authors do caution that the force is reduced inside the gap and switched off within 0.01 aIMBH, but these choices are also untested.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies the late evolution of a stellar-mass black hole (sBH) orbiting inside a gap-opening intermediate-mass black hole (IMBH) embedded in an AGN accretion disk. The authors first use 3D SPH simulations (PHANTOM) with two disk setups, InnerDisk and NoInnerDisk, to study the co-evolution of the disk and the migration of the sBH. They find that the gaseous torque, together with the tidal torque of the IMBH, accelerates the sBH migration and, in the NoInnerDisk 078 run, drives synchronized migration with the IMBH. They then use a post-Newtonian three-body code, augmented with a fictitious gas drag calibrated to the hydrodynamical runs, to follow the system from about 30 Schwarzschild radii into the GW-dominated regime. Over 100 phase-realization runs they report roughly 44% light-IMRI binary formation followed by an IMRI, 46% ejection after a temporary EMRI, 7% direct EMRI, and 3% IMRI-then-EMRI, leading to the central claim that two successive LISA-visible GW events are produced in most cases.","tokens_in":1896,"tokens_out":2810,"duration_ms":86173,"significance":"The hydrodynamical torque decomposition in Figures 4-5 is a valuable quantitative contribution: it separates the gaseous and tidal torque contributions and identifies the interfering density wave as an important early driver. The NoInnerDisk setup is a sensible way to bound the effect of inner-disk depletion, and the synchronized-migration state is demonstrated over about 300 orbital periods in the hydro runs. The PN three-body experiments are also useful as a proof of concept for Jacobi-capture outcomes in this astrophysical setting. However, the extrapolation from the hydro results to the two-event prediction relies on an untested constancy of the gas drag and on a scale-free argument for the inward extension to about 10 Schwarzschild radii, so the event-rate and LISA phenomenology claims are not yet robust. The paper is original and likely of interest to the AGN-EMRI community, but the central quantitative claim needs additional support.","major_comments":[{"comment":"The central claim that two successive GW events occur in most cases depends on a constant fictitious gas drag in the PN code, calibrated from hydrodynamical runs at about 100 Schwarzschild radii and held fixed while the system shrinks into the GW-dominated regime. The paper's own hydro results show that the inner disk surface density drops by about 0.5 dex over 200 P0 in the InnerDisk runs (Figure 7), and for the adopted disk parameters (h/r=0.02, alpha=0.02) the viscous depletion timescale at 20-30 Schwarzschild radii is of order 5-10 years, comparable to the roughly 8-year inspiral shown in Figures 10-12. If the gas torque on the sBH fades as the inner disk drains, the sBH can decouple from the IMBH before the close encounter, converting the 'temporary EMRI followed by IMRI' outcomes into single-IMRI ejections. No sensitivity study over the gas-force amplitude or the depletion timescale is presented, so the quoted approximately 96% two-event fraction is not robust. The citation to Cerioli et al. (2016) motivates the assumption but does not replace a test for the specific disk parameters used here.","section":"Section 5.1"},{"comment":"The synchronized migration is directly demonstrated only at the simulation radius r0=100 Schwarzschild radii and over about 200-300 P0, during which the sBH semimajor axis changes by only about 0.1% (Figure 9). The extension of this result until approximately 10 Schwarzschild radii relies on a scale-free argument that all torques and timescales rescale identically, and on the constant-gas-force assumption in the PN code. The scale-free argument requires the disk surface density profile to be in the same steady state over two decades in radius, but Figure 7 shows that the inner disk is not stationary in the simulated cases; moreover, at radii well below 100 Schwarzschild radii the inner disk is expected to be depleted by the very processes the authors identify. The claim 'synchronized until about 10 Schwarzschild radii' should either be supported by an explicit model of the inner disk evolution or be softened to reflect that it is an extrapolation.","section":"Section 4 and Section 5.1"},{"comment":"The generalization to IMBHs less massive than 1000 solar masses is not demonstrated. The hydrodynamical runs are performed only for a 1000 solar mass IMBH, and the discussion in Section 6 argues qualitatively that the torques and the GW-dominated phase are similar for smaller gap-opening IMBHs. However, for a smaller IMBH the GW-dominated transition occurs at smaller radii, where the inner disk is most depleted and where the constant-gas-force assumption from Cerioli et al. (2016) is least secure. Since the event-rate estimates and the LISA phenomenology in Sections 5.4 and 6 depend on this extrapolation, the paper should either present supporting runs or explicitly restrict the conclusions to the simulated mass range.","section":"Section 6"},{"comment":"The statistical outcomes are obtained by varying only the initial phase angle of the sBH, while the initial semimajor axis ratio asBH/aIMBH=0.67 and the gas-force prescription are fixed. Given the chaotic sensitivity demonstrated in Figures 10-12, the outcome probabilities (44% binary formation, 46% ejection after a temporary EMRI, 7% direct EMRI, 3% IMRI-then-EMRI) may depend on these fixed choices. At minimum, the paper should present the probability brackets from the 100 runs and state that the distribution is illustrative of the possible outcomes, not a robust probability prediction, until a sensitivity test over initial separation and gas-force parameters is available.","section":"Section 5.4"}],"minor_comments":[{"comment":"The initial phase angles appear to be swapped between the text and the figure captions. Section 5.2 describes the ejection case with initial phase angle 0.6 pi, while the caption of Figure 10 says 0.0 pi; Section 5.3 describes binary formation with initial phase angle 0.0 pi, while the caption of Figure 12 says 0.6 pi. These should be reconciled.","section":"Section 5.2, 5.3, and Figure captions"},{"comment":"There is a typo in the sentence 'or the parameters of our simulation' (should be 'for the parameters'), and Table 1 is formatted as 'T able 1' in the manuscript.","section":"Section 4"},{"comment":"The phrase 'tempoarary, failed EMRI' should be 'temporary, failed EMRI', and 'systen evolution' should be 'system evolution'.","section":"Section 5.2"},{"comment":"The event rate estimate of 1-10^2 per year is presented without a derivation of the systematic uncertainties from the number of sBHs per disk or the migration-trap efficiency; a brief quantitative breakdown would help readers assess the confidence in this number.","section":"Section 6"}],"recommendation":"major_revision","confidential_remarks":"The hydrodynamical part is solid and the torque decomposition is a genuinely useful contribution. The main issue is that the final two-event prediction rests on an untested constancy of the gas drag and on a scale-free extrapolation that the paper's own disk-depletion results partly undermine. I would support resubmission after a sensitivity study of the gas-force amplitude and depletion timescale, or after restricting the conclusions to the directly simulated regime."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe headline: this is a genuine advance over Paper I. The 3D hydro runs with a gap-opening IMBH show that a nearby sBH's inward migration is accelerated by both gas torques and the IMBH's tidal torque, and—more important—that synchronized migration survives even when the inner disk is initially absent (NoInnerDisk). The torque decomposition separating gas vs. tidal driving, and the identification of the interfering density wave giving way to Type-I–dominated migration, are genuinely new and well presented. The PN three-body simulations are the first to give outcome statistics for the final fate: roughly 44% capture into a light IMRI, 46% ejection after a temporary EMRI, so that in most cases two successive LISA events occur. That is an interesting prediction.\n\nThe soft spot is exactly where the stress-test note points: the fictitious gas drag in the PN code is calibrated to the same hydro results that establish synchronized migration, then held constant throughout the final ~8 yr inspiral from 30 RS inward, based on a single cited simulation (Cerioli et al. 2016) and with no sensitivity study. Given the adopted disk parameters (h/r=0.02, alpha=0.02), the viscous depletion timescale at 20–30 RS is only a few years, comparable to the inspiral time. If the gas torque fades as the inner disk drains, the sBH can decouple before the close encounter, and the ~96% two-event fraction drops. The authors do reduce the force inside the gap and switch it off within 0.01 aIMBH, but the constancy of the force outside the gap is load-bearing and untested. I would have also liked to see runs with different IMBH masses and gas-force amplitudes; as is, the outcome fractions are conditional on a single calibration.\n\nNone of this kills the paper. The hydro evidence for synchronized migration is convincing, and the PN results are honest dynamical outcomes, not built-in conclusions. The event-rate estimate is a rough extrapolation, appropriately hedged. What is missing is a sensitivity analysis around the one assumption that the two-event prediction actually rides on.\n\nFor a reader working on LISA source populations or IMBH formation in AGN disks, this is worth engaging with. I would send it to peer review and ask for that sensitivity study. It deserves a serious referee, not a desk reject.\n\nBest.","headline":"Careful two-stage simulation of sBH-IMBH encounters in AGN disks; the hydro part is solid, but the two-event rate leans on an untested constant-gas-force assumption.","tokens_in":22675,"tokens_out":3881,"would_cite":true,"duration_ms":34276,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A gap-opening intermediate-mass black hole in an AGN accretion disk can drive a stellar-mass black hole inward until the pair either merges as a light IMRI or the small black hole is ejected after a temporary EMRI, producing two…","keywords":["extreme-mass-ratio inspiral","intermediate-mass-ratio inspiral","active galactic nuclei","accretion disk","intermediate-mass black hole","stellar-mass black hole","gravitational waves","synchronized migration"],"falsifier":"A hydrodynamical simulation that lets the inner disk evolve self-consistently while the IMBH's orbit decays by gravitational waves from about 30 Rs to merger would settle the assumption: if the inner disk surface density at the sBH's location drops substantially before the IMBH reaches roughly 10 Rs, synchronized migration breaks too early, and the back-to-back two-event outcome would not occur. A LISA observation of a single IMRI with no accompanying EMRI-like signal in the preceding few years would not falsify the scenario by itself (the event rate allows such cases), but it would bound the fraction of encounters that end in ejection after a temporary EMRI.","tokens_in":21550,"feed_emoji":"🕳️","tokens_out":9563,"duration_ms":76108,"temperature":0.7,"pith_summary":"This paper aims to show that when a stellar-mass black hole (sBH) and an intermediate-mass black hole (IMBH) share an AGN accretion disk, the IMBH—which carves a gap in the disk—can drag the sBH inward in synchronized migration all the way to about 10 Schwarzschild radii from the central supermassive black hole. Using 3D hydrodynamical simulations, the authors show that this migration is driven by a combination of gaseous torques (a strengthened Type-I torque and the IMBH's interfering density wave) and the IMBH's tidal pull, and that it survives even when the inner part of the disk has been largely accreted. In the final gravitational-wave-dominated phase, a relativistic three-body code shows the sBH is either captured by the IMBH to merge as a 'light IMRI' or kicked out after a temporary EMRI-like phase. Either way, two successive gravitational-wave events are produced, which a planned space-based detector could observe as back-to-back signals encoding how black holes grow inside AGN disks.","feed_headline":"IMBH in an AGN disk yields two GW events in a row","feed_subtitle":"LISA could see a stellar-mass black hole captured or kicked out, then the IMRI that follows.","key_machinery":"The argument rests on two simulation tools joined in sequence. First, 3D smoothed-particle-hydrodynamics simulations (the PHANTOM code) evolve the disk together with three sink particles—the SMBH, the IMBH, and the sBH—measuring the separate contributions of gaseous and tidal torques to the sBH's migration, with InnerDisk and NoInnerDisk initial conditions bracketing the inner disk's surface density. Second, a post-Newtonian three-body code follows the GW-dominated phase, with a fictitious gaseous drag force calibrated to the hydro runs and assumed to remain constant until the IMBH reaches about 5 Rs, based on a cited disk-squeezing simulation. The dynamical pivot is the Hills-sphere (Jacobi) capture: when the sBH's separation from the IMBH drops below roughly $q^{{1/3}}$ a_IMBH, the two form a chaotic temporary binary, and whether gravitational radiation dissipates enough energy to bind them determines capture versus ejection.","core_discovery":"The paper's central claim is that a gap-opening IMBH in an AGN disk forces a nearby sBH to migrate inward at the same rate as the IMBH, and this synchronized migration continues until the pair reaches roughly 10 Schwarzschild radii from the central SMBH, where gravitational-wave emission takes over. At that point, the IMBH's faster GW-driven inspiral catches up with the sBH; when the sBH enters the IMBH's Hills sphere, the outcome is set by how much energy gravitational radiation can dissipate during the chaotic three-body interaction. In about 44% of the 100 simulated phase angles, the sBH–IMBH binary hardens and merges within a few orbits, producing a light IMRI, and the merged remnant then inspirals into the SMBH within about a year, yielding two successive IMRIs. In about 46% of cases the binary is unstable, the sBH is ejected after a transient stage, and a temporary EMRI in the LISA band is followed by the IMBH–SMBH IMRI. The authors conclude that in most encounters two successive GW events are produced, and that the probability of forming a bound sBH–IMBH binary is of order 0.1, consistent with Jacobi capture expectations.","pith_inferences":["A coupled disk-plus-GW simulation that allows the inner disk density to evolve during the final inspiral would test the constant-force assumption; if the disk drains faster than the single calibrated force model assumes, the two-event rate predicted here would be an upper limit.","LISA data searches could be designed to look for correlated pairs—an EMRI-like signal followed within a few years by an IMRI with a chirp mass near 10^4 solar masses—because this scenario predicts most encounters produce two sequential signals rather than one.","The chaotic dependence on initial phase angle means individual outcomes are unpredictable, but the roughly 50/50 split between capture and ejection may be a robust statistical feature of dissipative Jacobi capture, worth rechecking for different IMBH masses, gap widths, and disk viscosities."],"forward_implications":["When the sBH is captured, LISA would detect two successive IMRIs: the sBH–IMBH merger (chirp mass ~10^2 Msun) followed within about three years by the IMBH–SMBH merger (chirp mass ~10^4 Msun).","When the sBH is ejected, the sBH first spends roughly a year in the mHz band as a temporary EMRI (orbiting down to ~5 Rs), after which the IMRI of the IMBH into the SMBH follows.","Synchronized migration persists even when the inner disk has been largely accreted, provided some gas leaks across the IMBH's gap; in the simulated setup the synchronous equilibrium sits at about 0.78 times the IMBH's orbital radius.","Across 100 three-body runs with varying initial phase angles, about 44% end in sBH–IMBH binary formation (two IMRIs), roughly 46% end in ejection with a preceding temporary EMRI, and only about 4% yield a single IMRI.","If IMBHs form through hierarchical mergers at migration traps in AGN disks, the rate of successive EMRI/IMRI events would be roughly 1 to 100 per year."],"supporting_citations":[{"why":"Supplies the encounter scenario and the original synchronized-migration model that this paper extends with 3D hydrodynamics and relativistic three-body simulations.","marker":"Peng & Chen 2023 (Paper I)"},{"why":"The PHANTOM SPH code used to evolve the disk and the three black-hole sinks in the hydrodynamic stage.","marker":"Price et al. 2018"},{"why":"The post-Newtonian three-body integrator used to follow the GW-dominated phase and decide capture versus ejection.","marker":"Bonetti et al. 2016, 2021"},{"why":"The disk-squeezing simulation invoked to justify holding the gas force fixed during the final inspiral.","marker":"Cerioli et al. 2016"},{"why":"Provides the Hills-radius criterion that defines the Jacobi-capture stage in which the sBH enters the IMBH's sphere of influence.","marker":"Hills 1988"},{"why":"Type-I migration theory that the hydrodynamic runs are tested against and that underpins the gas-driven migration of the sBH.","marker":"Goldreich & Tremaine 1980; Ward 1997"}],"fun_headline_variants":["Two LISA events from one IMBH-sBH encounter in AGN disk","AGN disk IMBH triggers back-to-back gravitational waves","Simulations: IMBH in AGN yields sequential IMRI and EMRI","sBH capture or eject: IMBH sets up two LISA detections","One IMBH, two inspirals: LISA's double event from AGN disk"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the density of the inner disk, and therefore the gas force on the stellar-mass black hole, stays roughly constant through the final gravitational-wave-driven plunge, so that a single fixed gas-force model is enough to capture the disk's effect on the decisive close encounter.","fun_headline_variants_meta":{"raw":{"variants":["Two LISA events from one IMBH-sBH encounter in AGN disk","AGN disk IMBH triggers back-to-back gravitational waves","Simulations: IMBH in AGN yields sequential IMRI and EMRI","sBH capture or eject: IMBH sets up two LISA detections","One IMBH, two inspirals: LISA's double event from AGN disk"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000243,"raw_usage":{"total_tokens":1598,"prompt_tokens":1087,"completion_tokens":511,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":703,"completion_tokens_details":{"reasoning_tokens":407}},"tokens_in":703,"tokens_out":511,"duration_ms":4878,"temperature":1.0,"reasoning_tokens":407,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T13:35:15.223835+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A hydrodynamical simulation that lets the inner disk evolve self-consistently while the IMBH's orbit decays by gravitational waves from about 30 Rs to merger would settle the assumption: if the inner disk surface density at the sBH's location drops substantially before the IMBH reaches roughly 10 Rs, synchronized migration breaks too early, and the back-to-back two-event outcome would not occur. A LISA observation of a single IMRI with no accompanying EMRI-like signal in the preceding few years would not falsify the scenario by itself (the event rate allows such cases), but it would bound the fraction of encounters that end in ejection after a temporary EMRI.","supporting_citations":[],"review_version":1}