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Disruptions of stars and binary systems on chaotic orbits in an axisymmetric Milky Way center

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Pith's one-line read This paper claims that chaotic 'diving orbits' in the flattened, axisymmetric potential of the Milky Way's inner 200 pc can deliver stars and binaries to the central massive black hole without any two-body scattering, and that this…

desk verdict A credible, well-scoped case that collisionless chaotic orbits dominate binary disruptions in an axisymmetric galactic center, but the headline rates rest on an ergodicity assumption tested on timescales much longer than the disruption process, and no artifacts are released. read the letter →

arxiv 2505.06344 v3 pith:EXY46CMJ submitted 2025-05-09 astro-ph.GA astro-ph.HE

Zephyr Penoyre , Elena Maria Rossi , Nicholas C. Stone This is my paper · ORCID
classification astro-ph.GAastro-ph.HE
keywords chaoticorbitstidaldisruptioneventshypervelocitystarsgalacticcenteraxisymmetricpotentiallosswedgedivingnuclearstellarcluster
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

This paper claims that the flattened, axisymmetric potential of the Milky Way's inner 200 pc has its own, collisionless route for feeding stars and binaries to the central black hole. Orbits with near-zero vertical angular momentum can be chaotic, and chaotic 'diving' orbits randomly sample periapse angular momentum, so a system eventually passes inside the tidal radius without needing two-body scatterings. For a fixed tidal angular momentum, the paper derives a probability distribution for the 'diving factor' $\beta=(\ell_t/\ell_p)^2$ that scales as $\beta^{-3/2}$, and folds it into a model of the Galactic Center to compute disruption rates. The central quantitative claim is that this collisionless channel can dominate the collisional two-body scattering rate: by orders of magnitude for binaries and giants, and by a factor of a few for main-sequence tidal disruption events. If true, most Milky Way disruptions would arrive nearly perpendicular to the disk and eject debris or hypervelocity stars preferentially toward the galactic poles.

What carries the argument

The central object is the 'diving orbit': a chaotic trajectory in an axisymmetric potential whose polar angular momentum $\ell_\theta$ varies under the non-spherical torque while the vertical component $\ell_z$ is conserved, allowing periapse to wander down to the minimum permitted by $\ell_z$. The argument is carried by the periapse surface of section: periapsides of a chaotic orbit uniformly fill the accessible $(\theta_p,\ell_{\theta,p})$ region, so probabilities of disruption reduce to area integrals. That yields the key analytic identity $p(\beta)\propto\beta^{-3/2}$ for the diving factor $\beta=(\ell_t/\ell_p)^2$, steeper than the geometric $\beta^{-1}$ scaling, and the 'loss wedge' description of the vulnerable region $|\ell_z|<\ell_t$.

What would settle it

Integrate a set of low-$\ell_z$ chaotic trajectories in the paper's potential for more than $10^6$ radial periods and histogram periapse occupancy in the low-$\ell_{\theta,p}$ corner: if the count CDF deviates from the Poisson expectation beyond shot noise for $\ell_z/\ell_c \lesssim 0.1$, the uniform-filling assumption fails and the derived rates and $\beta$ distribution change. Observationally, a kinematically unbiased sample of hypervelocity stars with three-dimensional velocities showing no excess toward the galactic poles would contradict the predicted injection anisotropy.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that in an observationally benchmarked axisymmetric model of the Milky Way center, the loss wedge $|\ell_z|<\ell_t$ is fed primarily by chaotic orbits rather than by relaxation. Any trajectory that reaches the minimum pericenter permitted by its conserved $\ell_z$ is chaotic; regular orbits cannot dive. Because chaotic trajectories fill their accessible periapse phase space roughly uniformly, the probability per periapse passage of disruption is $p(D)=\lambda_t(1-|\gamma_z|)/F_{\rm dive}$, and the disruption time is $t_D\approx T_c F_{\rm dive}(1-|\gamma_z|)/\lambda_t$, producing encounter properties with $p(\beta)\propto\beta^{-3/2}$, a steep preference for shallow, grazing, near-parabolic encounters that are strongly misaligned with the disk. Integrating over the Galactic Center distribution function, the collisionless relative rate $\bar\Gamma_d$ exceeds the collisional $\bar\Gamma_s$ by orders of magnitude for large tidal angular momentum (binaries, giants) and by a factor of a few for small $\ell_t$ (solar-type TDEs).

Load-bearing premise

The load-bearing premise is that each chaotic diving orbit fills its allowed periapse region uniformly, so the probability of a deeply disruptive passage is simply the area of the tidal region divided by the area of the chaotic sea.

Editorial extensions

If this is right

  • For a Milky Way composed entirely of solar-type stars, the model gives a total TDE rate of a few $\times 10^{-5}\,\mathrm{yr}^{-1}$, with the collisionless channel responsible for the majority.
  • Binary and giant-star disruptions (the Hills mechanism and S-star formation) may be boosted by one to three orders of magnitude relative to scattering estimates, so observed hypervelocity star and S-star populations may be substantially fed by chaotic diving.
  • Encounter geometry makes ejecta anisotropic: hypervelocity stars and tidal debris should preferentially emerge along the galactic poles rather than isotropically.
  • The process is generic: any galaxy with a flattened nuclear cluster and a central massive black hole should have a comparable or stronger collisionless disruption channel, since chaotic diving appears even for nearly spherical nuclear cluster shapes.

Reading between the lines

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

  • Beyond the paper: the steep $\beta^{-3/2}$ distribution implies partial disruptions are far more common than full ones; if repeated weak encounters accumulate, they may measurably alter the spin, mass, and orbital energy of surviving stars before the final disruption, an effect the authors flag but do not model.
  • Beyond the paper: the same diving mechanism can supply extreme-mass-ratio inspirals to the central black hole without two-body relaxation; the authors mention EMRIs as a motivation but do not compute their rates.
  • Beyond the paper: if the assumed uniform phase-space filling is replaced by a sticky chaotic distribution, the relative rate ordering may shift; a direct test is to compare the observed sky distribution of hypervelocity stars with the predicted polar excess.
  • Beyond the paper: triaxiality, which the authors note may be present in the inner galaxy, would likely enlarge the chaotic sea and strengthen the collisionless channel further; quantifying this for observed bar and bulge shapes would be a natural next step.
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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

2 major / 6 minor

Summary. The paper studies the dynamics of low-angular-momentum orbits in an observationally benchmarked axisymmetric model of the Milky Way's inner 200 pc, focusing on chaotic 'diving orbits' that can bring stars or binaries arbitrarily close to the central massive black hole without two-body scattering. The authors show that such orbits are common for small conserved z-angular momentum, derive an analytic distribution p(beta) for the encounter depth assuming uniform filling of the chaotic region in periapsis phase space, compute disruption timescales t_D, and compare the resulting collisionless disruption rates with standard collisional loss-cone rates for a range of tidal angular momenta lt. They conclude that the collisionless channel can dominate the collisional one, by orders of magnitude for large lt (wide binaries, giants), and predict that disrupted material is preferentially ejected toward the galactic poles.

Significance. If the results hold, the paper identifies a potentially important, largely overlooked channel for tidal disruptions and hypervelocity-star production in axisymmetric galactic centers, with a distinctive polar ejection anisotropy that is testable with HVS surveys and TDE host-galaxy orientations. The analytic derivation of p(beta) ∝ beta^(-3/2) from a geometric area integral is elegant and parameter-free once uniform filling is assumed. The numerical work is substantial and reproducible in structure: 300,000-orbit integrations, Lyapunov exponent classification, Poisson-statistics checks of occupancy, and a clear comparison with Magorrian & Tremaine (1999). The sensitivity study of the NSC flattening (Section 4.5) is a useful addition. The main quantitative claims, however, rest on an ergodicity assumption whose validity on the relevant (short) timescales is not directly tested, and the headline 'orders of magnitude' statement applies to an idealized single-lt population; these points are addressed in the major comments.

major comments (2)
  1. [Section 4.3 and Eq. (58)] The uniform-filling assumption that underpins p(beta), t_D, and all subsequent rates is validated only through aggregate occupancy over ~300,000 radial periods (Figure 6), while the mean disruption time t_D = T_c F_dive / [lambda_t (1 - |gamma_z|)] is typically 10^2-10^3 radial periods for the systems dominating the rates (Rc ~ 0.5-3 pc, lt ~ 0.3-30 pc^2/Myr). If a chaotic trajectory experiences sticky phases near regular islands before exploring the low-l_theta,p region, the first-passage time to a disrupting pericenter can be substantially longer than 1/p(D), biasing the rates in Section 6.3 upward. The paper acknowledges sticky boundaries (Section 4.3) and notes that realistic DFs may violate the assumption (Section 5), but it does not test the short-time occupancy or the distribution of waiting times between low-l_theta excursions. I ask the authors to run targeted integrations that measure the first-passage-time distribution to beta >= 1 for representative (Rc, lz, lt) values, or to provide a quantitative argument that the long-time Poisson statistics imply exponential inter-arrival times with the same mean on the t_D timescale.
  2. [Abstract and Section 6.5 (Figure 14)] The abstract's claim that the 'relative collisionless rate can dominate by orders of magnitude' is only demonstrated for an idealized population consisting entirely of systems with a single, large lt (e.g., lt = 30 pc^2/Myr in Figure 14). For TDE-relevant lt ~ 0.3 pc^2/Myr the enhancement is only a factor of a few, and the paper explicitly cautions (Section 6) that the single-lt calculation cannot be integrated over a realistic lt distribution without additional assumptions about the population and survivability of binaries/giants. As written, the abstract overstates the generality of the 'orders of magnitude' conclusion. I recommend the abstract and discussion be qualified to state that the large enhancement applies to systems with large tidal angular momentum (wide binaries and giants), while for main-sequence-star TDEs the collisionless channel is competitive but only moderately dominant.
minor comments (6)
  1. [Section 6.4.1, Eq. (68)] Equation (68) appears to be missing a division sign: the full loss-cone differential rate should scale as n(rho, gamma)/T_r(rho, gamma), not n(rho, gamma) * T_r(rho, gamma), consistent with the subsequent integration in Eq. (71).
  2. [Abstract] The phrase 'Most of these disruptions involve stars come from the Nuclear Stellar Cluster' contains a grammatical error; 'come' should be removed.
  3. [Section 1] The sentence 'Stars are are scattered ... by two-body encounters' duplicates 'are'; please correct.
  4. [Section 2.1] The text refers to 'Noether's theorum'; the correct spelling is 'theorem'.
  5. [Section 5.1.2] The sentence 'These simplifying assumption can be complicated for Hills mechanism separations' should be 'These simplifying assumptions can be complicated ...'.
  6. [Figure 2] The axis labels in Figure 2 appear garbled in the compiled PDF (e.g., '½ = log10', '² [pc2 Myr¡2]'); please verify the rendering of the LaTeX labels.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity found: p(β) and the relative rates follow from numerically tested ergodicity and geometric area integrals, with Fdive canceling in the dominant full-wedge rate.

full rationale

The derivation chain is self-contained and non-circular. The central encounter-depth distribution p(β) ∝ β^{-3/2} (Eqs. 44–46) is an analytic Jacobian/area transformation of the assumed uniform periapse sampling in (x,y); that uniformity is not a fitted input but is tested directly against Poisson statistics in Fig. 6 for low lz/lc, with the paper explicitly acknowledging sticky-boundary caveats. Fdive is measured from independent orbit integrations (Figs. 7–8), and although it enters the rate formulae, in the full-loss-wedge regime that dominates the totals Fdive cancels between P(D) and tD (Eqs. 53, 57–58, 66), so the headline claim does not reduce to a fitted parameter. The collisional comparison uses the same GC model's DF fits (Table A1) and standard loss-cone formulae; using one self-consistent potential for both channels is modeling, not fitting the output to itself. Self-citations (Penoyre et al. 2025 in prep.; Sersante et al. 2025; Verberne et al. 2025) are forward-looking or used only for external sanity checks and do not carry the central argument. The paper itself flags the ergodicity caveat (Section 5) and the survivability limitations (Section 7), which are honest scope limitations rather than circular reductions. No step was found in which a prediction is equivalent by construction to its own input.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The central claim rests on a handful of modeling assumptions: an axisymmetric potential with conserved lz, uniform ergodic filling of the chaotic region, beta>=1 as disruption criterion, and the S22-based DF models. The first is standard mechanics; the second is tested numerically; the third is an acknowledged simplification; the fourth is observational benchmarking. Free parameters are mostly interpolation coefficients and hand-tuned timescale choices, not hidden degrees of freedom in the core derivation.

free parameters (5)
  • Galactic age tgal = 10 Gyr
    Assumed for the tmax vs tgal comparison in Section 6.2; rates for systems with tD or trel > 10 Gyr are suppressed.
  • GMC relaxation boost parameters (eq 76) = 100, 1/(1+e^{5(1-rho)}), floor 0.01
    Hand-chosen model of massive perturbers in the NSD; called 'relatively optimistic' by the authors.
  • Fdive smoothing spline = interpolated curve from simulations (Fig. 8)
    The diving fraction used in rates is a smoothed spline of noisy simulation measurements.
  • DF fitting coefficients (Appendix A, Table A1) = a, b, alpha, x, k, kappa per component
    Power-law/logistic fits to 1e6 Monte Carlo samples of the NSD and NSC distribution functions; used directly in equations 66-72.
  • lt grid = 0.3, 1, 3, 10, 30 pc^2 Myr^-1
    Explored values of tidal angular momentum mapping to tidal radii 0.5 to 5200 AU; not fitted, but the rates are shown only at these values.
assumptions (7)
  • standard math An axisymmetric potential with conserved lz
    Noether's theorem; central to the loss-wedge formalism (Section 2.1).
  • domain assumption Chaotic trajectories uniformly fill the accessible (theta_p, l_theta,p) region at periapse
    Used for all p(beta), p(ci), p(delta) derivations (Section 5); tested against Poisson statistics in Figure 6 for lz/lc <= 0.1.
  • domain assumption beta >= 1 is necessary and sufficient for disruption
    Binary flag D in Section 5.1.2; simplified from Sari et al. 2010, acknowledged as an approximation.
  • domain assumption Mean radial period equals circular period Tc
    Approximation in equation 58 for the disruption timescale tD.
  • domain assumption The Sormani et al. 2022 model plus Vasiliev et al. (in prep) NSC DF represents the Milky Way GC
    Benchmarks the potential and sampling in Sections 3 and 6.
  • domain assumption Spherical symmetry for the collisional loss-cone rate
    Section 6.4, acknowledged to be an oversimplification but used for the comparison.
  • domain assumption Coulomb logarithm ln Lambda = 20 and scatterer mass ms = 1 M_sun
    Standard choices in equation 62; affect trel values.

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Cite this review

Pith. "Pith review of Disruptions of stars and binary systems on chaotic orbits in an axisymmetric Milky Way center." pith.science (2026). https://pith.science/paper/EXY46CMJ

@misc{pith2026250506344,
  author       = {Pith},
  title        = {Pith review of: Disruptions of stars and binary systems on chaotic orbits in an axisymmetric Milky Way center},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EXY46CMJ}},
  note         = {Machine review of arXiv:2505.06344}
}
read the original abstract

Non-spherical potentials allow a wide range of trajectories, both regular and chaotic, whose periapse distances can vary orbit to orbit. In particular chaotic trajectories can bring a system arbitrarily close to the central massive black hole leading to a disruption. In this paper, we work with an observationally benchmarked model of the innermost 200 pc of the Milky Way and show that low z-angular momentum trajectories are commonly chaotic. We compute the timescales and properties of close pericenter passages, and compare the implied collisionless disruption rate to the well-studied collisional rate from 2-body scatterings. We find that the relative collisionless rate can dominate by orders of magnitude. Our calculations are relevant for a wide range of disruption phenomena, including the production of hypervelocity stars (HVSs) and tidal disruption events (TDEs). Most of these disruptions involve stars come from the Nuclear Stellar Cluster, with a pericenter distribution that strongly favours shallow encounters, and a preference for high inclination interactions. The latter implies that unbound disrupted material - whether ejected stars or stellar debris - would be preferentially directed towards the galactic poles. Many of our conclusions apply generally to any galaxy with a non-spherical galactic centre potential and central massive black hole.

Figures

Figures reproduced from arXiv: 2505.06344 by the authors.

Figure 1
Figure 1. The potential, Φ(R,z), of the galactic center model used to integrate orbits throughout the rest of this paper. The left panel expresses the potential through the virialized velocity dispersion (i.e. if all motion is random, obeying the virial theorem). We work in units of pc, Myr and M⊙ throughout this work, but note that 1.0227 pc Myr−1 is equal to 1 km s−1 allowing easy conversion. We also show the limiting radii… view at source ↗
Figure 2
Figure 2. Relevant energy, mass, time and angular momentum scales of our GC model shown as a function of (log) circular ra￾dius. From top to bottom we show: the energy, ε, the total mass enclosed within spherical radii r = Rc, the period of a circular or￾bit, Tc, and the angular momentum of a circular orbit, lc. The horizontal line in the ε plot shows Φ0 (see equation 22), the cen￾tral potential of our model excluding the MBH… view at source ↗
Figure 3
Figure 3. Examples of 5 closed trajectories in the GC potential, all with Rc(ε) = 50 pc and lz = 0. We label them by their classification, Dn or Rn (see section 4.1). For each we show the trajectory, in units of Rc, in the x, z plane (upper left) and R, z plane (lower left). The larger right-hand panel shows the evolution in θ (normalized to run from 1 at the north pole, at the 0 equator and -1 at the south pole) and lθ (norm… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Examples of 9 trajectories integrated in our GC potential with Rc = 50 pc and lz = 0. We integrate each over ∼100 orbits (solid line, large dots), then perturb the initial conditions slightly and integrate over ∼1000 orbits (translucent line, small dots). In the 9 smal…
Figure 5
Figure 5. Figure 5: The full range of possible orbits with Rc of 50 pc and lz = 0, shown in the reduced space of |lθ /lc| and |θ − π 2 |/ π 2 (which is 0 at the equator and 1 at the poles). We show 2,000 random trajectories integrated over approximately 300 orbits. The leftmost column sho…
Figure 6
Figure 6. Figure 6: For a given Rc and lz , we simulate one trajectory (with initial lθ,p = 0.01 lc and θp = π 3 ) over approximately 300,000 orbits. Each coloured SoS panel shows the count of how many periapsides access a given region of (θp,lθ,p) space, digitized over a 100x100 grid. We…
Figure 8
Figure 8. Figure 8: Fraction of lz = 0 trajectories that are physical, chaotic, and exhibit diving behaviour, shown as a function of Rc(ε). For each Rc simulated, we sample 300 trajectories with random θ0 and lθ,0/lc and follow them for approximately 500 radial periods. For Fdive we also …
Figure 7
Figure 7. Figure 7: Top panel: the fraction (Fdive) of trajectories which dive to arbitrarily small lθ,p and thus reach the minimum pericenter permitted by lz conservation. Middle panel: the fraction of chaotic trajectories that do not dive (1− Fdive Fchaos ). Bottom panel: the normal￾isi…
Figure 9
Figure 9. Figure 9: Top panel: The fraction of chaotic orbits (Fchaos, solid line) and physical orbits (Fphys, dashed line) for a given NSC axis ratio (qNSC) as a function of Rc. Bottom panel: The same but in a GC model with only BH and NSC (no NSD). We see that realistically flattened NS…
Figure 10
Figure 10. Figure 10: Properties of our GC model needed for calculating the relaxation time (equation 62), shown as a function of (log) circular radius. From top to bottom we show: the number density of stars (assuming m = M⊙ for all), the local circular velocity (which we use as an estima…
Figure 11
Figure 11. Figure 11: Dimensionless stellar concentrations (top row), rate-limiting timescales (second row), differential contribution to relative rates (third row) and cumulative relative rates (fourth row) for collisionless disruptions by diving orbits for a GC model composed entirely of…
Figure 12
Figure 12. Figure 12: The contribution to the relative rate of disruption (top panels) and cumulative relative rates (bottom panels) for disruptions by diving orbits (left panels) and scatterings (right panels) - for systems of a given lt (in units of [pc2 Myr−1 ]). We also give the approx…
Figure 13
Figure 13. Figure 13: The equivalent of figure 12 but now including a simple prescription for the impact on the relaxation time of massive perturbers (such as GMCs in the NSD). The previous rates (from figure 12) are shown with dashed lines (the full loss-cone rates are unchanged). The div…
Figure 14
Figure 14. Figure 14: The total relative rate of disruptions, Γ¯, for an ideal￾ized population composed entirely of systems with a given tidal angular momentum lt . We show both the implied rate from diving orbits (the collisionless channel) and 2-body scatterings (the col￾lisional channel…

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Forward citations

Cited by 2 Pith papers

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.