The S2 orbit and tidally disrupted binaries: indications for collisional depletion in the Galactic center

Shmuel Balberg (HUJI); Yotam Ashkenazy (IASA)

REVIEW 3 major objections 4 minor 1 cited by

The S2 orbit and tidally disrupted binaries: indications for collisional depletion in the Galactic center

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims that the S2 star's near-pure Einstein precession is evidence that destructive stellar collisions deplete the inner Milky Way cluster around Sagittarius A*, and that such depletion is required if stars captured from…

desk verdict A well-executed conditional argument that S2's small mass precession favors collisional depletion—provided the inner cluster is a relaxed, compact, single-mass cusp; the segregation degeneracy is acknowledged but not resolved. read the letter →

arxiv 2412.07491 v2 pith:LEAFQARR submitted 2024-12-10 astro-ph.GA

Yotam Ashkenazy (IASA) , Shmuel Balberg (HUJI) This is my paper · ORCID

classification astro-ph.GA

keywords GalacticcenterS2starSchwarzschildprecessiondestructivestellarcollisionstidaldisruptionofbinariescuspmassSagittariusA*

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

The paper claims that the observed precession of the star S2 around the Milky Way's central black hole is an indirect probe of stellar collisions in the innermost cluster. A relaxed stellar cluster with the standard Bahcall-Wolf profile would put thousands of solar masses inside S2's orbit, producing a retrograde precession that conflicts with the measured, almost purely general-relativistic precession. Adding stars captured from tidal disruptions of binaries makes the conflict worse unless the inner cluster is collisionally depleted. The paper shows that destructive collisions reduce the enclosed mass enough to make the S2 precession consistent with observation, even for binary-capture rates as high as $10^{-5}$ per year. If correct, the S2 orbit is a direct indication that the Galactic center is shaped by collisional depletion rather than by gravitational relaxation alone.

What carries the argument

The load-bearing object is the mass precession formula that converts a spherical extended mass distribution into a retrograde apsidal precession of S2, opposed to the prograde Schwarzschild precession of about 12.1 arcminutes. Around this sit the Bahcall-Wolf power-law cusp as the collisionless baseline, the Fragione-Sari profile for captured stars from binary disruptions, and a collision radius Rcol inside which the collision time is shorter than the relaxation time and destructive collisions evacuate the cluster. The steady-state balance between injection of captured stars and their destruction by collisions yields a characteristic N(<= r) proportional to $r^{{7/4}}$ profile, and the paper confirms these analytic estimates with N-body simulations that include both captured stars and destructive collisions.

What would settle it

A direct measurement that the extended mass inside S2's apocenter exceeds roughly 4000 solar masses, for instance from an observed retrograde mass precession of about 3 arcminutes or more, would falsify the claim that collisional depletion is necessary, because that is the mass the relaxed collisionless cluster predicts. Alternatively, a demonstrated binary-capture rate below about $10^{-6}$ per year would remove the need for collisions to reconcile the S2 precession.

Watch

Extended reading notes

Core claim

The central assertion is that astrometric tracking of S2 places a tight upper limit on the extended mass inside its orbit, and that the only natural way to meet this limit while keeping a dense stellar cluster and a substantial binary-capture rate is destructive stellar collisions. For a dynamically relaxed cluster with a radius of influence around 2 pc, the collisionless steady state gives about 5000 solar masses inside S2's apocenter, yielding a mass precession around -3.85 arcminutes, roughly 2.5 times the current 1-$\sigma$ error. Adding captured stars from binary disruptions at $10^{-5}$ per year increases the enclosed mass to about 1.2 x $10^{4}$ solar masses and the retrograde precession to about -9.2 arcminutes, ruling out the collisionless model at about 6 $\sigma$. When destructive collisions below a collision radius of about 8 mpc are included, the enclosed mass drops to roughly 1900 solar masses and the mass precession to about -1.2 arcminutes, within one $\sigma$ of observation even at the high capture rate. The paper also demonstrates that random fluctuations from the finite number of stars are an order of magnitude too small to replace collisional depletion as a way to reconcile the models with the data.

Load-bearing premise

The paper assumes the stellar cluster around the black hole is dynamically settled and follows a standard steep density cusp that extends in to S2's orbit; if the cluster is actually less settled, more spread out, or holds most of its inner mass in heavy dead stars, the same precession data can be matched without invoking collisions.

Editorial extensions

If this is right

If the conclusion holds, a dense, relaxed stellar cusp with several thousand solar masses inside S2's orbit is excluded, and the inner roughly 10 mpc around the black hole is largely collisionally evacuated.
Binary tidal disruption rates as high as about 10^-5 per year become compatible with S2's observed precession, because destructive collisions cap the mass that captured stars can contribute.
The S2 precession becomes a general mass constraint on all extended matter inside its orbit, including a possible dark matter component, not just on stars.
Continued astrometric monitoring of S2, especially near its apocenter in 2026, should tighten the bound and provide a direct test of whether collisional depletion is really needed.
Destructive collisions should produce bright transient flares near the Galactic center, giving a potentially observable signature of the depletion mechanism proposed here.

Reading between the lines

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

Our inference: if collisional depletion is as efficient as the paper argues, the Milky Way's center becomes a template for other galactic nuclei with resolved stellar orbits, where similar apparent paradoxes between relaxed cusp theory and clean GR precession would point to collisions.
Our inference: a population of stellar-mass black holes in weak segregation could, in principle, mimic the low enclosed mass without collisions, since heavy remnants can carry much of the mass in fewer objects and evade the S2 visibility constraint; distinguishing this from collisional depletion requires multi-mass models and observable collision transients.
Our inference: the model predicts a definite equilibrium between binary capture and collision destruction, so a dedicated search for nuclear collision flares around Sgr A* could independently measure the destruction rate and test the paper's central mechanism.
Our inference: extending the same analysis to other S-stars with different orbital sizes could map the radial extent of the depleted region, effectively measuring the collision radius Rcol observationally.

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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

Short version: this is a solid, clearly written paper that combines existing precession formulae with the authors' collision simulations to make a conditional case for collisional depletion in the Galactic center. The new element is the combination: S2 astrometry as an indirect probe of destructive collisions, strengthened by a careful treatment of finite-number fluctuations. It is not a proof that DCs occur; the paper says as much by using "indications" and by stating the dependence on capture rate.

The central argument holds under the model assumptions: given a relaxed Bahcall-Wolf cusp with Rh = 2.1 pc and capture rates above a few x 1e-6 /yr, collisionless profiles overproduce retrograde precession, while adding DCs brings the prediction within 1 sigma. The fluctuation section is a genuine plus: they run 100 realizations, show scatter of order 10% of the mean, and correctly conclude that granularity cannot rescue the collisionless case.

Soft spots, in order. First, the "necessity" claim is conditional on the cluster being a relaxed, compact, single-mass population. The paper itself (Sec 5.3) cites the GRAVITY Collaboration weak-segregation model with Rh ~ 2.7 pc, sBH-dominated mass, M(<=raS2) ~ 1200 Msun, no DCs, consistent with precession. So DCs are not necessary if sBHs carry the enclosed mass. The paper argues that adding captured stars to that scenario would restore the need for DCs, but this is qualitative—no simulation or analytic calculation combines sBH segregation, captured stars, and no DCs. Since fbh ~ 1e-3 is plausible and poorly constrained, this is a real degeneracy, not a straw man. Second, Rcol = 8 mpc is an ansatz; the results are not extremely sensitive to it, but the completeness of depletion is idealized. Third, the N-body code and error bars are not provided; the paper relies on self-cited prior work, which is acceptable but limits independent checking.

Who this is for: Galactic center dynamicists and anyone using S-star astrometry to constrain the extended mass. It deserves a serious referee; the conditional claim is well-supported and the segregation issue is addressable in revision rather than fatal. I would ask the authors for a quantitative exploration of the sBH-dominated weak-segregation case with captured stars and no DCs, or a clear statement of what observations would break the degeneracy.

Referee Report

3 major / 4 minor

Summary. The paper argues that the observed S2 apsidal precession, which is consistent with pure 1PN Schwarzschild precession, constrains the extended mass enclosed by the S2 orbit, and that standard relaxed stellar cusp models supplemented by stars captured through tidal disruption of binaries overproduce the retrograde mass precession unless destructive collisions deplete the inner cluster. Using analytic power-law estimates and Monte Carlo/N-body profiles from the authors' earlier code, the paper shows that with a compact Rh=2.1 pc single-mass cluster, collisionless models give mass precessions from -3.85 arcmin to -9.21 arcmin depending on the binary capture rate, while models including destructive collisions with Rcol=8 mpc give -0.29 arcmin to -1.20 arcmin, consistent with observations. The paper also argues that finite-number fluctuations cannot reconcile the collisionless models with the data, and concludes that S2 astrometry indicates collisional depletion if the binary capture rate exceeds a few 1e-6 yr^-1, while acknowledging in Sec. 5.3 that a weakly segregated, stellar-mass-black-hole-dominated cluster without collisions can also satisfy the same precession bound.

Significance. If the central claim is established, the paper would be an important, observationally grounded indication that destructive stellar collisions shape the innermost Galactic center, with implications for nuclear cluster modeling, the interpretation of S2 precession, and predictions for nuclear transients. The analytic machinery (Merritt's mass-precession formula, Bahcall-Wolf and Fragione-Sari profiles) is standard and correctly applied, and the simulated profiles reproduce the expected power-law slopes. The finite-N fluctuation analysis in Sec. 4 is a useful quantitative check showing that granularity cannot rescue high-mass collisionless models. The paper is also transparent about its main structural assumptions. However, the central 'necessity' conclusion is conditional on the assumed cluster structure—a dynamically relaxed, single-mass, relatively compact (Rh=2.1 pc) cusp—and on the exclusion of the weakly segregated, sBH-dominated collisionless scenario that the authors themselves cite in Sec. 5.3. The paper therefore establishes a strong consistency argument for collisional depletion in a well-defined subset of cluster models, but not a model-independent proof.

major comments (3)

[Sec. 5.3, Eq. (26)] The central claim that collisional depletion is 'necessary' is not established against the weakly segregated, sBH-dominated collisionless scenario. The paper itself cites GRAVITY Collaboration (2024a) with MH(<=raS2) about 800 Msun, ML(<=raS2) about 400 Msun, Rh about 2.7 pc, and no destructive collisions, which is consistent with the S2 precession bound. The argument that including captured stars makes the main-sequence component non-negligible and therefore forces collisional depletion is qualitative; the Rcrit estimate in Eq. (26) is not evaluated for the combined case of sBH segregation plus Hills-captured stars with no DCs, and no simulation or analytic model is provided for that scenario. Please add a quantitative exploration of the (eta_B, fbh) parameter space for a weakly segregated cluster with captured stars and without DCs, or explicitly restrict the necessity claim to clusters in which main-sequence stars dominate the mass enclosed by the S2 orbit.
[Sec. 2.2 and Sec. 3.2, Eq. (5)] The claimed tension with collisionless models is set up by assuming a dynamically relaxed, single-mass Bahcall-Wolf cusp with Rh=2.1 pc. The paper itself notes in Sec. 2.2 that a collisionless BW cluster with Rh greater than about 2.66 pc is consistent with the same precession bound, and the GRAVITY example in Sec. 5.3 has Rh about 2.7 pc. Since Rh is an input assumption rather than a derived quantity in this analysis, the conclusion that DCs are required should be framed as conditional on Rh approximately less than 2.7 pc and on the validity of the relaxed-cusp assumption. Please quantify how the eta_B threshold for 'necessary' varies with Rh and with plausible deviations from full dynamical relaxation.
[Sec. 2.4, Table 1, Fig. 2] The depletion efficiency, and hence the central numerical results in Table 1 and Fig. 2, is set by the ansatz that collisions with impact parameter b <= R_sun at r <= Rcol are completely destructive while all other collisions are neglected, with Rcol=8 mpc chosen as an example. The paper asserts that the conclusions are general, but it does not show how M(<=raS2) and Delta_omega_M depend on Rcol or on a more realistic collision prescription. Please include a sensitivity study over an observationally motivated range of Rcol, and discuss how partially destructive collisions with a spectrum of outcomes, as in Rose & MacLeod (2024), would shift the required binary capture rate threshold.

minor comments (4)

[Eq. (5)] The relation M(<=raS2) = (raS2/rsS2)^1.25 M(<=rsS2) is stated without noting that it holds only for the pure power-law BW profile; please state that explicitly.
[Sec. 2.4] The phrase 'removing mass of from a system' contains a duplicated word and should read 'removing mass from the system'.
[Sec. 3.1, Fig. 1 caption] The caption contains repeated words ('injected at at rate') in two places; these should be corrected.
[Sec. 2.3] The statement that eta_B about 1e-5 yr^-1 'can be ruled out' is stronger than the quantitative statement in Sec. 3.2, where the same case is described as more than six standard deviations under the assumed cluster model; please qualify the statement because the sigma refers to the observational uncertainty under a specific structural assumption.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the S2 precession constraint is external GRAVITY astrometry, and the analytic mass-precession estimates rest on published formulas rather than on the paper's own fitted parameters.

full rationale

The paper's derivation chain is: (1) GRAVITY Collaboration astrometry independently constrains S2's apsidal precession to be consistent with 1PN general relativity; (2) Merritt's analytic formula translates a spherical density profile into a retrograde mass precession; (3) Bahcall-Wolf and Fragione-Sari analytic profiles provide the no-DC baseline; (4) the authors' own N-body code generates profiles with and without destructive collisions and with and without binary-capture injection; (5) the predicted mass precession is compared to the observed bound. No parameter is fitted to the S2 precession: Rh = 2.1 pc, Rcol = 8 mpc, and eta_B are chosen or varied, not calibrated. Rcol is introduced explicitly as an ansatz with physical motivation (Rc > raS2), and the paper checks robustness against the independent Rose & MacLeod simulation. Self-citations to Balberg & Yassur (2023) and Balberg (2024) supply the code and earlier statements that DCs deplete the inner cluster, but the central tension for collisionless models is derived analytically from external formulas (Fragione & Sari 2018; Merritt 2013) and then supported by the N-body runs. The paper itself identifies the weakly segregated sBH-dominated cluster as a collisionless alternative in Sec. 5.3, so the 'necessity' claim is conditional on an unresolved astrophysical degeneracy; that is a correctness or assumption concern, not a circular reduction. The self-citations are not load-bearing in the sense required for a circularity finding, and no equation is redefined as its own output.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The analysis combines standard precession formulas with several model choices that set the baseline: a relaxed Bahcall-Wolf cusp, log-normal binary separations, a hand-set collision radius, a single solar-mass population, and a varied capture rate. These choices are not fitted to the measured precession, but they determine how large the no-collision tension is, so they carry much of the argument.

free parameters (5)

Rcol = 8 mpc
Collision radius below which stars are assumed completely destroyed; chosen in Sec. 2.4 as an example with Tcol/T2B~0.1. It directly sets the depleted mass enclosed by S2's orbit and hence the predicted mass precession.
Rh = 2.1 pc in simulations; analytical examples up to 3 pc
Radius of influence assumed for simulated profiles in Sec. 3.1. A compact Rh creates the no-collision tension; larger Rh weakens it, as the authors state.
aB,max = 0.5 au
Upper cutoff for binary separations of captured stars (Sec. 2.3), determining the fraction of captured stars with orbits inside S2's apocenter. Set conservatively but uncertain.
m_star = 1 M_sun
Single-mass population assumed throughout; controls collision times, relaxation times, mass precession amplitude, and fluctuation scaling.
eta_B = 10^-7 to 10^-5 yr^-1
Binary capture rate is a scenario parameter, not fitted. The central claim that collisions are necessary above a few 10^-6 yr^-1 depends on this parameter.

assumptions (6)

domain assumption Inner cluster is dynamically relaxed (Bahcall-Wolf steady state)
Sec. 2.2: 'We hereafter assume that the cluster is dynamically relaxed.' This sets the no-DC baseline profile that generates the tension.
domain assumption Steady state cusp profile N(<=r) ~ r^{5/4} (alpha=7/4) for single-mass stars
Used to estimate M(<=raS2) and the Rh limit in Eq. (5). Relaxation may be incomplete near Sgr A*.
domain assumption Binary separations follow log-normal dN/daB ~ 1/aB up to aB,max=0.5 au
Sec. 2.3: determines the CS radial distribution; a different mass function or survival cutoff changes the fraction of captured stars inside S2.
ad hoc to paper Collisions with b <= R_sun at r <= Rcol are completely destructive; other collisions are neglected
Sec. 2.4 ansatz; simplified treatment of partial collisions, mergers, and impact parameter. The depletion efficiency and MP output depend on it.
domain assumption S2 is a test particle; the extended mass is spherical and smooth
Used in Secs. 2 and 3; the fluctuation section partially relaxes smoothness, and Sec. 5 partially relaxes the single-mass spherical assumption.
standard math Mass precession formula Eq. (2) from Merritt 2013 is valid
Used throughout as the orbit-averaged result for a small extended mass.

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Cite this review

Pith. "Pith review of The S2 orbit and tidally disrupted binaries: indications for collisional depletion in the Galactic center." pith.science (2026). https://pith.science/paper/LEAFQARR

@misc{pith2026241207491,
  author       = {Pith},
  title        = {Pith review of: The S2 orbit and tidally disrupted binaries: indications for collisional depletion in the Galactic center},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LEAFQARR}},
  note         = {Machine review of arXiv:2412.07491}
}

abstract

The properties of the stellar cluster surrounding Sagittarius A* can be assessed indirectly through the motion of the S-stars. Specifically, the current accuracy to which the prograde precession of the S2 star is measured allows to place significant constraints on the extended mass enclosed by its orbit. We suggest that high velocity destructive collisions (DCs) offer a natural mechanism for depleting the mass inside the S2 orbit, thus allowing to reconcile the measured precession and the existence of a dense stellar cluster. Such a solution is especially necessary when considering that stars are supplied to the inner part of the cluster by both dynamical relaxation and by stars being captured in tight orbits during tidal disruption of binaries. We use analytic arguments and results from simulations to demonstrate that in order to obtain a precession that is consistent with observations, collisional depletion is necessary if the capture rate is greater than a few $10^{-6} yr^{-1}$. We also show that fluctuations arising from the finite number of stars cannot serve as an alternative to DCs for generating consistency with the observed S2 precession. We conclude that astrometric observations of the S-stars provide a meaningful indication that the inner part of our galactic center is shaped by collisional depletion, supporting the hypothesis that DCs occur in galactic nuclei at an astrophysically significant rate.

Figures

Figures reproduced from arXiv: 2412.07491 by the authors.

**Figure 2.** Calculated mass precession, ∆ωM = ∆ωtot − ∆ωS P, of S2 resulting in stellar profiles calculated numerically as a function of the assumed injected rate of CSs, ηB. Shown are the results for simulations that do not allow DCs (black) and those that include DCs at r ≤ Rcol = 8 mpc (red). Also shown is the effective 1σ error estimated for the observationally inferred precession of S2. level. Obviously, the problem worsen… view at source ↗

**Figure 3.** Calculated mass precession, ∆ωM = ∆ωtot − ∆ωS P, of S2 for schematic profiles as a function of the mass enclosed by raS2. Shown are curves for (i) a BW profile dominated by twobody relaxation (black); (ii) an FS (Fragione & Sari 2018) profile dominated by captured stars following tidal disruption of binaries (red); and (iii) the Plummer (1911) profile (blue). Destructive collisions are not accounted for in these … view at source ↗

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Forward citations

Cited by 1 Pith paper

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On the Orbital Effects of Stellar Collisions in Galactic Nuclei: Tidal Disruption Events and Ejected Stars
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Stellar collisions in galactic nuclei can deflect stars into the supermassive black hole's tidal radius or eject them at speeds up to the hypervelocity regime, producing a small but observable population of TDEs and r...

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