Galactic double neutron stars as dual-line gravitational-wave sources: Prospects with LISA and Cosmic Explorer

Lijing Shao; Wen-Fan Feng

REVIEW 4 major objections 4 minor 86 references

Galactic double neutron stars as dual-line gravitational-wave sources: Prospects with LISA and Cosmic Explorer

T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Galactic double neutron stars can act as dual-line gravitational-wave sources, and joint LISA–Cosmic Explorer observations could measure the neutron star moment of inertia to about 8%.

desk verdict A useful dual-line DNS forecast whose central waveform terms are asserted rather than derived; the population synthesis is transparent, but the headline 8% accuracy needs its caveats restored. read the letter →

arxiv 2505.05900 v2 pith:FSXMEA5G submitted 2025-05-09 gr-qc astro-ph.HE

Wen-Fan Feng , Lijing Shao This is my paper · ORCID

classification gr-qcastro-ph.HE PACS 04.30.-w95.55.Ym97.60.Jd

keywords doubleneutronstarsgravitationalwavesLISACosmicExplorercontinuousstarmomentofinertiaprecessingtriaxialpopulationsynthesis

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

Double neutron stars in the Milky Way can emit gravitational waves on two very different frequency scales at once: the binary orbit radiates in the millihertz band, where LISA can see it, and each triaxially deformed, precessing neutron star radiates near its spin frequency and its second harmonic, where next-generation ground detectors like Cosmic Explorer are sensitive. The paper extends the waveform model for such spinning neutron stars to second order in the two structural parameters that control nonsphericity and wobble, then plugs in a simulated population of 35 LISA-detectable DNS systems. It predicts that a 4-year Cosmic Explorer search directed at these LISA sources will recover 6 spinning components under log-uniform parameter sampling and 22 under uniform sampling, with median signal-to-noise ratios around 20–30. For systems detected in both bands, the three amplitudes near twice the spin frequency can be inverted to solve for the neutron star's nonsphericity and wobble angle, and the moment of inertia can be inferred to roughly 8% relative accuracy. If right, this gives a direct route from gravitational-wave data to neutron star interior physics.

What carries the argument

The load-bearing object is the six-component waveform of a triaxially deformed neutron star undergoing geodetic precession in a binary, written as h+ and h× sums oscillating at Ωr+Ωp, Ωr−Ωp, Ωr+3Ωp, 2Ωr, 2(Ωr+Ωp), and 2(Ωr−Ωp), with amplitude factors h2a0, h2b0, and h2c0 at the 2Ωr family. The crucial identities are the inversion formulas $\gamma = 2\sqrt{(h_{2b0}-h_{2c0})h_{2c0}}/(h_{2a0}+4h_{2c0})$ and $\kappa = h_{2c0}/[4(h_{2a0}+4h_{2c0})]$, plus the moment-of-inertia error propagation that combines the SNRs of h2a, h2c, and the LISA DNS SNR. These formulas convert line amplitudes into structural parameters, which is what lets a dual-line detection measure I3.

What would settle it

Direct a 4-year Cosmic Explorer search at the sky position, orbital frequency, and eccentricity of the loudest LISA-resolved Galactic double neutron star from the same population model; if no h(2a) line appears above an SNR of 7 with the amplitude predicted by Eq. (20a), the optimistic count of 6–22 and the waveform amplitudes behind it are falsified for that source.

Watch

Extended reading notes

Core claim

The paper's central claim is that a resolved double neutron star binary is simultaneously a millihertz gravitational-wave source and a source of two high-frequency line families, and that observing both bands with LISA and Cosmic Explorer turns the high-frequency amplitudes into a measurement of neutron-star structure. Concretely, the paper forecasts that among the ~35 DNS systems LISA would resolve in 4 years under the optimistic population model, 6 (log-uniform sampling) or 22 (uniform sampling) spinning neutron star components would also be detected by Cosmic Explorer, with median SNR between roughly 20 and 30. It further claims that once the h(2a), h(2b), and h(2c) lines are measured, the nonsphericity κ and wobble angle γ can be algebraically inverted from amplitude ratios, and with the LISA-derived distance the moment of inertia I3 follows with relative accuracy ~8%. The 8% figure is presented as insensitive to the two sampling choices; detection counts are not.

Load-bearing premise

The forecast rests on treating the neutron star's nonsphericity κ and wobble angle γ as independent and expanding the waveform to second order in both; if the new O(γκ) and O($κ^{2}$) terms in the polarization amplitudes are wrong, the inversion formulas for γ, κ, and I3 fail and the detection counts shift.

Editorial extensions

If this is right

A 4-year Cosmic Explorer directed search pointed at the ~35 LISA DNS positions should yield a few to a few dozen h(2a) detections, with central values 22 (uniform) and 6 (log-uniform), so the two sampling priors can be empirically distinguished by counting.
The h(1b) and h(1c) sidebands are predicted to be below threshold for both sampling schemes, meaning the usable dual-line information sits in the 2Ωr family and the h(1a) line.
When h(2a) and h(2c) are both measured, the relative moment-of-inertia error is centered at 8% with a 16%–84% spread from 4% to 13%, independent of the sampling choice.
If multiple dual-line DNS systems are detected, a Bayes factor on the number counts can decide whether NS structural parameters follow a log-uniform or uniform distribution.
Under the more conservative LISA model with only 8 DNS detections, the dual-line counts shrink to roughly a quarter of the optimistic values, so the 6–22 forecast scales with the LISA catalog size.

Reading between the lines

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

Editorial extension: the same amplitude inversion could be applied to any precessing triaxial neutron star with two detected sidebands, even without LISA, so the method generalizes to isolated pulsars if h(2b) and h(2c) are ever seen.
Editorial extension: the SNR-only error budget ignores covariances among κ, γ, and I3; a full Bayesian recovery on simulated data would likely widen the 8% error, so the quoted accuracy is an idealized lower bound.
Editorial extension: LISA and TianQin both cover the millihertz band, so the orbit-finder role in the dual-line strategy could be played by either space mission, and the same population forecast could be tested against future LISA mock data challenges.

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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

Honest take: this is a competent scenario forecast, not a breakthrough. The genuinely new pieces are the O(γ², κ²) extension of the spinning-NS waveform (including the O(γκ) and O(κ²) terms) and the integration of the Wagg et al. LISA DNS catalog with a population of spinning NS components. The Monte Carlo work is transparent: 1000 iterations, uniform vs log-uniform priors, detector antenna patterns, and the main caveats are openly stated (35 systems is optimistic, only ~60% of DNSs are reliably identifiable, conservative models give ~8). The spin-period/eccentricity fit to the Dewi et al. data is a sensible way to assign spins.

The soft spot is exactly where the reader and stress-test put it. Eqs. (4)-(5) present the extended waveform without derivation. Since Eq. (21) inverts those amplitudes to solve for γ and κ, and Eq. (23) propagates them into a moment-of-inertia accuracy, any missing or miscomputed term at the same order changes the conclusions. The references [17,52,59] point to the formalism, but the specific reduction to independent κ,γ is not shown. This is load-bearing and fixable: the authors should either supply the derivation or verify the coefficients numerically against a known code.

Two smaller issues. The selection rule in Sec. III B is worded confusingly — 'exclude cases where the combined SNR exceeds 7' cannot be what they mean, given the counts in Table II; I assume they meant exclude cases where no individual component reaches threshold. And Table I omits the equatorial ellipticity ε that enters κ through Eq. (14), so the κ prior is under-specified. Both are easy fixes. Also, the abstract's ~8% I3 accuracy applies only to the subpopulation where both the h(2a) and h(2c) lines are detected; the joint count is smaller than the individual counts in Table II, so the claim needs that qualifier.

No circularity or fatal error. The algebra in Eqs. (20)-(21) is internally consistent, and the paper is honest about the caveats. The citation pattern looks fine — self-citations here are to prior work that this paper directly extends.

Who it's for: CW search strategists and anyone interested in a concrete list of targets for LISA + Cosmic Explorer. The population part is useful even if the waveform details are pending. But I would not cite the waveform extension until the derivation is out.

Recommendation: send to peer review. It deserves referee time, with the request that the derivation of Eqs. (4)-(5) be added or verified, and the selection rule and ε prior clarified. If the expansion holds up, this is a solid forecast; if not, the numbers shift. A serious referee can sort that out.

Referee Report

4 major / 4 minor

Summary. The paper studies Galactic double neutron star (DNS) systems as dual-line gravitational-wave sources, combining low-frequency binary inspiral signals detectable by LISA with high-frequency continuous waves from individual spinning, precessing, triaxially deformed neutron stars detectable by Cosmic Explorer. The authors extend a previously published waveform expansion to second order in the structural parameters κ (nonsphericity) and γ (wobble angle), treating them as independent, and use a LISA-detectable DNS population from Wagg et al. (2022) to synthesize a spinning-neutron-star population under uniform and log-uniform priors. They report detectable counts and SNRs for the h(1a), h(2a), h(2b), and h(2c) components, derive algebraic inversion formulas for κ and γ from the h(2x) amplitudes, and estimate a median relative moment-of-inertia accuracy of about 8%.

Significance. If the waveform expansion is correct, the paper supplies a concrete, testable pathway for using dual-line DNS detections to constrain neutron-star internal structure, and it provides an explicit comparison of how prior choices affect detectability forecasts. The inversion formulas in Eq. (21) are transparent and internally consistent, and the Monte Carlo framework is clearly described. However, the central quantitative claims—the detection counts, the SNR distributions, and the 8% moment-of-inertia accuracy—depend directly on waveform terms that are asserted without derivation, and on a population-selection rule that is stated ambiguously. The paper would be valuable after these load-bearing issues are resolved, but in its current form the headline numbers are not yet fully supported.

major comments (4)

[Sec. II B, Eqs. (4)-(5) and Sec. III C, Eq. (20)] The waveform expansion is the load-bearing element of the paper, yet it is presented without derivation. The inversion formulas in Eq. (21) and the error budget in Eq. (23) are algebraic consequences of the amplitude coefficients in Eq. (20), which in turn come from the expansions in Eqs. (4)-(5). A missing, mis-normalized, or incomplete term of the same order—for example, an O(γ^2) correction to h(2a), an O(γκ) term in h(2c), or a different O(κ^2) coefficient in h(2b)—would directly bias the inferred κ, γ, and I3. Please provide a derivation of the independent-κ,γ expansion starting from Refs. [17,52,59], or at least a detailed consistency check that verifies completeness to O(γ^2,κ^2), including the limit ε→0, the limit κ~O(γ^2), and order-by-order comparison with Ref. [17].
[Sec. III B, selection rule] The selection rule for the detectable-source counts is ambiguous. The sentence "we exclude cases where the combined SNR of all waveform components exceeds 7" appears to remove the loudest cases, while the following clause suggests that the intended exclusion is of cases where only the combined SNR is above threshold but no individual waveform component is detectable. The counts in Table II and the moment-of-inertia accuracy sample in Fig. 5 depend directly on this choice, so the exact criterion used in the Monte Carlo simulation needs to be stated precisely.
[Sec. II C 2, Eq. (14), and Table I] Table I lists the moment of inertia I3, the oblateness ǫ, and the wobble angle γ, but it does not list the equatorial ellipticity ε, even though Eq. (14) defines κ in terms of both ε and ǫ. Without specifying how ε is sampled—its range and whether uniform or log-uniform sampling is applied—the κ prior is not fully defined and the population simulation is not reproducible. Please add ε to Table I and state its sampling distribution explicitly.
[Sec. III C and Fig. 5] The sample over which the ~8% moment-of-inertia accuracy is computed is not defined. The inversion in Eq. (21) requires the amplitudes h2a0, h2b0, and h2c0, so systems with only one detectable h(2x) component cannot contribute to this measurement. The paper should state whether the median reported in Fig. 5 is conditioned on all three components being detectable, give the size of that subset, and clarify how the selection rule in Sec. III B affects this subset. As written, the headline accuracy is not tied to a well-defined population.

minor comments (4)

[Sec. II B, Eq. (6)] The phrase "In the limit as Ωpre→0" is confusing because the displayed frequencies still contain Ωp, the free-precession frequency; please state explicitly that this limit sets α=0 while leaving Ωp unchanged.
[References] Reference [56] lists duplicated author names ("T. Wagg, T. Wagg, K. Breivik, K. Breivik"); the entry should be corrected.
[Fig. 3] The histograms in Fig. 3 are labeled "Probability" for counts obtained from 1000 Monte Carlo simulations; please specify the binning and use a consistent label such as "frequency" or "probability".
[Sec. III B and Table II] The statement that h(1b) and h(1c) are "too weak to exceed the detection thresholds" would be more informative if accompanied by their median SNR or an upper bound, so the reader can assess how far below threshold they fall.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the inversion formulas are algebraic identities and the detection counts are conditional forecasts with stated assumptions.

full rationale

The paper's quantitative claims are Monte Carlo forecasts under explicitly stated population and waveform assumptions, followed by algebraic error propagation. No load-bearing step reduces by construction to its own input. The amplitude-inversion formulas in Eq. (21) directly solve the amplitude definitions in Eq. (20); substituting (20) into (21) yields κ and γ identically, so they are consistency relations of the model, not independent empirical predictions that reuse a fitted parameter. Equation (23) is standard 1/SNR error propagation applied to the simulated SNRs; it is a Fisher-type forecast, not a claimed measurement from real data. The spin-period relation Eq. (7) is fitted to Ref. [61] simulated data and used as a population input, transparently labeled as such; it is not fitted to the Cosmic Explorer detection counts or to the ~8% moment-of-inertia accuracy that it later feeds. The waveform expansion in Eqs. (4)-(5) extends the authors' prior work [17,52] and is written out explicitly; whether the O(γκ) and O(κ^2) coefficients are complete or correctly normalized is a correctness risk, not a circularity. The paper's own conclusion states that results are contingent on the Wagg et al. LISA-detectable DNS catalog and that conservative assumptions reduce the predicted counts, confirming that the claims are conditional forecasts. Self-citations appear, but they are not invoked as an unverified uniqueness theorem and they do not force the numerical results by construction.

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

The central forecast rests on fitted spin-period relation, hand-chosen structural parameter ranges, a published LISA DNS catalog, and an unverified waveform extension. No new physical entities are introduced; the dual-line strategy uses existing waveform and population models.

free parameters (7)

Spin period-eccentricity fit slope and intercept = slope 163 ms, intercept 19.7 ms
Fitted to simulated DNS data from Dewi et al. (2005) with R^2=0.95; used to assign spin periods to every simulated DNS, which sets GW frequencies and amplitudes.
Spin period noise width sigma_P = 33.3 ms (3 sigma_fit)
Chosen by hand so that simulated spin periods reproduce the dispersion of the Dewi et al. simulation; directly shapes the SNR distributions.
Moment of inertia range = 1e38 to 3e38 kg m^2
Adopted from LIGO document [62]; used as a uniform/log-uniform prior in the population.
Oblateness ellipticity range = 1e-9 to 1e-5
Assumed range for ǫ; drives the GW amplitude through ǫ and κ, and is a major source of uncertainty (uniform vs log-uniform changes counts by factor ~3-4).
Equatorial ellipticity range = 5e-10 to 2e-6
Minimum from PSR J1023+0038 spin-down [69] and maximum from crust breaking strain [64]; input to κ via Eq. (14).
Wobble angle range = 1e-3 to 0.05
Assumed from van Eysden & Link [71] and PSR B1828-11; controls the h(1x) and h(2b,c) amplitudes.
SNR detection threshold = 7
Chosen standard threshold for Cosmic Explorer detection; affects all detectable counts.

assumptions (7)

domain assumption The waveform model of a precessing triaxial neutron star under spin-orbit coupling (geodetic precession) is valid.
Invoked in Sec. II B; waveform components in Eqs. (3)-(5) rely on this model, originally from Refs. [17,51,52].
domain assumption κ and γ are independent small parameters, and the expansion to O(γ^2, κ^2) captures the GW emission.
Stated in Sec. II B as the departure from the earlier κ ~ O(γ^2) hierarchy; no derivation of the new terms is given.
domain assumption The Wagg et al. (2022) COMPAS population synthesis of 35 LISA-detectable DNS systems is accurate.
Used as the base catalog for all sampling; the paper acknowledges the 8-detection conservative case reduces counts by ~4.
domain assumption Each LISA-detectable DNS contains a rapidly spinning NS.
Assumed in Sec. II D; spin periods are generated from the fitted P-e relation, but the presence of a recycled pulsar in every system is not observationally guaranteed.
domain assumption The spin period-eccentricity correlation P = 163 e + 19.7 ms from Dewi et al. applies to the LISA-detectable DNS population.
Fitted to simulated data and used in Eq. (7) to assign spin periods.
standard math Amplitude measurement errors are inversely proportional to SNR (1/ρ).
Standard matched-filter / Cramér-Rao result, used in Eqs. (22)-(23).
domain assumption The free precession frequency gives ǫ through Ω_p ≈ ǫ Ω_r.
From Van Den Broeck (2005), used to claim ǫ can be determined to <1e-4, needed for the I3 error budget.

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Cite this review

Pith. "Pith review of Galactic double neutron stars as dual-line gravitational-wave sources: Prospects with LISA and Cosmic Explorer." pith.science (2026). https://pith.science/paper/FSXMEA5G

@misc{pith2026250505900,
  author       = {Pith},
  title        = {Pith review of: Galactic double neutron stars as dual-line gravitational-wave sources: Prospects with LISA and Cosmic Explorer},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FSXMEA5G}},
  note         = {Machine review of arXiv:2505.05900}
}

abstract

Double neutron star (DNS) systems could serve as intriguing dual-line gravitational-wave (GW) sources, emitting both high- and low-frequency GWs, arising respectively from the asymmetric spinning bodies of individual neutron stars (NSs) and the binary orbital inspiral. Detecting such dual-line signals could provide novel perspectives on binary orbital geometry and NS internal physics. We expand upon previously calculated spinning NS waveforms by incorporating higher-order terms of NS structural parameters. A population simulation is performed for spinning NS components in DNS systems potentially detectable by the space-based Laser Interferometer Space Antenna (LISA). Based on 4-year LISA observation of 35 resolvable DNS systems under an optimistic scenario, we estimate that 6 (22) spinning NS components could be detected by the next-generation ground-based GW detector, Cosmic Explorer, under log-uniform (uniform) sampling of NS structural parameters. For these dual-line sources, the median signal-to-noise ratio achievable with Cosmic Explorer is approximately 20--30. Through the dual-line GW detection strategy, the relative measurement accuracy of the NS moment of inertia is estimated to be $\sim 8\%$.

Figures

Figures reproduced from arXiv: 2505.05900 by the authors.

**Figure 2.** FIG. 2. Parameter distributions of detectable DNSs for a 4-y [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** FIG. 3. Histograms of the number of detectable dual-line GW s [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4. Similar to Fig [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: FIG. 5. The relative measurement accuracy of the moment of in [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

86 extracted references · 29 canonical work pages

[17]

Kuroda, W.-T

K. Kuroda, W.-T. Ni, and W.-P . Pan, Int. J. Mod. Phys. D 24, 1530031 (2015) , arXiv:1511.00231 [gr-qc]

arXiv 2015
[1]

[ 48] form through electron-capture supernovae and ultra-stripped supernov ae

spin period The majority of DNS systems in Ref. [ 48] form through electron-capture supernovae and ultra-stripped supernov ae. For these types of supernovae, natal kick magnitudes follow a Maxwellian velocity distribution with a one-dimensional root- mean-square (rms) velocity dispersion of σrms = 30 km s −1. According to the population synthesis in Ref. ...
[2]

(5f) These waveforms depend on the binary inclination angle ι, spin precession cone opening angle θS , and precession angle α [17, 51]

as follows: h+ = h(1a) + + h(1b) + + h(1c) + + h(2a) + + h(2b) + + h(2c) + + · · ·, (3a) h× = h(1a) × + h(1b) × + h(1c) × + h(2a) × + h(2b) × + h(2c) × + · · ·, (3b) where h(1a) + =Gb2I3ǫ(γ − 8γκ) 4c4D {[ sin 2θS ( 6 sin2ι − (3 + cos 2ι) cos 2α) + 4 cos 2θS cosα sin 2ι ] cos [( Ωr + Ωp ) t ] + 2 [ − 2 cosθS sin 2ι sinα + ( 3 + cos 2ι) sinθS sin 2α ] sin [...
[3]

Geometry angles The other parameters, such as binary inclination ι (the an- gle between the total angular momentum and line of sight) and opening angle of spin precession cone θS (the angle be- tween the spin and the total angular momentum) follow the distributions below, cosι ∼ U [−1, 1], (16) cosθS ∼ U [−1, 1]. (17) 6 m1 m2 1.20 1.25 1.30 1.35 1.40 1.45...
[4]

The linear relation with added noise eﬀectively reproduces the simulation in Ref. [ 61]
[5]

(9) Here, I3 represents the NS moment of inertia with respect to the principal axis that is aligned with the spin axis, with it s range adopted from theoretical predictions in Ref

NS structural parameters In the case of a nonprecessing triaxial NS where the axis of rotation coincides with one of its principal axes of inertia , the equatorial ellipticity of the NS is deﬁned as ε ≡ (I2 − I1)/I3, which can be related to the mass quadrupole moment Q22, via ε = √ 8π 15 Q22 I3 . (9) Here, I3 represents the NS moment of inertia with respe...
[6]

B. P . Abbott et al. (KAGRA, LIGO Scientiﬁc, Virgo), Living Rev. Rel. 23, 3 (2020), arXiv:1304.0670 [gr-qc]

arXiv 2020
[7]

with added Gaussian noise ( 8); apply log-uniform and uni- form sampling for NS structural parameters; sample an- gular parameters within deﬁned ranges. (iii) Repeat Steps (i) and (ii) for 1000 iterations to ensure ro- bust statistical characterization, compute SNRs, and gen- erate the ﬁnal distributions of detectable source counts and SNRs with the Cosmi...

work page

Show all 86 references

[8]

B. P . Abbott et al. (LIGO Scientiﬁc, Virgo), Phys. Rev. Lett. 116, 061102 (2016) , arXiv:1602.03837 [gr-qc]

2016 arXiv
[9]

B. P . Abbott et al. (LIGO Scientiﬁc, Virgo), Phys. Rev. Lett. 119, 161101 (2017) , arXiv:1710.05832 [gr-qc]

2017 arXiv
[10]

Abbott et al

R. Abbott et al. (KAGRA, VIRGO, LIGO Scientiﬁc), Phys. Rev. X 13, 041039 (2023) , arXiv:2111.03606 [gr-qc]

2023 arXiv
[11]

Quantum Grav

LIGO Scientiﬁc Collaboration, Class. Quantum Grav. 32, 074001 (2015) , arXiv:1411.4547 [gr-qc]

2015 arXiv
[12]

Acernese, M

F. Acernese, M. Agathos, et al. , Class. Quantum Grav. 32, 024001 (2015) , arXiv:1408.3978 [gr-qc]

2015 arXiv
[13]

Punturo, M

M. Punturo, M. Abernathy, and et al., Class. Quantum Grav. 27, 194002 (2010)

2010
[14]

Kalogeraet al., (2021), arXiv:2111.06990 [gr-qc]

V . Kalogeraet al., (2021), arXiv:2111.06990 [gr-qc]

2021 arXiv
[15]

Abac et al., (2025), arXiv:2503.12263 [gr-qc]

A. Abac et al., (2025), arXiv:2503.12263 [gr-qc]

2025 arXiv
[16]

Zhao et al., Chin

W. Zhao et al., Chin. Astron. Astrophys. 42, 487 (2018)

2018
[18]

Shao, Chin

L. Shao, Chin. Sci. Bull. 65, 4013 (2020)

2020
[19]

Srivastava, D

V . Srivastava, D. Davis, K. Kuns, P . Landry, S. Ballmer, M. Evans, E. D. Hall, J. Read, and B. S. Sathyaprakash, Astrophys. J. 931, 22 (2022) , arXiv:2201.10668 [gr-qc]

2022 arXiv
[20]

Chen, Phys

W.-C. Chen, Phys. Rev. D 103, 103004 (2021) , arXiv:2104.05910 [astro-ph.HE]

2021 arXiv
[21]

Amaro-Seoane et al

P . Amaro-Seoane et al. (LISA), (2017), arXiv:1702.00786 [astro-ph.IM]

2017 arXiv
[22]

Luo et al

J. Luo et al. (TianQin), Class. Quant. Grav. 33, 035010 (2016) , arXiv:1512.02076 [astro-ph.IM]

2016 arXiv
[23]

Hu and Y .-L

W.-R. Hu and Y .-L. Wu,Natl. Sci. Rev. 4, 685 (2017)

2017
[24]

W.-F. Feng, T. Liu, J.-W. Chen, Y . Wang, and S. D. Mohanty, Phys. Rev. D 108, 063035 (2023) , arXiv:2307.01055 [gr-qc]

2023 arXiv
[25]

Feng, J.-W

W.-F. Feng, J.-W. Chen, T. Liu, Y . Wang, and S. D. Mohanty, Phys. Rev. D 109, 043033 (2024) , arXiv:2401.11241 [astro-ph.HE]

2024 arXiv
[26]

T. M. Tauris, Phys. Rev. Lett. 121, 131105 (2018) , [Erratum: Phys.Rev.Lett. 124, 149902 (2020)], arXiv:1809.03504 [astro-ph.SR]

2018 arXiv
[27]

Soldateschi and N

J. Soldateschi and N. Bucciantini, Galaxies 9, 101 (2021), arXiv:2110.06039 [astro-ph.HE]

2021 arXiv
[28]

A. G. Suvorov, Mon. Not. Roy. Astron. Soc. 503, 5495 (2021) , arXiv:2103.09858 [astro-ph.HE]

2021 arXiv
[29]

Palomba, Mon

C. Palomba, Mon. Not. Roy. Astron. Soc. 359, 1150 (2005) , arXiv:astro-ph/0503046

2005 arXiv
[30]

Knispel and B

B. Knispel and B. Allen, Phys. Rev. D 78, 044031 (2008) , arXiv:0804.3075 [gr-qc]

2008 arXiv
[31]

L. Wade, X. Siemens, D. L. Kaplan, B. Knispel, and B. Allen, Phys. Rev. D 86, 124011 (2012) , arXiv:1209.2971 [gr-qc]

2012 arXiv
[32]

Cie´ slar, T

M. Cie´ slar, T. Bulik, M. Curyło, M. Sieniawska, N. Singh, and M. Bejger, Astron. Astrophys. 649, A92 (2021) , arXiv:2102.08854 [gr-qc]

2021 arXiv
[33]

B. T. Reed, A. Deibel, and C. J. Horowitz, Astrophys. J. 921, 89 (2021) , arXiv:2104.00771 [astro-ph.HE]

2021 arXiv
[34]

Beniwal, P

D. Beniwal, P . Clearwater, L. Dunn, A. Melatos, and D. Ottaway, Phys. Rev. D 103, 083009 (2021) , arXiv:2102.06334 [astro-ph.HE]

2021
[35]

Pagliaro, M

G. Pagliaro, M. A. Papa, J. Ming, J. Lian, D. Tsuna, C. Maraston, and D. Thomas, Astrophys. J. 952, 123 (2023) , arXiv:2303.04714 [gr-qc]

2023 arXiv
[36]

Y . Hua, K. Wette, S. M. Scott, and M. D. 11 Pitkin, Mon. Not. Roy. Astron. Soc. 527, 10564 (2023) , arXiv:2309.01133 [gr-qc]

2023 arXiv
[37]

Pitkin, Mon

M. Pitkin, Mon. Not. Roy. Astron. Soc. 415, 1849 (2011) , arXiv:1103.5867 [astro-ph.HE]

2011 arXiv
[38]

B. P . Abbott et al. (LIGO Scientiﬁc, Virgo), Astrophys. J. 839, 12 (2017) , [Erratum: Astrophys.J. 851, 71 (2017)], arXiv:1701.07709 [astro-ph.HE]

2017 arXiv
[39]

B. P . Abbott et al. (LIGO Scientiﬁc, Virgo), Astrophys. J. 879, 10 (2019) , [Erratum: Astrophys.J. 899, 170 (2020)], arXiv:1902.08507 [astro-ph.HE]

2019 arXiv
[40]

Abbott et al

R. Abbott et al. (LIGO Scientiﬁc, Virgo), Astrophys. J. Lett. 902, L21 (2020) , arXiv:2007.14251 [astro-ph.HE]

2020 arXiv
[41]

Zhang, M

Y . Zhang, M. A. Papa, B. Krishnan, and A. L. Watts, Astrophys. J. Lett. 906, L14 (2021) , arXiv:2011.04414 [astro-ph.HE]

2021 arXiv
[42]

Abbott et al

R. Abbott et al. (LIGO Scientiﬁc, VIRGO, KAGRA), Astrophys. J. 935, 1 (2022) , arXiv:2111.13106 [astro-ph.HE]

2022 arXiv
[43]

A. G. Abac et al. (LIGO Scientiﬁc, VIRGO, KAGRA), Astrophys. J. 983, 99 (2025) , arXiv:2501.01495 [astro-ph.HE]

2025
[44]

Leaci and R

P . Leaci and R. Prix, Phys. Rev. D 91, 102003 (2015) , arXiv:1502.00914 [gr-qc]

2015 arXiv
[45]

P . B. Covas and A. M. Sintes, Phys. Rev. D 99, 124019 (2019) , arXiv:1904.04873 [astro-ph.IM]

2019 arXiv
[46]

Abbott et al

R. Abbott et al. (LIGO Scientiﬁc, Virgo, VIRGO), Phys. Rev. D 103, 064017 (2021) , [Erratum: Phys.Rev.D 108, 069901 (2023)], arXiv:2012.12128 [gr-qc]

2021 arXiv
[47]

P . B. Covas and A. M. Sintes, Phys. Rev. Lett. 124, 191102 (2020) , arXiv:2001.08411 [gr-qc]

2020 arXiv
[48]

For a 4-year LISA mission, the expected number of DNS detections is 3–35

estimates their detectability. For a 4-year LISA mission, the expected number of DNS detections is 3–35. The parame- ter distributions of 35 LISA-detectable DNS systems are sum - marized below [ 48], forming the basis for our study of the NS population in Sec. II D. •Component...
[49]

P . B. Covas, M. A. Papa, and R. Prix, (2024), arXiv:2409.16196 [gr-qc]

2024 arXiv
[50]

Nelemans, L

G. Nelemans, L. R. Y ungelson, and S. F. Portegies Zwart, Astron. Astrophys. 375, 890 (2001) , arXiv:astro-ph/0105221

2001 arXiv
[51]

Belczynski, M

K. Belczynski, M. Benacquista, and T. Bulik, Astrophys. J. 725, 816 (2010) , arXiv:0811.1602 [astro-ph]

2010 arXiv
[52]

Liu and Y

J. Liu and Y . Zhang, Publ. Astron. Soc. Pac. 126, 211 (2016) , arXiv:1404.3848 [astro-ph.SR]

2016 arXiv
[53]

M. Y . M. Lau, I. Mandel, A. Vigna-G´ omez, C. J. Neijssel, S. Stevenson, and A. Sesana, Mon. Not. Roy. Astron. Soc. 492, 3061 (2020) , arXiv:1910.12422 [astro-ph.HE]

2020 arXiv
[54]

Breivik et al

K. Breivik et al. , Astrophys. J. 898, 71 (2020) , arXiv:1911.00903 [astro-ph.HE]

2020 arXiv
[55]

T. Wagg, F. S. Broekgaarden, S. E. de Mink, L. A. C. van Son, N. Frankel, and S. Justham, Astrophys. J. 937, 118 (2022) , arXiv:2111.13704 [astro-ph.HE]

2022 arXiv
[56]

J. J. Andrews, K. Breivik, C. Pankow, D. J. D’Orazio, and M. Safarzadeh, Astrophys. J. Lett. 892, L9 (2020) , arXiv:1910.13436 [astro-ph.HE]

2020 arXiv
[57]

Feng, J.-W

W.-F. Feng, J.-W. Chen, Y . Wang, S. D. Mo- hanty, and Y . Shao, Phys. Rev. D 107, 103035 (2023) , arXiv:2305.05202 [astro-ph.HE]

2023 arXiv
[58]

W.-F. Feng, T. Liu, Y . Wang, and L. Shao, Phys. Rev. D 111, 023053 (2025) , arXiv:2410.09540 [gr-qc]

2025 arXiv
[59]

Y . Gao, L. Shao, R. Xu, L. Sun, C. Liu, and R.- X. Xu, Mon. Not. Roy. Astron. Soc. 498, 1826 (2020) , arXiv:2007.02528 [astro-ph.HE]

2020 arXiv
[60]

Riley et al

J. Riley et al. (COMPAS Team, Team COMPAS), Astrophys. J. Supp. 258, 34 (2022) , arXiv:2109.10352 [astro-ph.IM]

2022 arXiv
[61]

F. S. Broekgaarden, E. Berger, C. J. Neijssel, A. Vigna- G´ omez, D. Chattopadhyay, S. Stevenson, M. Chruslin- ska, S. Justham, S. E. de Mink, and I. Man- del, Mon. Not. Roy. Astron. Soc. 508, 5028 (2021) , arXiv:2103.02608 [astro-ph.HE]

2021 arXiv
[62]

F. S. Broekgaarden et al. , Mon. Not. Roy. Astron. Soc. 516, 5737 (2022) , arXiv:2112.05763 [astro-ph.HE]

2022 arXiv
[63]

T. Wagg, T. Wagg, K. Breivik, K. Breivik, S. E. de Mink, and S. E. de Mink, Astrophys. J. Supp. 260, 52 (2022) , [Erratum: Astrophys.J.Supp. 262, 35 (2022)], arXiv:2111.08717 [astro-ph.HE]

2022 arXiv
[64]

Poisson and C

E. Poisson and C. M. Will, Gravity: Newtonian, post- Newtonian, Relativistic (Cambridge University Press, 2014)

2014
[65]

Zimmermann, Phys

M. Zimmermann, Phys. Rev. D 21, 891 (1980)

1980
[66]

V an Den Broeck, Class

C. V an Den Broeck, Class. Quant. Grav. 22, 1825 (2005) , arXiv:gr-qc/0411030

2005 arXiv
[67]

Y . Gao, L. Shao, G. Desvignes, D. I. Jones, M. Kramer, and G. Yim, Mon. Not. Roy. Astron. Soc. 519, 1080 (2023) , arXiv:2211.17087 [astro-ph.HE]

2023 arXiv
[68]

J. D. M. Dewi, P . Podsiadlowski, and O. R. Pols, Mon. Not. Roy. Astron. Soc. 363, L71 (2005) , arXiv:astro-ph/0507628

2005 arXiv
[69]

Abbott, R

B. Abbott, R. Abbott, R. Adhikari, et al. (LIGO Scientiﬁc Col- laboration), Phys. Rev. D 76, 042001 (2007)

2007
[70]

C. J. Horowitz and K. Kadau, Phys. Rev. Lett. 102, 191102 (2009) , arXiv:0904.1986 [astro-ph.SR]

2009 arXiv
[71]

B. J. Owen, Phys. Rev. Lett. 95, 211101 (2005) , arXiv:astro-ph/0503399

2005 arXiv
[72]

Ushomirsky, C

G. Ushomirsky, C. Cutler, and L. Bild- sten, Mon. Not. Roy. Astron. Soc. 319, 902 (2000) , arXiv:astro-ph/0001136

2000 arXiv
[73]

J. A. Morales and C. J. Horowitz, Mon. Not. Roy. Astron. Soc. 517, 5610 (2022) , arXiv:2209.03222 [gr-qc]

2022 arXiv
[74]

Haskell, N

B. Haskell, N. Andersson, D. I. Jones, and L. Samuelsson, Phys. Rev. Lett. 99, 231101 (2007) , arXiv:0708.2984 [gr-qc]

2007 arXiv
[75]

N. K. Johnson-McDaniel and B. J. Owen, Phys. Rev. D 88, 044004 (2013) , arXiv:1208.5227 [astro-ph.SR]

2013 arXiv
[76]

Haskell and A

B. Haskell and A. Patruno, Phys. Rev. Lett. 119, 161103 (2017) , arXiv:1703.08374 [astro-ph.HE]

2017 arXiv
[77]

G. Woan, M. D. Pitkin, B. Haskell, D. I. Jones, and P . D. Lasky, Astrophys. J. Lett. 863, L40 (2018) , arXiv:1806.02822 [astro-ph.HE]

2018 arXiv
[78]

C. A. van Eysden and B. Link, Astrophys. J. 865, 60 (2018) , arXiv:1806.00967 [astro-ph.HE]

2018 arXiv
[79]

I. H. Stairs, A. G. Lyne, and S. L. Shemar, Nature 406, 484 (2000)

2000
[80]

Jaranowski, A

P . Jaranowski, A. Krolak, and B. F. Schutz, Phys. Rev. D 58, 063001 (1998) , arXiv:gr-qc/9804014

1998 arXiv
[81]

T. Wagg, K. Breivik, M. Renzo, and A. M. Price-Whelan, The Astrophysical Journal Supplement Series 276, 16 (2025)

2025
[82]

Fragos et al

T. Fragos et al. , Astrophys. J. Suppl. 264, 45 (2023) , arXiv:2202.05892 [astro-ph.SR]

2023 arXiv
[83]

J. J. Andrews et al., (2024), arXiv:2411.02376 [astro-ph.GA]

2024 arXiv
[84]

Paxton et al

B. Paxton et al. , Astrophys. J. Suppl. 220, 15 (2015) , arXiv:1506.03146 [astro-ph.SR]

2015 arXiv
[85]

Paxton et al

B. Paxton et al. , Astrophys. J. Suppl. 243, 10 (2019) , arXiv:1903.01426 [astro-ph.SR]

2019 arXiv
[86]

Chattopadhyay, S

D. Chattopadhyay, S. Stevenson, J. R. Hurley, L. J. Rossi, and C. Flynn, Mon. Not. Roy. Astron. Soc. 494, 1587 (2020) , 12 arXiv:1912.02415 [astro-ph.HE]

2020 arXiv

Pith tools

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

[1] [17]

Kuroda, W.-T

K. Kuroda, W.-T. Ni, and W.-P . Pan, Int. J. Mod. Phys. D 24, 1530031 (2015) , arXiv:1511.00231 [gr-qc]

arXiv 2015

[2] [1]

[ 48] form through electron-capture supernovae and ultra-stripped supernov ae

spin period The majority of DNS systems in Ref. [ 48] form through electron-capture supernovae and ultra-stripped supernov ae. For these types of supernovae, natal kick magnitudes follow a Maxwellian velocity distribution with a one-dimensional root- mean-square (rms) velocity dispersion of σrms = 30 km s −1. According to the population synthesis in Ref. ...

[3] [2]

(5f) These waveforms depend on the binary inclination angle ι, spin precession cone opening angle θS , and precession angle α [17, 51]

as follows: h+ = h(1a) + + h(1b) + + h(1c) + + h(2a) + + h(2b) + + h(2c) + + · · ·, (3a) h× = h(1a) × + h(1b) × + h(1c) × + h(2a) × + h(2b) × + h(2c) × + · · ·, (3b) where h(1a) + =Gb2I3ǫ(γ − 8γκ) 4c4D {[ sin 2θS ( 6 sin2ι − (3 + cos 2ι) cos 2α) + 4 cos 2θS cosα sin 2ι ] cos [( Ωr + Ωp ) t ] + 2 [ − 2 cosθS sin 2ι sinα + ( 3 + cos 2ι) sinθS sin 2α ] sin [...

[4] [3]

Geometry angles The other parameters, such as binary inclination ι (the an- gle between the total angular momentum and line of sight) and opening angle of spin precession cone θS (the angle be- tween the spin and the total angular momentum) follow the distributions below, cosι ∼ U [−1, 1], (16) cosθS ∼ U [−1, 1]. (17) 6 m1 m2 1.20 1.25 1.30 1.35 1.40 1.45...

[5] [4]

The linear relation with added noise eﬀectively reproduces the simulation in Ref. [ 61]

[6] [5]

(9) Here, I3 represents the NS moment of inertia with respect to the principal axis that is aligned with the spin axis, with it s range adopted from theoretical predictions in Ref

NS structural parameters In the case of a nonprecessing triaxial NS where the axis of rotation coincides with one of its principal axes of inertia , the equatorial ellipticity of the NS is deﬁned as ε ≡ (I2 − I1)/I3, which can be related to the mass quadrupole moment Q22, via ε = √ 8π 15 Q22 I3 . (9) Here, I3 represents the NS moment of inertia with respe...

[7] [6]

B. P . Abbott et al. (KAGRA, LIGO Scientiﬁc, Virgo), Living Rev. Rel. 23, 3 (2020), arXiv:1304.0670 [gr-qc]

arXiv 2020

[8] [7]

with added Gaussian noise ( 8); apply log-uniform and uni- form sampling for NS structural parameters; sample an- gular parameters within deﬁned ranges. (iii) Repeat Steps (i) and (ii) for 1000 iterations to ensure ro- bust statistical characterization, compute SNRs, and gen- erate the ﬁnal distributions of detectable source counts and SNRs with the Cosmi...

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