Dynamics of recaptures, ejections and mergers of stellar mass binaries over multiple encounters with SgrA*

Biancamaria Sersante; Elena Maria Rossi; Zephyr Penoyre

REVIEW 5 major objections 6 minor 3 cited by

Dynamics of recaptures, ejections and mergers of stellar mass binaries over multiple encounters with SgrA*

T0 review · 5 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Multiple periapsis passages increase the Hills-mechanism disruption rate by at least 20 percent, and can make mergers a 31 percent outcome for example binaries.

desk verdict A useful multi-passage extension of Hills-mechanism calculations held back by an unsampled binary phase distribution and a few unshown validations. read the letter →

arxiv 2505.08499 v1 pith:W2ISFKXR submitted 2025-05-13 astro-ph.GA astro-ph.HE

Biancamaria Sersante , Zephyr Penoyre , Elena Maria Rossi This is my paper · ORCID

classification astro-ph.GAastro-ph.HE

keywords HillsmechanismhypervelocitystarsSgrA*tidaldisruptionstellarbinariesmultipleencountersrestrictedthree-bodyproblemgalacticcentre

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 argues that a stellar binary's encounter with the supermassive black hole SgrA* cannot be judged from a single close passage. Using a restricted three-body formalism, the authors follow initially circular binaries through up to three periapsis passages and show that binaries that survive the first passage often return, become more eccentric and more prograde, and then resolve into disruptions or ejections. The cumulative disruption fraction rises from about 46 percent after one passage to about 60 percent after three, a boost of 20 percent or more, and for an example massive binary, mergers occur 31 percent of the time when finite stellar sizes and lifetimes are included. If correct, single-passage treatments systematically underestimate how many binaries are disrupted or merged by the Hills mechanism.

What carries the argument

The load-bearing object is the restricted three-body formalism, in which the binary's centre of mass follows a fixed Keplerian orbit around the stationary massive black hole and the internal binary motion is integrated under the linearized tidal force. Between passages the binary's final internal energy and angular-momentum changes are transferred to the centre-of-mass orbit through $E_{\rm cm}^{n+1}=E_{\rm cm}^n-\Delta E_b$ and $\mathbf{L}_{\rm cm}^{n+1}=\mathbf{L}_{\rm cm}^n-\Delta \mathbf{L}_b$, yielding a new periapsis distance and eccentricity for the next encounter. The encounter is parameterized by the diving factor $\beta=r_t/r_p$ (the ratio of tidal radius to periapsis distance) and the binary inclination; because the integration is rescaled by $\lambda=(m/M)^{1/3}r_p$ and $\tau=\sqrt{r_p^3/GM}$, the results are independent of the binary's physical properties.

What would settle it

A full three-body (or N-body) integration that propagates the centre-of-mass orbital plane and orientation between encounters, without the fixed-frame assumption, would settle the claim: if the resulting fractions of disruptions, fly-aways, and mergers after three passages differ by more than the quoted boosts (roughly 20 percent for disruptions), the paper's central conclusion fails.

Watch

Extended reading notes

Core claim

The central claim is that multiple periapsis passages materially change the outcome distribution of the Hills mechanism. A binary whose centre of mass remains bound to SgrA* after one encounter comes back on a slightly altered, now elliptical orbit; because the binary itself has gained eccentricity and often a more prograde orientation, the next encounter is statistically more destructive. Tracked across three passages, the overall fraction of disrupted binaries increases from 45.6 percent to 59.6 percent (a boost of 20 percent or more for $\beta_0 > 1$), the fly-away binary fraction grows from 28.4 to 32.3 percent, and, for an example 0.1 AU, 4 solar mass binary with radii following mass, mergers make up 31 percent of outcomes after three passages, reducing the disruption boost to roughly 10 percent once stellar lifetimes and mergers are included.

Load-bearing premise

The load-bearing premise is that a returning binary's centre-of-mass orbit keeps the same spatial orientation between passages, so only the energy and angular-momentum magnitudes need updating; if the orbital plane or orientation rotates significantly, the second- and third-passage geometries—and the reported disruption, fly-away, and merger fractions—would change.

Editorial extensions

If this is right

Single-passage estimates of Hills-mechanism outcomes undercount disruptions: including three passages raises the disruption fraction by 20 percent or more for deep encounters, and extends disruptions to shallower encounters below the single-passage threshold $\beta_{\rm lim}$.
Fly-away binaries form a distinct population ejected at speeds about two orders of magnitude lower than individual ejected stars, on marginally hyperbolic orbits, and their numbers are boosted by about 10 percent by later passages.
For stellar binaries with finite sizes, mergers are a major channel: about 31 percent of example systems merge by the third passage, mostly systems that would otherwise disrupt or fly away.
Hypervelocity stars are produced predominantly on the first passage; later passages add lower-velocity ejecta and matter most for shallow encounters near $\beta_{\rm lim}$.
Inclination and eccentricity control fate: non-retrograde, highly eccentric, or deep encounters preferentially disrupt, while retrograde binaries resist disruption and dominate the remaining come-back population.

Reading between the lines

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

If multi-passage boosts hold generally, rate estimates for transient phenomena tied to the Hills mechanism—tidal disruption events, extreme-mass-ratio inspirals, and quasi-periodic eruptions in galactic nuclei—should be revised upward by tens of percent.
The formalism's scale-independence means the same qualitative boost should apply to compact-object binaries (white dwarfs, neutron stars, black holes) around SgrA*, for which stellar lifetime cuts vanish; the merger fraction there could be larger than the 31 percent quoted for main-sequence stars.
A direct test would compare the predicted low-velocity tail of ejected stars and the predicted population of eccentric fly-away binaries against future survey data in the Galactic Centre.
The three-passage truncation likely captures most of the effect, but the persistent retrograde come-back population suggests a slow tail: extending to more passages would test how quickly the cumulative fractions converge.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The genuinely new thing here is the restricted three-body treatment of multiple pericentre passages, which no one has done systematically, and the detailed description of fly-away binaries, which Mandel & Levin only mentioned. The framework is transparent, the fractions in Table 1 sum consistently, and the rescaled units let the results scale to arbitrary binary masses and separations. The headline claim that multiple encounters boost disruptions by 20% or more is plausible and worth taking seriously.

The soft spot I would focus on is not the one the authors flag. Footnote 4 admits the CM orbital frame is not reoriented between passages, but the stress-test note is right: that inconsistency changes the encounter geometry only at the 1e-4 level because Delta L_b / L_cm ~ Q^{-2/3}. The real problem is the redrawn binary phase. Section 4.1 says each comeback binary is simulated with random phases, but it never states the distribution. If the phase is uniform in true anomaly phi, as Eq. (8) suggests, then for the eccentric binaries that come back (e_b up to ~0.8) the draw overweights pericentre by a factor of several relative to a time-weighted distribution. The physical phase at a random time is uniform in mean anomaly, and dN/dphi is proportional to (1-e^2)^{3/2}/(1+e cos phi)^2. This is an O(1) bias in the initial conditions of the very passages that produce the paper's central boost claim. The authors need to sample uniform mean anomaly, or demonstrate that the choice does not matter.

Two smaller issues: the REBOUND validation is claimed but never shown quantitatively, and no code or data are released, which makes it hard to check the phase convention retroactively. The merger fraction (31%) and the period/merger cuts are sensitive to the example system, which is fine, but the phase sampling affects the general claim independently of that example.

If the phase issue is fixed, the paper becomes a solid contribution to GC rate estimates for HVSs, S-stars, mergers, and possibly EMRI progenitors. As it stands, the qualitative conclusion (multi-encounters matter) is likely correct, but the quantitative boost should not be taken at face value. This deserves peer review, with a required revision on the phase sampling and a shown REBOUND comparison.

Referee Report

5 major / 6 minor

Summary. The paper extends the restricted three-body treatment of the Hills mechanism to multiple pericentre passages around SgrA*. Starting from initially circular binaries on parabolic CM orbits, it integrates the linearized equations of motion to classify outcomes as disruptions (Ds), fly-away binaries (FAs), coming-back binaries (CBs), and, for a chosen example system, mergers (Ms). The central claims are that multiple encounters boost the disruption fraction by 20% or more relative to a single passage, that the example system produces mergers 31% of the time, and that these effects depend strongly on inclination and diving factor. The paper presents phase-space maps of outcomes, distributions of ejected and captured star properties, and the effect of finite stellar lifetimes and sizes.

Significance. If the central claim holds, single-passage treatments systematically underestimate the disruption and merger yields of binaries interacting with SgrA*, with consequences for HVSs, S-stars, EMRI progenitors, and Galactic-centre transients. The paper's main strength is that the restricted formalism yields predictions that are claimed to be independent of binary physical properties, and the results are obtained by direct numerical integration rather than by fitting to data. The fraction table (Table 1) is internally consistent, and the paper gives useful, checkable definitions of the outcome channels. The significance is currently conditional, however, because the multi-passage results rest on a phase-sampling convention that is not stated or justified, on a validation claim that is not shown quantitatively, and on an admitted inconsistency in the CM-frame update between passages.

major comments (5)

[§4, phase randomization; Eq. (8)] The re-initialization of binary phases for CBs is not specified as time-weighted. Since Eq. (8) parameterizes the binary orbit by the true anomaly φ, drawing phases uniformly on [0,2π) samples a non-uniform distribution in time: for an eccentric binary the physical phase density is dN/dφ ∝ (1−e^2)^{3/2}/(1+e cosφ)^2. CBs after the first passage reach e_b up to about 0.8, so a uniform-φ draw overweights pericentre phases by a factor of several and underweights apocentre phases relative to the time-weighted ensemble. The second- and third-passage D/F/C/M fractions, and hence the headline '20% or more' disruption boost, are averaged over this initial-condition distribution. Please state the sampling distribution explicitly, recompute the multi-passage fractions using a mean-anomaly (or otherwise time-uniform) phase draw, and at minimum quantify the sensitivity of the reported boosts to this choice.
[§3.1; footnote 1; §6] The validation against full three-body integration is asserted but never shown quantitatively. The text says that comparison simulations with REBOUND show 'excellent agreement' and footnote 1 mentions a test, but no comparison figure, table, parameter ranges, or error statistics are provided. Because the restricted EOM and, especially, the iterative multi-passage update depend on this approximation, please supply a quantitative validation, for example relative differences in final a_b, e_b, and outcome classifications as a function of β0 and inclination, including at least one repeated passage.
[§4.1, footnote 4] Footnote 4 acknowledges that L_cm is inconsistent with the simulated r_cm and v_cm and that the CM orbital frame is not reoriented between passages, with ω_cm and Ω_cm left undefined. The multi-passage geometry therefore assumes that this omission is negligible. Given Q ≈ 10^6 the effect is plausibly tiny, but the paper should demonstrate this quantitatively—for example by propagating the full L_cm direction and recomputing the fractions, or by estimating the resulting change in the binary orientation relative to the updated CM orbital plane—before the multi-passage boosts can be taken at face value.
[Abstract; Table 1; §6 bullets] The abstract states that, for the example system with finite stellar sizes and lifetimes, mergers occur 31% of the time, but Table 1's 'Mergers and lifetime' row at passage 3 gives 26.54%, with 30.70% corresponding to the merger cut only. The §6 bullet similarly reports ≈31% for mergers before the lifetime cut and 26.54% after combining both cuts. Please harmonize the abstract, the text, and Table 1, and specify explicitly which combination of cuts produces each number.
[§3.3.1 and §4.2] Reclassifying CBs whose CM period exceeds the primary's lifetime as FAs conflates 'does not return for another passage' with 'unbound from the MBH'. These binaries remain on bound CM orbits but their stars expire before the next pericentre passage; they are not physically flying away. This reclassification changes the reported FA fractions and the physical interpretation of FAs as surviving binaries on unbound trajectories. Please either introduce a separate category for such systems or clearly state in all fraction tables and discussion that the FA fraction in the lifetime-cut case includes binaries that are not actually unbound.

minor comments (6)

[Fig. 1 caption] The caption contains a typo: 'calcualtions' should be 'calculations'.
[§1] There are several typos in the introduction, including 'SgRA∗' for 'SgrA*' and 'torwards' for 'towards'.
[§3.2] In the paragraph beginning 'In Fig. 2 we provide some examples', 'dirsupted' should be 'disrupted'.
[§6] The first bullet of the Discussion contains 'thid' instead of 'third'; please proofread throughout.
[§3.1 and Fig. 3] The text says initial orientations and phases are chosen 'uniformly and randomly', but it is not explicit whether the inclination i0 is drawn uniformly in cos(i0) or in i0. Since Fig. 3 uses cos(i0) as the ordinate, please state the sampling convention explicitly.
[§5.3, Fig. 15] The lower panels of Fig. 15 show |1−e_cm|/δ_B and v_ej/ν_B, but the text and caption do not state whether the medians shown refer to the first or third passage in the bottom two panels; please clarify.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: fate fractions and boosts are direct numerical outputs, not fits or renamed inputs.

full rationale

The paper's central claims—single- vs multi-passage D/F/C/M fractions and the ~20% disruption boost—are computed by integrating the linearized restricted three-body EOM (Eqs. 22-23) for sampled initial conditions; the fate of each system is read off from the sign of the final binary and CM energies (Sec. 3.2), not from any fitted parameter. The multi-passage iteration (Eqs. 37-44) carries forward energy and angular-momentum magnitudes and re-samples binary phases, but the resulting fractions are measured from the integrations. The characteristic units used for normalization are derived analytically in Appendix B from energy/angular-momentum scaling (Eqs. B9-B37) and are not adjusted to reproduce the reported fractions. Self-citations to Sari et al. (2010), Kobayashi et al. (2012), and Rossi et al. (2014) supply the standard restricted-three-body framework and the reference value beta_lim, but the paper independently reproduces the single-passage phenomenology and validates the EOM against REBOUND full three-body integrations (Sec. 3.1), so these citations are not load-bearing in a circular sense. The acknowledged limitation in footnote 4—that the CM frame is not reoriented and L_cm is inconsistent with the simulated r_cm and v_cm—is a physical-accuracy caveat, not a definitional circularity; similarly, the uniform-in-phi resampling of binary phase in Sec. 4 is a sampling assumption for eccentric returning binaries, not a reduction of the output to an input. No step of the derivation is equivalent by construction to its own input, so there is no circularity to report.

Assumptions & free parameters 5 free parameters · 8 assumptions · 0 invented entities

The general fate maps depend on the restricted three-body EOM, the initial population choices, and the multi-passage update rules; those are listed as axioms. The example-system fractions (mergers, period cut) additionally depend on chosen physical scales: a_b,0 = 0.1 AU, m = 4 M_sun, q = 1/3, a 10^8 yr lifetime threshold, and a Roche-lobe merger radius of about 0.048 AU. No new particles or forces are introduced.

free parameters (5)

example binary semi-major axis a_b,0 = 0.1 AU
Chosen to set physical scales for the period cut, merger cut, and HVS threshold in Sections 3.3 and 5.2; not fitted to data.
example binary total mass m = 4 M_sun
Chosen for the example system; sets Q ~ 10^6 for SgrA* and the characteristic velocity scale.
example binary mass ratio q = 1/3
Chosen for the example system; determines merger radius via the Eggleton formula and the period cut via primary lifetime.
main-sequence lifetime threshold for period cut = 10^8 yr
Approximate lifetime of the 3 M_sun primary; CBs with longer CM periods are reclassified as FAs (Section 3.3.1).
merger radius r_merge = ~0.048 AU (about half a_b,0)
Derived from the Eggleton Roche-lobe formula with q=1/3 and R/R_sun = M/M_sun; systems reaching r_b <= r_merge are counted as mergers (Section 3.3.2).

assumptions (8)

domain assumption Restricted three-body approximation: the MBH is stationary and the binary CM follows a fixed Keplerian trajectory during each passage (Eqs. 1-2; EOM linearized in Eq. 21).
Requires Q >> 1 (SgrA* gives Q ~ 10^6) and initial binary separation a_b << r_cm; higher-order tidal terms O((r_b/r_cm)^2) are neglected (Section 2).
domain assumption Linearized tidal force is a valid description of binary evolution up to and through pericentre, including deep encounters with beta0 up to 3.3.
The EOM (23) drops second-order terms that grow as the binary approaches the MBH; the paper cites REBOUND agreement but shows no quantitative comparison (Section 3.1).
domain assumption Initial population consists of circular binaries (e_b,0=0) on parabolic CM orbits (e_cm=1), with omega, Omega and binary phase uniformly random.
Defines the parameter space for the central results (Section 3.1); eccentric initial binaries are treated only in Appendix A.
ad hoc to paper Between passages, the CM energy and angular momentum update by conservation, but the CM orbital plane and orientation angles (omega_cm, Omega_cm) are not updated; i_cm is assumed small.
Explicitly stated in Section 4.1 and footnote 4: "our calculated Lcm is inconsistent with our simulated rcm and vcm"; this supports the multi-passage iteration but is an acknowledged approximation.
ad hoc to paper The binary phase at the start of each subsequent passage is uniformly random and independent of the previous phase.
Section 4: phase diffusion over many binary periods is assumed to erase memory, so each CB is re-simulated with N random phases.
ad hoc to paper Merger condition: a binary merges when the primary fills its Roche lobe (Eggleton 1983, Eq. 36), with stellar radii obeying R/R_sun = M/M_sun.
Section 3.3.2: finite stellar sizes are introduced only for the example system; the radius-mass relation is a rough proxy and no post-merger evolution is modeled.
ad hoc to paper CBs with CM period longer than the primary's main-sequence lifetime (~10^8 yr) are reclassified as FAs.
Section 3.3.1: order-of-magnitude lifetime constraint applied to the example system only.
standard math The characteristic scales nu_D, alpha_D, delta_D from Appendix B (following Kobayashi et al. 2012) accurately normalize the outcome distributions across all beta0.
Used to express velocities and semi-major axes in dimensionless units; derived under high-beta radial infall but claimed to hold within a factor of a few across beta.

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Cite this review

Pith. "Pith review of Dynamics of recaptures, ejections and mergers of stellar mass binaries over multiple encounters with SgrA*." pith.science (2026). https://pith.science/paper/W2ISFKXR

@misc{pith2026250508499,
  author       = {Pith},
  title        = {Pith review of: Dynamics of recaptures, ejections and mergers of stellar mass binaries over multiple encounters with SgrA*},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W2ISFKXR}},
  note         = {Machine review of arXiv:2505.08499}
}

read the original abstract

A common origin for a host of stellar phenomena in galactic centres is the tidal encounter between stellar binaries and a massive black hole (MBH), known as the ``Hills mechanism''. Following the encounter, binaries may disrupt into an ejected star and a captured one, they may merge, or survive to either fly away or come back for one or more subsequent encounters, until they are either disrupted or fly away. In this paper, we analyse how a binary's fate depends on its orbital parameters, by following its evolution through up to three subsequent pericentre passages. We choose an initial population of circular binaries on parabolic orbits. We present results from our restricted three-body formalism, whose strength lies in the ability to easily explore a multidimensional parameter space and make predictions independent of the binary physical properties. We find that fates depend strongly on orbital inclination, how deep the encounter is into the MBH tidal sphere and on the binary eccentricity, developed during encounters. Generally, non retrograde trajectories, high eccentricities or deep encounters produce disruptions preferentially. Disruption is the most common fate. A significant fraction of the surviving binaries fly away at velocities typically two orders of magnitude smaller than those of ejected stars. Multiple encounters boost disruptions by 20\% or more. Finally, using an example system, we investigate the effect of finite stellar sizes and lifetimes, showing that mergers occur 31\% of the time, and that disruptions are still boosted by 10\% through subsequent passages.

Figures

Figures reproduced from arXiv: 2505.08499 by the authors.

**Figure 2.** Examples of orbits for a CB (orange), a FA (blue) and a disrupted binary (green) obtained from initially-circular binaries on parabolic trajectories for a set of phases and angular parameters sampled as described in the text. In all panels coordinates are expressed in code units (see 2.2.2) Upper panel: secondaries’ orbits in the comoving frame of their respective primaries (colors change from lighter to darker as … view at source ↗

**Figure 3.** Fractions of disruptions (D), fly-aways (F) and coming-backs (C) as a function of the diving factor 𝛽0 and the initial inclination 𝑖0. The green, blue and orange contour lines highlight the regions of parameter space where D,F and C, are, respectively, at least 0.5. Lines are thicker when the contour is in the corresponding panel. This figure is generated for 100,000 interactions with random initial conditions, exce… view at source ↗

Figures from the paper (10 more)

**Figure 4.** Figure 4: Upper panel: Fractions of Ds, FAs and CBs (green, blue and orange, respectively), after one pericentre passage. Central panel: Comparison between the fractions of Ds, FAs and CBs before (thin lines, same as in the upper panel) and after period cut (dotted lines, same …

**Figure 5.** Figure 5: Set of FAs resulting from one interaction between an initial population of 100000 circular binaries on a parabolic orbit and the MBH in the 𝛽0-cos(𝑖0 ) plane (marginalized over 𝜔, Ω and the binary phase), coloured by the final FA binary eccentricity (top panel) and by…

**Figure 6.** Figure 6: Similar to [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: Distributions of the periods of the CM-trajectory of CBs as a function of 𝛽0, coloured by the cosine of the initial binary inclination (𝑖0). The vertical dashed line corresponds to 𝛽lim. The horizontal dotted black line marks periods of the order 108 years (approximate…

**Figure 8.** Figure 8: Set of 100000 initially-circular binaries on a parabolic orbit in the 𝛽0-cos(𝑖0 ) plane, coloured by the ratio between the minimum dimensionless distance rmin and the initial binary semi-major axis 𝑎b0, after one pericentre passage (marginalized over 𝜔, Ω and the binar…

**Figure 9.** Figure 9: Top row: Fractions of Ds (𝐷𝑖 , green), FAs (𝐹𝑖 , blue) and CBs (𝐶𝑖 , coral) as a function of 𝛽0 at the end of the 𝑖-th passage. The vertical dashed grey line marks 𝛽lim. Panel 1 corresponds to passage 1 (bold lines), panel 2 to passage 2 (dashed lines), and panel 3 to …

**Figure 10.** Figure 10: Upper panel: Percentage boosts in the fractions of Ds (dark green) and FAs (navy), between the first and third pericentre passage, as a function of 𝛽0. Bottom panel: Same as above, but accounting for Ms (gold) and stellar ages for a 𝑎b,0 = 0.1 AU, 𝑚 = 4𝑀⊙, 𝑞 = 1 3 exa…

**Figure 11.** Figure 11: Upper panel: Fraction of Ds, FAs, CBs and Ms after 3 passages (dotted lines - green, blue, red and yellow respectively) including period and merger cuts based on our example binary. We compare these to the fraction of Ds, FA and CBs without cuts (thin lines). Lower pa…

**Figure 13.** Figure 13: Similar to [PITH_FULL_IMAGE:figures/full_fig_p014_13.png]

**Figure 14.** Figure 14: Top panel: fractions of HVSs (unbound stars with vej > 1000 km s −1 ) ejected after three passages, using our example binary, as a function of 𝛽0. Before any cuts (dark red), after period cut (Pcut = 108yr) (yellow), after merger cut (dark blue) and after applying bot…

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write newline

" write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

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

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