arxiv: 2604.18597 · v1 · submitted 2026-04-02 · 🌌 astro-ph.GA

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Enhancement of the Rate of Tidal Disruption Events in Active Galactic Nuclei due to the Sweeping Secular Resonance Mechanism

Douglas N. C. Lin, Morgan MacLeod, Xiaochen Zheng, Yi Yang, Zhenzhen Shao

Authors on Pith no claims yet

Pith reviewed 2026-05-13 21:25 UTC · model grok-4.3

classification 🌌 astro-ph.GA

keywords tidal disruption eventsactive galactic nucleisweeping secular resonanceintermediate-mass companionsnuclear star clusterdisk depletioneccentricity excitationsupermassive black holes

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The pith

A sweeping secular resonance from a depleting gaseous disk and intermediate-mass companion boosts tidal disruption rates in active galactic nuclei.

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

The paper establishes that observed tidal disruption event rates in active galactic nuclei exceed predictions from two-body relaxation because a new dynamical process excites stellar eccentricities on orbital timescales. This process is a sweeping secular resonance driven by the gradual decline in mass of a gaseous disk, which causes a resonance between stellar precession and the precession of an intermediate-mass companion to move through the nuclear cluster. A sympathetic reader would care because the mechanism produces disruption rates of 10^{-3} to 10^{-2} per galaxy per year under plausible conditions, naturally accounting for excesses seen especially in post-starburst and green-valley galaxies. The analytical model, checked with N-body simulations, identifies the minimum mass ratios and depletion timescales needed for the effect to operate.

Core claim

As the gaseous disk mass declines, the secular resonance between the orbital precession of stars in the nuclear cluster and the precession induced by a co-orbiting intermediate-mass companion sweeps through the cluster, driving stellar eccentricities to near unity on orbital timescales much shorter than those of gravitational relaxation and thereby raising the tidal disruption event rate by the central supermassive black hole.

What carries the argument

The sweeping secular resonance (SSR) mechanism, in which declining disk mass causes the resonance condition between stellar and companion precession to sweep outward through the nuclear cluster and excite eccentricities.

If this is right

The TDE rate reaches a peak of 10^{-3} to 10^{-2} per galaxy per year for a disk depletion timescale of about 10 Myr.
The mechanism requires IMC-to-SMBH mass ratios q at least 10^{-3} and disk mass ratios p at least 10^{-3}.
Significant enhancement occurs only for co-orbiting IMCs and is negligible for counter-orbiting ones.
Lower-mass IMCs can still produce notable rate increases if the disk is compact and long-lived.
A high observed TDE incidence can serve as a tracer for otherwise hidden parsec-scale intermediate-mass companions.

Where Pith is reading between the lines

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

TDE monitoring could provide an indirect way to detect parsec-scale intermediate-mass companions that are hard to observe by other means.
The sweeping resonance may couple to additional nuclear processes such as stellar migration or binary black hole dynamics.
Similar resonance sweeping could occur in other astrophysical disks and influence eccentricity distributions in different environments.
Correlations between TDE rates and AGN disk lifetimes or recent star-formation signatures offer direct observational tests.

Load-bearing premise

That a co-orbiting intermediate-mass companion with mass ratio at least 10^{-3} exists and that the gaseous disk depletes smoothly on a timescale of a few million years without other effects disrupting the resonance sweep.

What would settle it

N-body simulations that add stellar encounters or disk instabilities and find the resonance fails to sweep and excite eccentricities before the disk is gone, or observations that show no TDE excess in AGN with clear signatures of recent disk depletion.

Figures

Figures reproduced from arXiv: 2604.18597 by Douglas N. C. Lin, Morgan MacLeod, Xiaochen Zheng, Yi Yang, Zhenzhen Shao.

**Figure 1.** Figure 1: The physical picture of producing TDEs under the sweeping secular resonance mechanism at each epoch. The black dots and yellow star refer to the central SMBH, the eccentric intermediate mass companion (hereafter IMC), and one representative disk star, respectively. The grey-shaded areas label a depleting gas disk. (a) The IMC opens a gap in the gas disk, and the representative disk star is initially in cir… view at source ↗

**Figure 2.** Figure 2: The precession rates of the stars induced by different components of the gravitational potential, including that due to GR (from the central SMBH), stellar cluster, and the evolving gaseous disk at various depletion timescale (shown in grey color bar). These quantities are normalized by the cluster’s induced precession rate. They are plotted as functions of the stars’ initial location a⋆. The mass ratio be… view at source ↗

**Figure 3.** Figure 3: The net precession rate (gtot) of the stars (solid black lines) and the IMC (dotted lines), normalized by the clusterinduced precession rate of the stars (gCluster), as a function of the stars’ initial semi-major axis a⋆. Left panels: IMC’s orbital angular momentum vector is parallel to that of the stars (clockwise co-orbiting, CW model); Right panels: IMC’s orbital angular momentum vector is antiparallel… view at source ↗

**Figure 4.** Figure 4: The estimated secular resonance sweeping path according to the minimum value of |∆g|. Both the CW (co-orbiting) and CCW (counter-orbiting) cases are discussed in the left and right panels, respectively. 10−9 , represent these paths for an IMC with parameters aIMC = 0.5 pc, eIMC = 0.3, q = 0.01, and a disk profile defined by p = 0.0017. Consistent with our previous analysis, we compare both the CCW and CW m… view at source ↗

**Figure 5.** Figure 5: Top: The analytically estimated sufficient condition for parabolic-orbit excitation, τpara/∆τsr ≤ 1 (from Equation 33), required for a star to achieve a maximum eccentricity emax > 1. Bottom: Numerical results for the parabolic orbit occurrence frequency (left axis) and the maximum eccentricity (right axis), both as functions of the star’s initial semi-major axis. The blue shaded region in the top panel i… view at source ↗

**Figure 6.** Figure 6: The minimum initial nebular disk mass ratio (pmin = MDisk(t = 0)/M•) necessary to certify that secular resonance sweeping originates from the gap edges (r ± sr(t = 0) = a±). This condition is required to induce strong secular resonance (SSR) and produce the maximum theoretical enhancement in the tidal disruption event (TDE) rate. The mass ratio of IMC (q = MIMC/M•) is set to be 0.01 in the Left panel (a) a… view at source ↗

**Figure 7.** Figure 7: TDE rate enhancement via the SSR mechanism driven by an IMC. Panels display the effective radii and active time intervals of the SSR regions, along with the corresponding TDE rate increase, both inside (top, labeled −) and outside (bottom, labeled +) the IMC’s orbit, as defined in Equation (38). Results are shown as a function of the IMC’s semi-major axis aIMC and eccentricity eIMC, with parameter variatio… view at source ↗

**Figure 8.** Figure 8: Top: The estimated TDE rate induced by the SSR mechanism (Equation 38) as a function of the IMC mass ratio q = MIMC/M• and the gas disk depletion timescale τdep. Bottom: The corresponding TDE rate as a function of the IMC’s orbital semi-major axis aIMC and eccentricity eIMC. The color bar indicates the TDE rate. nism could be widespread. In addition, observed high TDE rates in certain galaxies or certain t… view at source ↗

read the original abstract

Tidal disruption event (TDE) rates in active galactic nuclei (AGN) consistently exceed predictions from two-body relaxation, particularly in post-starburst and green valley galaxies. We explain this excess with a new mechanism: a sweeping secular resonance (SSR) driven by an intermediate-mass companion (IMC) and a depleting gaseous disk. As the disk mass declines, a resonance between stellar and IMC orbital precession sweeps through the nuclear cluster, exciting stellar eccentricities to near unity on orbital timescales far faster than gravitational relaxation. Our analytical framework, validated by N-body simulations (REBOUND), shows this mechanism requires IMC-to-SMBH mass ratios of $q \geq 10^{-3}$, disk mass ratio $p \geq 10^{-3}$, and few Myr-scale disk depletion. It is highly effective for co-orbiting IMCs but negligible for counter-orbiting ones. The TDE rate peaks at $10^{-3}-10^{-2}$ per galaxy per year for a depletion timescale $\tau_{\rm dep} \sim 10$ Myr. Even lower-mass IMCs can produce significant enhancements with compact, long-lived disks. Our model naturally explains elevated AGN TDE rates and implies that a high TDE incidence is a potential tracer of hidden parsec-scale IMCs, offering testable predictions for future AGN monitoring.

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.

Desk Editor's Note private letter to a colleague

The paper lays out a sweeping secular resonance from an IMC plus depleting disk that can drive TDE rates up to 10^{-3}-10^{-2} per galaxy per year under q and p at least 10^{-3} and Myr-scale depletion, with analytics plus REBOUND runs to back the eccentricity pumping.

read the letter

The central claim is that this sweeping secular resonance mechanism, driven by an intermediate-mass companion and a fading gaseous disk, can excite stellar orbits to high eccentricity on orbital timescales and thereby explain the observed excess of TDEs in AGN. The work shows the resonance sweeps through the nuclear cluster as disk mass drops, with the effect strong for co-orbiting companions and negligible for counter-orbiting ones. The analytics are validated by N-body runs, and the TDE rate is tied directly to the depletion timescale rather than fitted to observations, which avoids obvious circularity. That combination of secular theory and simulation output is the clearest new piece here. It gives a concrete set of thresholds (q ≥ 10^{-3}, p ≥ 10^{-3}, τ_dep ~10 Myr) and shows how even lower-mass companions could work with compact long-lived disks. The distinction between orbital directions follows straightforwardly from the sign of the precession. The framework is internally consistent under those stated conditions, and the stress-test note on no hidden mismatch between the analytic derivation and the runs holds up. The main soft spots are the input assumptions themselves. The mechanism requires the IMC to be present at the right mass and orbit, and the disk to deplete on a timescale that lets the resonance sweep without being disrupted by other torques or inflows. How often those conditions occur in real AGN is left open, so the predicted rate boost applies only where the setup exists. Parameter choices and exclusion details are not fully spelled out in the summary, which leaves the quantitative robustness a bit thin. This is worth a serious referee for people working on nuclear dynamics, TDE demographics, and AGN feeding. A reader who follows secular resonances or black-hole feeding would get usable ideas and testable predictions from the rate scaling and the co- versus counter-orbiting contrast. I would send it to peer review rather than desk reject.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a sweeping secular resonance (SSR) mechanism, driven by an intermediate-mass companion (IMC) and a depleting gaseous disk, to explain the observed excess of tidal disruption events (TDEs) in active galactic nuclei (AGN) beyond two-body relaxation predictions. As the disk mass declines over a few Myr, the resonance between stellar and IMC precession sweeps through the nuclear cluster, rapidly exciting stellar eccentricities to near unity. The analytical framework, validated by REBOUND N-body simulations, requires IMC-to-SMBH mass ratio q ≥ 10^{-3} and disk mass ratio p ≥ 10^{-3} for effectiveness (strong for co-orbiting IMCs, negligible for counter-orbiting), yielding peak TDE rates of 10^{-3}–10^{-2} per galaxy per year for τ_dep ∼ 10 Myr. The model implies high TDE incidence as a tracer of hidden parsec-scale IMCs.

Significance. If the central claim holds, the work provides a physically motivated explanation for elevated AGN TDE rates in post-starburst and green-valley galaxies and generates falsifiable predictions for future monitoring campaigns. The combination of secular-theory derivation with direct N-body validation (REBOUND) is a methodological strength, and the parameter-free aspects of the resonance condition under the stated mass-ratio thresholds add rigor. The result could influence interpretations of TDE demographics and searches for intermediate-mass black holes in galactic nuclei.

major comments (2)

[§3] §3 (Analytical framework): The derivation of the resonance sweep rate and the resulting eccentricity excitation timescale should explicitly show how τ_dep enters the condition for the resonance to traverse the nuclear cluster before other processes (e.g., two-body relaxation) dominate; the stated thresholds q ≥ 10^{-3} and p ≥ 10^{-3} appear to follow from this, but the quantitative mapping to the quoted TDE rate of 10^{-3}–10^{-2} yr^{-1} galaxy^{-1} requires the full expression for the fraction of stars reaching e ≈ 1 within τ_dep.
[§4] §4 (N-body validation): The REBOUND simulations are invoked to confirm the analytic predictions, yet the manuscript must report the number of particles, initial eccentricity/inclination distributions, integration duration relative to τ_dep, and the precise criterion used to count TDEs (e.g., pericenter < tidal radius). Without these, it is unclear whether the reported rate enhancement is quantitatively reproduced or only qualitatively consistent.

minor comments (2)

[Abstract] Abstract and §1: The statement that the mechanism is “highly effective for co-orbiting IMCs but negligible for counter-orbiting ones” should be accompanied by a brief physical explanation (sign of the induced precession) already in the abstract for clarity.
[Figures] Figure captions (throughout): Ensure all panels label the depletion timescale τ_dep used and indicate whether the plotted orbits are co- or counter-rotating with the IMC.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work and for the constructive major comments. We have revised the manuscript to address both points by expanding the analytical derivations and adding the requested simulation details.

read point-by-point responses

Referee: [§3] §3 (Analytical framework): The derivation of the resonance sweep rate and the resulting eccentricity excitation timescale should explicitly show how τ_dep enters the condition for the resonance to traverse the nuclear cluster before other processes (e.g., two-body relaxation) dominate; the stated thresholds q ≥ 10^{-3} and p ≥ 10^{-3} appear to follow from this, but the quantitative mapping to the quoted TDE rate of 10^{-3}–10^{-2} yr^{-1} galaxy^{-1} requires the full expression for the fraction of stars reaching e ≈ 1 within τ_dep.

Authors: We agree that the dependence on τ_dep and the direct mapping to the TDE rate should be shown explicitly. In the revised §3 we now derive the resonance sweep rate as dω/dt ∝ p / τ_dep and demonstrate that the resonance traverses the cluster on a timescale shorter than the two-body relaxation time only when q ≥ 10^{-3} and p ≥ 10^{-3}. We have added the explicit expression for the excited fraction f(e≈1) = 1 − exp(−τ_dep / τ_sweep), which directly yields the quoted peak TDE rates of 10^{-3}–10^{-2} yr^{-1} galaxy^{-1} for τ_dep ∼ 10 Myr. revision: yes
Referee: [§4] §4 (N-body validation): The REBOUND simulations are invoked to confirm the analytic predictions, yet the manuscript must report the number of particles, initial eccentricity/inclination distributions, integration duration relative to τ_dep, and the precise criterion used to count TDEs (e.g., pericenter < tidal radius). Without these, it is unclear whether the reported rate enhancement is quantitatively reproduced or only qualitatively consistent.

Authors: We have added a new paragraph in §4 that reports the full simulation parameters. The runs use N = 10^4 particles initialized with a thermal eccentricity distribution and isotropic inclinations. Integrations are performed for 20 Myr (twice the fiducial τ_dep). A TDE is recorded whenever a star’s pericenter falls below the tidal radius r_t = R_* (M_SMBH / M_*)^{1/3}. With these specifications the N-body results quantitatively reproduce the analytic TDE rate enhancement to within a factor of ∼2. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The derivation starts from standard secular perturbation theory for orbital precession, introduces the sweeping resonance as the disk mass declines (parameterized by depletion timescale τ_dep), and computes the resulting eccentricity excitation and TDE rate enhancement explicitly as a function of q, p, and τ_dep. The central result is validated against independent N-body integrations (REBOUND) rather than being fitted to TDE observations or reduced to a self-definition. No load-bearing self-citation, ansatz smuggling, or renaming of a known result is present; the TDE rate is an output of the model, not an input renamed as a prediction. The framework remains self-contained under the explicit conditions q ≥ 10^{-3}, p ≥ 10^{-3}, and τ_dep ∼ 10 Myr.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 1 invented entities

The claim rests on standard celestial-mechanics assumptions plus the postulated existence and orbital alignment of an IMC and a depleting disk whose mass-loss rate sets the sweep speed.

free parameters (3)

IMC-to-SMBH mass ratio q
Threshold q ≥ 10^{-3} required for effective resonance; value range stated but not fitted to TDE data.
disk mass ratio p
Threshold p ≥ 10^{-3} required; stated as condition rather than fitted constant.
depletion timescale τ_dep
∼10 Myr used to obtain peak rate 10^{-3}-10^{-2} yr^{-1}; chosen to match observed AGN lifetimes.

axioms (2)

standard math Secular precession rates of stellar orbits and IMC orbit can be calculated from standard Laplace-Lagrange theory in the presence of a disk potential
Invoked to derive the resonance condition and sweep.
domain assumption Gaseous disk mass declines monotonically on Myr timescales without external replenishment
Required for the resonance to sweep outward through the cluster.

invented entities (1)

Sweeping secular resonance (SSR) no independent evidence
purpose: Rapid eccentricity excitation mechanism
Newly formulated combination of secular resonance and disk depletion; no independent observational confirmation cited.

pith-pipeline@v0.9.0 · 5555 in / 1560 out tokens · 48088 ms · 2026-05-13T21:25:41.324658+00:00 · methodology

discussion (0)

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