Amplified capture rate of dark matter in compact binaries and constraints on bosonic dark matter from GW170817

David O'Neill; J\'anos Tak\'atsy; Johan Samsing; Lorenz Zwick

REVIEW 3 major objections 5 minor 130 references

Amplified capture rate of dark matter in compact binaries and constraints on bosonic dark matter from GW170817

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper shows that neutron stars in binaries capture dark matter four to five times faster than isolated stars, tightening bosonic dark-matter bounds from GW170817.

desk verdict Plausible new amplification factor for DM capture in binaries, worth refereeing, but the central factor rests on an unsupported five-order-of-magnitude extrapolation that needs to be shown. read the letter →

arxiv 2509.03272 v1 pith:OAGFQTSX submitted 2025-09-03 astro-ph.HE gr-qchep-ph

János Takátsy , Lorenz Zwick , David O'Neill , Johan Samsing This is my paper · ORCID

classification astro-ph.HEgr-qchep-ph

keywords darkmattercaptureneutronstarbinariesGW170817bosonicdynamicalfrictionrestrictedthree-bodyproblemgravitationalwaveconstraintsamplificationfactor

topics Dark Matter

open problems Dark Matter

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 argues that dark matter accretion onto a compact object is not an isolated-star process: in a binary, dark-matter particles on chaotic three-body orbits repeatedly pass close to the neutron stars, so the effective capture flux is amplified by a factor of about 4–5 for circular binaries, mass ratios above roughly 0.3, and dark-matter velocity dispersions below the binary orbital speed. Using this amplification, the paper tightens the upper bound on the scattering cross section of non-annihilating bosonic dark matter with nucleons, using the observed binary neutron star merger GW170817 as the anchor. It further shows that dynamical friction from ambient dark matter limits how much dark matter neutron stars in binaries can accumulate before merger, capping the accreted mass fraction at roughly one part in a thousand. A sympathetic reader would care because most neutron stars that merge spent their lives in binaries, so the isolated-star rates used in earlier constraints may have underestimated the dark-matter exposure by about a factor of four.

What carries the argument

The load-bearing object is the restricted three-body scattering problem: test particles with a fixed velocity at infinity are injected toward a circular binary of masses $m_1,m_2$, and their orbits are integrated numerically, recording close encounters within the Hill sphere of each component. Because the test-particle orbits are non-integrable, a single particle can have multiple close encounters with the same star or with both stars, and the resulting flux ratio $R_q=\Sigma_b/\Sigma_s$ is the amplification factor. Gravitational dynamics is scale-free, so $R_q$ depends only on the dimensionless ratio $v/V_b$ of dark-matter velocity to binary orbital velocity, not on the individual values. The amplification is then folded into the standard capture-rate formula for neutron stars and integrated along the standard gravitational-wave inspiral for circular binaries, while the same scattering machinery supplies the dynamical-friction hardening rate that caps the total accreted mass.

What would settle it

Measure the eccentricity distribution of merging neutron-star binaries from gravitational-wave waveforms: if a substantial fraction merge with eccentricity larger than about 0.1 at frequencies where the orbital velocity is comparable to the dark-matter velocity dispersion, the circular-orbit integration fails as a description of the accretion history. Equivalently, a single old neutron-star merger in a high-dark-matter-density host whose delay time and dark-matter profile are well measured would let the bound be recomputed from event-specific parameters rather than the assumed 0.1 GeV/cm$^3$ and 220 km/s values, checking whether the factor-of-four tightening survives.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the accretion flux of dark matter on neutron stars in a circular binary is not the sum of two isolated fluxes but a larger flux described by an amplification factor $R_q(v/V_b)$, which saturates near 4.5 when the dark-matter velocity is small compared with the binary orbital velocity and drops to unity when $v\gg V_b$. The factor is computed with few-body Monte Carlo scattering, fitted empirically as $R(x)=1+R_0[1+(x/w)^6]^{-1/2}$, and shown to be nearly constant over many orders of magnitude in encounter radius for $r\ll a$. Integrated over a gravitational-wave-driven inspiral, this gives about a fourfold increase in the number of captured particles for binaries that merge in roughly a Hubble time with a standard velocity dispersion of 220 km/s. From that increase, the paper derives a tighter upper bound on the bosonic dark-matter–nucleon scattering cross section from GW170817, and derives an upper bound of $\lesssim10^{-3}$ on the dark-matter mass fraction inside neutron stars at merger, enforced by the dynamical-friction drag of the ambient dark matter on the binary orbit.

Load-bearing premise

The calculation assumes the neutron stars spend essentially their whole lifetime as a circular binary whose separation shrinks only by gravitational waves and dark-matter dynamical friction; if real merger progenitors have significant eccentricity, form late from previously isolated neutron stars, or are hardened by other environmental processes, the integrated amplification and the derived constraints shift.

Editorial extensions

If this is right

Dark-matter capture onto neutron stars in merging binaries is roughly four to five times the isolated-star rate over the inspiral, so earlier constraints built on isolated stars are conservative by about that factor.
The upper bound on the bosonic dark-matter–nucleon scattering cross section derived from the observed binary neutron star merger GW170817 is correspondingly tighter than the isolated-star bound for the same host-galaxy assumptions.
The accreted dark-matter mass fraction in binary neutron stars at merger is at most about $10^{-3}$, even in extreme dark-matter spikes, because dynamical friction drives the binary to merge before much mass can accumulate.
The dynamical-friction cap applies to fermionic as well as bosonic dark matter, since it does not rely on collapse or annihilation inside the star.
For the highest ambient dark-matter densities, the dynamical-friction dephasing of the gravitational-wave signal could become observable with upcoming space-based detectors.

Reading between the lines

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

The authors apply the amplification to neutron stars, but the mechanism is purely gravitational and scale-free, so the same factor should multiply dark-matter capture in other compact or stellar binaries, such as white-dwarf binaries and black-hole–neutron-star binaries, whenever the binary spends a Hubble time at separations where $v_\chi\lesssim V_b$.
They leave implicit that the amplification also raises the effective dark-matter exposure of old binaries in dense environments; a statistical sample of mergers with measured host-galaxy delay times could convert the single-event GW170817 bound into a population-level constraint.
A testable extension is to check eccentric binaries: if a population of neutron-star mergers is found with non-negligible eccentricity, the circular-orbit integration used here would need to be repeated, and the resulting integrated amplification could be either larger or smaller depending on how much time the binary spends at wide separations.
Because the amplification is geometric, it applies to any weakly interacting particle captured by neutron stars, not just bosonic ones; the authors note this for the mass-fraction cap, but the cross-section improvement would also propagate to other capture-based probes such as kinetic heating.

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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 result is the ~4-5 amplification factor for DM capture in circular compact binaries and the resulting boost to bosonic DM bounds from NS mergers. The paper is the first to quantify this for DM on neutron stars and to propagate it into cross-section constraints, and it does that cleanly. The MC setup is standard restricted three-body scattering in the spirit of Quinlan, described in enough detail to follow, and the empirical fit is simple and sensible. The timescale checks on ZKL, flybys, and Bondi accretion are useful, and the authors are honest about the circular-orbit limitation in the Discussion. That part is not hidden.

The soft spots are real but not necessarily fatal. The biggest is the r/a extrapolation. Encounters are recorded at r < 0.1 r_H, which for equal-mass NSs is about 0.05a, while the NS surface is roughly 10^-6 a. That is five orders of magnitude, and there is no plot, table, or error estimate showing that R_q has actually converged over that range. The scale-free argument fixes the dependence on v/V_b but not a possible residual dependence on r/a. Since Eq. (20) and all the derived constraints scale linearly with R_q, even a 20% error in that extrapolation shifts the bounds by 20%. The stress-test note is on target: the authors assert constancy without showing it, and the absence of code or data makes the check impossible right now.

Smaller issues: Fig. 2 has no error bars, the fit parameters in Table I have no uncertainties, only two mass ratios are simulated, and the interpolation to q > 0.3 is an assumption. None of these is disqualifying, but they should be quantified. The circular-orbit caveat is a real astrophysical limitation, especially for late-formed binaries, but the authors flag it explicitly. The single-scattering capture model is standard for the mass range considered, and the GW170817 density choice is conservative. The citation pattern is fine; the relevant stellar-dynamics and TDE literature is cited, and the self-citations are not load-bearing.

Who is this for? People working on DM capture in compact objects and on using NS mergers as DM probes. It deserves a serious referee, not a desk reject. I would send it out with a specific request: show the convergence of R_q over radius with error bars, or release the simulation code and data, and either add a third mass ratio or state clearly how the interpolation error affects the constraints.

Referee Report

3 major / 5 minor

Summary. The paper argues that the flux of dark matter particles onto a stellar-mass compact object is amplified when the object is in a circular binary, because test-particle orbits in the restricted three-body problem are chaotic and can undergo repeated close encounters. The authors measure this amplification R_q(v/V_b) with a Monte Carlo simulation for two mass ratios (q=1 and q=0.28), fit the result to an empirical curve saturating at R_0 ~ 3.5-4.0, and then apply the factor to the DM capture rate of neutron stars in inspiraling binaries. Using this amplified capture rate, they derive updated upper bounds on the DM-nucleon scattering cross section from the non-collapse of the GW170817 binary, and they derive a cap on the accreted DM mass fraction enforced by dynamical friction from ambient DM. The main quantitative claim is that the amplification factor is approximately 4-5 for circular binaries with q ≳ 0.3 and small DM velocity dispersion, and that this tightens previous bosonic DM constraints by the same factor.

Significance. If the central amplification factor is correct, the paper adds a genuinely new physical ingredient to DM capture calculations: binary gravitational scattering can enhance the effective accretion flux beyond the isolated-star value. The simulation setup follows the established method of Quinlan (1993) and is described in enough detail that the procedure is credible. The amplification factor is computed independently of the DM-nucleon cross section, so there is no circularity in the resulting constraints. The GW170817-based bounds and the dynamical-friction mass-fraction cap are concrete, falsifiable predictions. The main risks are the unsupported small-radius extrapolation of R_q and the absence of statistical or systematic error estimates on the fitted amplification curve; both directly affect the claimed constraints. No code or data release is mentioned, which limits reproducibility of the central numerical result.

major comments (3)

[Sec. II A, Eq. (7)] The constancy of R_q as a function of r/a is asserted but not demonstrated. The simulation records close encounters at r < 0.1 r_H, and for an equal-mass NS binary r_H = a (m_i/3M)^{1/3} ~ 0.55 a, so 0.1 r_H ~ 0.055 a, whereas the NS capture surface is at r_NS/a ~ 10^{-6}. The scale-free argument fixes only the dependence on v and V_b at fixed r/a; it does not exclude an additional r/a dependence at intermediate radii. Since Eqs. (17) and (20) and Figs. 4-5 all scale linearly with R_q, an unquantified 20% change in the extrapolation would directly shift the derived cross-section bounds and the DM-fraction cap. Please provide a figure or table showing R_q as a function of r/a for several v/V_b values down to the smallest resolved radius, together with statistical uncertainties, and state the range over which the plateau is actually verified.
[Fig. 2, Table I] The empirical fit parameters R_0 and w are quoted without uncertainties, and the data points in Fig. 2 carry no error bars. Because the amplification factor enters as a linear prefactor in Eq. (17), the Monte Carlo statistical error in R_0 and the systematic uncertainty of the fitting form in Eq. (10) should be propagated into the cross-section bounds in Fig. 4. Additionally, the abstract's claim for q ≳ 0.3 rests on only two simulated mass ratios, q = 1 and q = 0.28; if that claim is retained, the authors should either simulate additional mass ratios or provide an explicit interpolation uncertainty for the q-dependence.
[Discussion (final paragraph), Sec. IV] The final Discussion correctly acknowledges that the calculations assume negligible eccentricity and that eccentricity can significantly change the GW inspiral time. However, the GW170817 cross-section constraint and the DM-fraction limit in Figs. 4-5 are derived under the circular-orbit, GW-only inspiral assumption. Since the title highlights the GW170817 constraint, the authors should quantify how the integrated amplification changes for moderate initial eccentricities, for example by integrating Eq. (20) using Peters' eccentric-orbit inspiral rate, or explicitly restrict the title claim to binaries that circularize early.

minor comments (5)

[Sec. IV A] In the sentence 'it is a topic of strong debate wether NS binaries', 'wether' should be 'whether'.
[Fig. 2] The figure would benefit from explicit axis labels for x = v/V_b and y = R_q, and a legend identifying the error bars or noting their absence.
[Table I] The table should report the uncertainties in R_0 and w obtained from the fit, and the text should state the reduced chi-squared or equivalent goodness-of-fit measure.
[Sec. II A] The sentence 'All the orbits are unstable and thus eventually become expelled except for a set of initial condition with a volume of zero in the initial parameter space' is too strong given that integrations are truncated at 10^6 steps; please clarify how the truncation affects the recorded encounter statistics.
[Sec. IV, abstract] The abstract refers to mass ratios q ≳ 0.3, but Section IV restricts the constraints to binary NSs with q = 1; aligning the wording would avoid overstating the coverage.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the amplification factor is a Monte Carlo output, and the GW170817 and collapse constraints use external inputs without author overlap.

full rationale

The derivation chain is self-contained. The central amplification factor R_q(v/V_b) is obtained in Sec. II A from Monte Carlo restricted-three-body scattering simulations, recorded as close-encounter fluxes and summarized by an empirical fit (Eq. 10, Table I); it is not fitted to any quantity derived from GW170817 or from the collapse thresholds. The subsequent capture-rate formula (Eq. 17) combines this simulated flux with the independently sourced single-scattering optical-depth threshold and collapse thresholds from Singh et al. [11], whose authors do not overlap with the present paper. The GW170817 bound (Sec. IV C 1) only inserts external astrophysical inputs (density, velocity dispersion, delay time) into the same formula. The maximum accreted fraction (Sec. IV D) uses the same simulated R_q and a dynamical-friction hardening rate from Quinlan [93], again external. The only author-overlapping citations (refs. 122-125) appear in a peripheral discussion of possible dephasing detectability and are not load-bearing for any derived constraint. A numerical-support gap exists in the assertion that R_q is constant from r < 0.1 r_H down to the NS radius without shown convergence data in the paper, but this is an extrapolation and reproducibility concern, not circularity: no equation defining R_q encodes the target observable, and no fitted parameter is renamed as a prediction.

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

The central claim rests on the numerical amplification factor, which itself rests on the restricted-three-body scattering model and a Maxwell-Boltzmann DM halo. The cross-section and fχ constraints additionally import collapse thresholds from [11] and a constant dynamical friction factor from [93]. The only genuinely fitted quantities are R0 and w (the empirical shape of Rq); the environmental inputs ρχ and vχ are chosen conservatively.

free parameters (5)

R0 (amplification plateau) = 3.45 for q=1; 4.00 for q=0.28
Empirical fit parameter in Eq. (10) set to the simulated low-velocity plateau of Rq.
w (velocity falloff scale) = 0.59 for q=1; 0.51 for q=0.28
Empirical fit parameter in Eq. (10) setting the v/Vb scale where Rq drops toward unity.
H (dynamical friction factor) = ≈28
Constant numerical factor in the hardening rate Eq. (41) taken from the stellar-dynamics literature; assumed independent of vχ.
Dark matter density at GW170817 location = 0.1 GeV/cm3
Hand-chosen conservative value for NGC 4993 based on Ref. [121]'s central density; normalizes the cross-section bound.
Dark matter velocity dispersion = 220 km/s
Standard halo value chosen as conservative; enters both the capture rate and the amplification factor integration.

assumptions (7)

domain assumption Test particles in the restricted three-body problem are non-interacting and do not perturb the binary orbit.
Section II A fixes the binary on a circular orbit and integrates test-particle trajectories; this ignores back-reaction from DM onto the binary except in the separate dynamical friction model.
domain assumption The DM velocity distribution is Maxwell-Boltzmann with dispersion vχ.
Eq. (5); captures the standard halo velocity ansatz but may be inaccurate in DM spikes or near the galactic center.
domain assumption The capture rate factorizes as F·min(σ/σth,1) with σth≈2e-45 cm2 and single-scattering energetics valid for mχ≲10^5-10^6 GeV.
Sec. III, Eqs. (14)-(17); imported from the NS capture literature, and assumes each passage through the star is an independent scattering trial.
domain assumption The binary is circular and spends most of its lifetime in the GW-driven inspiral phase.
Sec. IV A assumes tH-dominated inspiral; Discussion says finite eccentricity changes the inspiral time significantly, so the assumption is load-bearing.
domain assumption Accreted non-annihilating bosonic DM collapses the NS when N_capt reaches NBH from Eqs. (34)-(36), with thresholds taken from Ref. [11].
Sec. IV B; the collapse criterion is a physical model from prior literature, not derived in this paper.
domain assumption Rq depends only on v/Vb and is constant for r/a over many orders of magnitude, by the scale-free property of gravity.
Sec. II, Eqs. (7)-(9); this extrapolates the Monte Carlo encounter counts to NS-radius scales.
domain assumption The dynamical friction hardening rate follows Eq. (41) with H≈28 for vχ/Vb≲0.5.
Sec. IV D, based on Quinlan [93]; the assumption of constant H is used for the fχ bound.

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Cite this review

Pith. "Pith review of Amplified capture rate of dark matter in compact binaries and constraints on bosonic dark matter from GW170817." pith.science (2026). https://pith.science/paper/OAGFQTSX

@misc{pith2026250903272,
  author       = {Pith},
  title        = {Pith review of: Amplified capture rate of dark matter in compact binaries and constraints on bosonic dark matter from GW170817},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OAGFQTSX}},
  note         = {Machine review of arXiv:2509.03272}
}

abstract

The accretion of dark matter (DM) onto compact objects and the potential gravitational collapse of neutron stars due to this accretion has become a promising indirect probe of DM properties, complementing terrestrial experiments. We show that the accretion flux of DM on stellar objects is amplified in binary systems due to the complex gravitational interaction of said particles with the binary. We perform few-body Monte Carlo simulations to show that this amplification factor is $\sim4-5$ for circular binaries, small DM velocity dispersions and mass ratios $q\gtrsim0.3$. We use this factor to improve previous constraints on the scattering cross section of non-annihilating bosonic DM with baryonic matter, and derive upper bounds on this cross section from the observation of the binary NS merger associated with GW170817. We also show that the maximally accretable mass fraction of DM by binary NSs is $\lesssim10^{-3}$, even for extreme DM densities only possible in DM spikes, due to the dynamical friction exerted by the ambient DM.

Figures

Figures reproduced from arXiv: 2509.03272 by the authors.

**Figure 2.** FIG. 2. The amplification factor of the cross section for DM [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. The averaged amplification factor [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4. Upper bounds on the microscopic scattering cross [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: FIG. 5. Upper bound on the mass fraction of accreted DM [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

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