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Tidal deformation and strain accumulation of solid compact stars

T0 review · 3 major / 5 minor · reviewed 2026-07-14 · grok-4.5

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Pith's one-line read Solid strangeon stars show ~40% less tidal deformability than fluid ones and can fracture mid-inspiral, releasing energy for GRB precursors.

desk verdict Clean relativistic solid-star calculation for the strangeon EOS that delivers a robust ~40% Λ difference and center-peaking strain maps once μ is fixed; free parameters and single-layer idealization keep the multi-messenger claim conditional. read the letter →

arxiv 2607.11780 v1 pith:UNRKMTFN submitted 2026-07-13 astro-ph.HE gr-qchep-phnucl-th

Hongxiang Shen , Yong Gao , Hong-Bo Li , Ren-Xin Xu This is my paper · ORCID
classification astro-ph.HEgr-qchep-phnucl-th
keywords densematterequationofstategravitationalwavesstars:interiorsgamma-rayburst:generaltidaldeformabilitystrangeonstarselasticstrain
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 asks whether pulsar-like compact stars are fluid or solid throughout, and shows that the answer would leave clear imprints in gravitational waves and gamma-ray precursors. Using the strangeon-star equation of state and a shear modulus of 10^34 erg cm^{-3}, the authors compute that a 1.4-solar-mass solid star has roughly 40% smaller tidal deformability than its fluid counterpart, enough to produce a ~10% departure from the usual I–Love relation. As a binary inspirals, tidal strain builds from the center outward; once it exceeds the breaking strain, large-scale fracturing sets in at several hundred hertz and can liberate up to ~10^46 erg of elastic energy—enough to power short-GRB precursors. The solid-to-fluid transition then changes the tidal response, imprinting on the waveform phase. Together the electromagnetic precursor and the gravitational-wave signature therefore constitute a multi-messenger test of whether these stars are rigid solids.

What carries the argument

The relativistic elastic-perturbation system for a solid star: six first-order ODEs for the metric and displacement variables (H_0, J, W, V, Z_r, Z_perp) that incorporate a nonzero shear modulus, solved with regular center conditions and continuous surface stress to yield both the Love number and the internal strain field.

What would settle it

A binary neutron-star merger whose measured tidal deformability, combined with an independent moment-of-inertia estimate, lies on the fluid I–Love curve rather than the ~10% solid offset, or whose gravitational-wave phase shows no abrupt change near a few hundred hertz accompanied by a short-GRB precursor of ~10^{46} erg.

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Extended reading notes

Core claim

With a fiducial shear modulus of 10^{34} erg cm^{-3}, solid strangeon stars of 1.4 solar masses differ by approximately 40% in tidal deformability from fluid strangeon stars, corresponding to a ~10% deviation from the universal I–Love relation. Internal strain peaks at the stellar center; when the gravitational-wave frequency reaches several hundred hertz, large-scale fracturing can release up to ~10^{46} erg of elastic energy, sufficient for short-GRB precursors, and the resulting solid-to-fluid transition alters the tidal waveform.

Load-bearing premise

The calculation treats the shear modulus as a fixed constant 10^{34} erg cm^{-3} everywhere and adopts a single breaking-strain value of order 0.001; both numbers are free parameters that could differ by orders of magnitude for real strangeon matter.

Editorial extensions

If this is right

  • Next-generation gravitational-wave detectors could distinguish solid from fluid compact stars via the ~40% tidal-deformability offset and the ~10% I–Love deviation.
  • Large-scale fracturing near several hundred hertz would imprint a sudden change in waveform phase that encodes both shear modulus and breaking strain.
  • Precursor intensity and waiting time of short GRBs would jointly constrain the same two material parameters.
  • A multi-messenger non-detection of both the elastic-energy release and the solid-to-fluid waveform shift would disfavour a fully solid interior.

Reading between the lines

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

  • If the center-first fracture geometry is generic, it may also organise glitch recovery and the difficulty of measuring spin periods in repeating fast radio bursts.
  • A time-dependent two-layer (fractured core + solid envelope) calculation would convert the present upper-bound energy release into a more realistic light-curve prediction.
  • The same elastic framework can be re-run with crystalline colour-superconducting quark-matter parameters to test whether the 40% offset is unique to strangeons or common to any high-modulus solid.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper develops a relativistic framework for static tidal deformations of solid compact stars in the strangeon-star model. Starting from a Lennard-Jones EOS, the authors derive a system of six first-order ODEs for the metric and elastic variables (Appendix A), regular central eigensolutions (Appendix B), and surface/vacuum matching that recovers the Love number k2 and the dimensionless tidal deformability Λ. With a constant shear modulus μ=10^34 erg cm^{-3} they report a ~40% relative difference between solid and fluid Λ at 1.4 M⊙, corresponding to a ~10% deviation from the universal I–Love relation. They further compute the strain invariant s^2 during binary inspiral, show that it peaks near the stellar center, and estimate that large-scale fracturing at several hundred Hz can release up to ~10^46 erg of elastic energy, enough to power short-GRB precursors and to imprint a solid-to-fluid transition on the GW waveform.

Significance. If the solid-star premise and the adopted values of μ and σ hold, the work supplies a concrete, multi-messenger test of solid interiors that is inaccessible to fluid-only analyses. The ~40% Λ difference and the associated I–Love deviation are large enough to be relevant for next-generation GW detectors, while the elastic-energy budget offers a quantitative link to observed GRB precursors. Strengths include a carefully derived and cross-checked perturbation system (verified against Lau et al.), an independent Newtonian analytic Love-number formula (Appendix C) that recovers ~37% of the numerical difference, and explicit falsifiable predictions for the frequency and energy of fracturing. The free parameters μ and σ remain uncertain by orders of magnitude, so the observational claims are conditional, but the calculational framework itself is a useful addition to the solid-star literature.

major comments (3)
  1. Section 3.1 and Fig. 4 adopt a single constant μ=10^34 erg cm^{-3} throughout the star. While the authors correctly show that the relative Λ difference vanishes as μ o0, the central claim of a ~40% effect (and the ~10% I–Love deviation) is therefore tied to this fiducial value. A more systematic exploration of the μ range expected for strangeon matter (or an explicit mapping of Λ(μ) onto detector sensitivity) is needed before the multi-messenger test can be regarded as robust.
  2. Section 3.2 and Eq. (50) assume that all elastic energy inside the region D={r | s≥σ} is released while the exterior remains intact, and that fracturing begins at the center. The paper itself notes (Conclusions) that a two-layer fluid-core/solid-envelope model would be more realistic and that the single-layer idealization is valid only while the fluid core radius stays below ~0.5 R. Because the energy-release estimate and the timing of the solid-to-fluid transition are load-bearing for the GRB-precursor and waveform-imprint claims, at least a schematic two-layer calculation (or a clear quantification of the bias introduced by the single-layer assumption) should be provided.
  3. The breaking strain is fixed at σ=0.001 for the energy and frequency results in Figs. 7–9, yet the text acknowledges that estimates for dense matter span ~10^{-5} to ~0.1. Fig. 9 already shows the strong dependence of the 50%-fracture frequency on σ; the abstract and conclusions should therefore present the ~10^46 erg and “several hundred Hz” figures as illustrative for this particular σ rather than as generic predictions.
minor comments (5)
  1. Abstract and Introduction: the phrase “corresponding to a ~10% deviation from the universal I–Love relation” is slightly ambiguous; clarify whether the 10% refers to the vertical offset in the I–Λ plane or to a relative difference in Λ at fixed I.
  2. Fig. 2 caption and axis label use “(Λ Fluid □ Λ Solid)/Λ Fluid”; the box character should be replaced by a proper minus sign for readability.
  3. Eq. (49) for s^2 contains a factor 1/μ^2 in the denominator of the prefactor while the subsequent terms already include μ^2 V^2; a brief check that the overall dimensions are consistent would help the reader.
  4. Section 2.1: the lattice constants A12=6.2, A6=8.4 and the choice Nq=18 are taken from earlier works; a one-sentence reminder of their physical origin would improve self-containment.
  5. Appendix C, Eq. (C36): the Newtonian strain profile is said to confirm the center-peaking result, but a short quantitative comparison (e.g., the ratio s_center/s_surface) would make the cross-check more transparent.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the ~40% Lambda difference and strain/energy results are independent numerical outputs of the perturbation ODEs, not forced by definition or self-citation.

full rationale

The paper adopts the strangeon EOS (Eqs. 2-3, from Zhang et al. 2023) and a constant fiducial shear modulus mu=10^34 erg cm^{-3} (Section 3.1) as model inputs, then solves a self-contained system of six first-order ODEs (Appendix A) subject to regular central eigensolutions (Appendix B) and surface/vacuum matching that recovers the Love number k2 (Eqs. 38-41). The relative difference (Lambda_fluid - Lambda_solid)/Lambda_fluid ~40% at 1.4 M_sun is a direct numerical output of that boundary-value problem; it is independently corroborated by the Newtonian analytic estimate tilde-mu/(1+tilde-mu)~0.37 (Eq. 46 and Appendix C) and by reproduction of Lau et al. (2019) results. Strain s^2 (Eq. 49) and E_release (Eq. 50) likewise follow from the same solved fields once a free breaking strain sigma is chosen; they are not fitted to data nor defined in terms of the claimed observables. Self-citations supply the model premise (solid strangeon star) but do not close a loop that forces the tidal or energy numbers by construction. The free parameters mu and sigma are already flagged as uncertain; they do not render the derivation circular.

Assumptions & free parameters 5 free parameters · 4 assumptions · 1 invented entities

The central numerical claims rest on a fixed strangeon EOS (itself parameterized), a constant shear modulus chosen by hand, an assumed breaking strain, and the idealization of a fully solid single-layer star. These free choices and domain assumptions are what convert the general solid-star formalism into the quoted 40% and 10^46 erg figures.

free parameters (5)
  • shear modulus μ = 10^{34} erg cm^{-3}
    Set by hand to the fiducial value 10^{34} erg cm^{-3} (Section 3.1); the relative Λ difference vanishes as μ→0 (Fig. 4) and scales with μ, so the 40% figure is directly controlled by this choice.
  • breaking strain σ = 0.001
    Fixed at 0.001 for the energy-release and fracture-frequency plots (Figs. 7–9); literature range spans 10^{-5}–0.1, so the hundreds-of-Hz onset and 10^{46} erg release are parameter-dependent.
  • Lennard-Jones well depth ε = 25 MeV
    EOS parameter taken as 25 MeV from prior strangeon papers; controls the stiffness that enters both the background TOV solution and the tidal response.
  • surface baryon density n_s = 0.36 fm^{-3}
    Set to 0.36 fm^{-3} to fix the surface density discontinuity and thus the stellar radius for a given mass.
  • quarks per cluster N_q = 18
    Taken as 18; enters the rest-mass term of the EOS and therefore the mass–radius relation.
assumptions (4)
  • domain assumption Strangeon matter is described by a classical solid lattice interacting via a Lennard-Jones potential, yielding the EOS of Eqs. (2)–(3).
    Adopted from Zhang et al. (2023) and earlier Xu-group papers; the entire background stellar model rests on it.
  • ad hoc to paper The star is a pure solid with constant shear modulus throughout its volume (no fluid core or thin crust).
    Stated in the introduction and used for all solid calculations; the authors themselves note that a two-layer model would be more realistic (Section 4).
  • standard math Static, linear elastic perturbations in the Regge–Wheeler gauge with ω=0 are sufficient to compute the tidal Love number and the strain field.
    Standard relativistic stellar-perturbation theory (Hinderer, Damour & Nagar, Thorne & Campolattaro); the derivation in Appendix A follows this framework.
  • ad hoc to paper Upon fracturing, all elastic energy inside the region where s≥σ is released while the exterior remains intact.
    Used to obtain the upper-bound energy release of Eq. (50); acknowledged as a simplified single-layer idealization.
invented entities (1)
  • strangeon (quark cluster preserving three-flavor symmetry)
    purpose: Provides the microscopic constituents whose lattice yields both the EOS and the large shear modulus that distinguish solid SnSs from fluid neutron stars.
    Introduced in earlier Xu-group papers and taken as given; no new independent evidence is supplied in this work beyond the multi-messenger signatures that would test it.

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Pith. "Pith review of Tidal deformation and strain accumulation of solid compact stars." pith.science (2026). https://pith.science/paper/UNRKMTFN

@misc{pith2026260711780,
  author       = {Pith},
  title        = {Pith review of: Tidal deformation and strain accumulation of solid compact stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UNRKMTFN}},
  note         = {Machine review of arXiv:2607.11780}
}
abstract

The tidal deformability of compact stars encodes the equation of state of dense matter, and gravitational-wave observations such as GW170817 have begun to constrain it under the assumption of a fluid interior. Yet whether the interior of pulsar-like compact stars is fluid or solid remains largely untested, despite the distinct tidal responses the two states predict. In this work, based on the strangeon-star model, we develop a framework for modeling tidal deformation in solid compact stars. Adopting a shear modulus of $\mu = 10^{34}\,\mathrm{erg}\,\mathrm{cm}^{-3}$, we find a relative difference of approximately $40\%$ in tidal deformability between solid and fluid strangeon stars of $1.4\,M_\odot$, corresponding to a $\sim 10\%$ deviation from the universal I--Love relation. We further model the accumulation of internal strain during binary inspiral and find that it peaks near the stellar center. When the gravitational-wave frequency reaches several hundred $\rm Hz$, large-scale fracturing occurs and can release up to $\sim 10^{46}\,\mathrm{erg}$ of elastic energy, sufficient to power short $\gamma$-ray-burst precursors. This solid-to-fluid transition alters the tidal response and imprints on the waveform and phase of the emitted gravitational radiation. Combined with the precursor electromagnetic emission, these gravitational-wave signatures offer a multi-messenger avenue to test the solid nature of pulsar-like compact stars.

Figures

Figures reproduced from arXiv: 2607.11780 by the authors.

Figure 1
Figure 1. Mass–radius relation for compact stars. The red curve corresponds to the strangeon matter EOS with the parameters described in Section 2.1. The green curves represent several representative neutron star EOSs for com￾parison. 2.3 Perturbation equations We begin by establishing a spherical coordinate system with the polar axis aligned toward the companion star. Given the rotational symme￾try of the tidal field around … view at source ↗
Figure 2
Figure 2. Tidal deformability Λ as a function of stellar mass for strangeon stars, showing a ∼ 40% relative difference at intermediate masses. The red curve corresponds to solid stars (𝜇 = 1034 erg cm−3 ), and the blue curve to fluid stars. The relative difference (Λfluid − Λsolid )/Λfluid is also shown. in tidal deformability between the two states reaches approximately 40%. In contrast, calculations for neutron stars with a… view at source ↗
Figure 4
Figure 4. Relative difference in tidal deformability between solid and fluid strangeon stars as a function of shear modulus 𝜇, for three representative stellar masses. As expected, the difference vanishes in the limit 𝜇 → 0. where 𝜇˜ = 19𝜇/(2𝜌𝑔𝑅), 𝑔 is the surface gravitational acceleration, and 𝑅 is the stellar radius. For a constant-density, incompressible solid star, this relation is exact; we confirm this explicitly in Ap… view at source ↗
Figures from the paper (3 more)
Figure 6
Figure 6. Figure 6: Distribution of the strain 𝑠 within the stellar interior at a GW frequency of 100 Hz, for a 1.4 𝑀⊙ strangeon star with 𝜇 = 1034 erg cm−3 . The polar axis points toward the companion star. The full three-dimensional distribution can be obtained by rotating this cross-se…
Figure 7
Figure 7. Figure 7: Progressive fracturing of a 1.4 𝑀⊙ strangeon star during binary inspiral, with 𝜇 = 1034 erg cm−3 and breaking strain 𝜎 = 0.001. From left to right, the panels show the strain distribution at GW frequencies corresponding to 14%, 50%, and 86% of the stellar volume exceed…
Figure 9
Figure 9. Figure 9: GW frequency at which 50% of the stellar volume is fractured, as a function of the breaking strain 𝜎, for strangeon stars of different masses with a 1.4 𝑀⊙ companion. The shaded bands span the frequency range between 14% and 86% fractured volume. offer a valuable test …

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Works this paper leans on

81 extracted references · 38 canonical work pages

  1. [1]

    and Kuan, Hao-Jui and Kokkotas, Kostas D

    Suvorov, Arthur G. and Kuan, Hao-Jui and Kokkotas, Kostas D. Premerger Phenomena in Neutron Star Binary Coalescences. Universe. 2024. doi:10.3390/universe10120441. arXiv:2408.16283

    arXiv doi:10.3390/universe10120441 2024

  2. [2]

    and Hinderer, Tanja

    Flanagan, Eanna E. and Hinderer, Tanja. Constraining neutron star tidal Love numbers with gravitational wave detectors. Phys. Rev. D. 2008. doi:10.1103/PhysRevD.77.021502. arXiv:0709.1915

    arXiv doi:10.1103/physrevd.77.021502 2008

  3. [3]

    Precursor flares of short gamma-ray bursts from crust yielding due to tidal resonances in coalescing binaries of rotating, magnetized neutron stars

    Suvorov, Arthur G. and Kokkotas, Kostas D. Precursor flares of short gamma-ray bursts from crust yielding due to tidal resonances in coalescing binaries of rotating, magnetized neutron stars. Phys. Rev. D. 2020. doi:10.1103/PhysRevD.101.083002. arXiv:2003.05673

    work page Pith review arXiv doi:10.1103/physrevd.101.083002 2020

  4. [4]

    and Shibata, Masaru

    Gao, Yong and Kuan, Hao-Jui and Xia, Cheng-Jun and Silva, Hector O. and Shibata, Masaru. Nonradial oscillations of stratified neutron stars with solid crusts: Mode characterization and tidal resonances in coalescing binaries. Phys. Rev. D. 2025. doi:10.1103/nbk7-8kts. arXiv:2509.00257

    work page doi:10.1103/nbk7-8kts 2025

  5. [5]

    and Kokkotas, Kostas D

    Kuan, Hao-Jui and Suvorov, Arthur G. and Kokkotas, Kostas D. General-relativistic treatment of tidal g-mode resonances in coalescing binaries of neutron stars I. Theoretical framework and crust breaking. Mon. Not. Roy. Astron. Soc. 2021. doi:10.1093/mnras/stab1898. arXiv:2106.16123

    arXiv doi:10.1093/mnras/stab1898 2021

  6. [6]

    and Kokkotas, Kostas D

    Kuan, Hao-Jui and Suvorov, Arthur G. and Kokkotas, Kostas D. General-relativistic treatment of tidal g-mode resonances in coalescing binaries of neutron stars II. As triggers for precursor flares of short gamma-ray bursts. Mon. Not. Roy. Astron. Soc. 2021. doi:10.1093/mnras/stab2658. arXiv:2107.00533

    arXiv doi:10.1093/mnras/stab2658 2021

  7. [7]

    Frequency of Pulsar Starquakes

    Smoluchowski, R. Frequency of Pulsar Starquakes. Phys. Rev. Lett. 1970. doi:10.1103/PhysRevLett.24.923

    work page doi:10.1103/physrevlett.24.923 1970

  8. [8]

    Caplan, M. E. and Schneider, A. S. and Horowitz, C. J. Elasticity of Nuclear Pasta. Phys. Rev. Lett. 2018. doi:10.1103/PhysRevLett.121.132701. arXiv:1807.02557

    work page Pith review arXiv doi:10.1103/physrevlett.121.132701 2018

Show all 81 references
  1. [9]

    Abbott, B. P. and others. GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral. Phys. Rev. Lett. 2017. doi:10.1103/PhysRevLett.119.161101. arXiv:1710.05832

    2017 doi arXiv

  2. [10]

    and Fortin, M

    Malik, Tuhin and Alam, N. and Fortin, M. and Provid \^e ncia, C. and Agrawal, B. K. and Jha, T. K. and Kumar, Bharat and Patra, S. K. GW170817: constraining the nuclear matter equation of state from the neutron star tidal deformability. Phys. Rev. C. 2018. doi:10.1103/PhysRevC...

    2018 doi arXiv

  3. [11]

    Delineating the properties of matter in cold, dense QCD

    Kojo, Toru. Delineating the properties of matter in cold, dense QCD. AIP Conf. Proc. 2019. doi:10.1063/1.5117813. arXiv:1904.05080

    2019 doi arXiv

  4. [12]

    Quakes of compact stars

    Lu, Ruipeng and Yue, Han and Lai, Xiaoyu and Wang, Weihua and Zhang, Shenjian and Xu, Renxin. Quakes of compact stars. Mon. Not. Roy. Astron. Soc. 2023. doi:10.1093/mnras/stad270. arXiv:2301.10615

    2023 doi arXiv

  5. [13]

    Lai, X. Y. and Yun, C. A. and Lu, J. G. and L. Pulsar Glitches in a Strangeon Star Model. Mon. Not. Roy. Astron. Soc. 2018. doi:10.1093/mnras/sty474. arXiv:1707.07471

    2018 doi arXiv

  6. [14]

    Lai, X. Y. and Wang, W. H. and Yuan, J. P. and Lu, R. P. and Yue, H. and Xu, R. X. Pulsar glitch in a strangeon star model III. The recovery. Mon. Not. Roy. Astron. Soc. 2023. doi:10.1093/mnras/stad1653. arXiv:2301.09088

    2023 doi arXiv

  7. [15]

    and Dong, J

    Li, A. and Dong, J. M. and Wang, J. B. and Xu, R. X. Structures of the Vela pulsar and the glitch crisis from the Brueckner theory. Astrophys. J. Suppl. 2016. doi:10.3847/0067-0049/223/1/16. arXiv:1512.00340

    2016 doi arXiv

  8. [16]

    Strangeon Ergostars

    Xia, Haojia and Chen, Shichuan and Li, Hong-Bo and Zhou, Enping and Xu, Ren-Xin. Strangeon Ergostars. 2026. arXiv:2601.01949

    2026

  9. [17]

    Astrophysical and Laboratory Studies on the Equation of State of Neutron Stars

    LI, Ang. Astrophysical and Laboratory Studies on the Equation of State of Neutron Stars. Nucl. Phys. Rev. 2024. doi:10.11804/NuclPhysRev.41.2023CNPC36

    2024 doi

  10. [18]

    Tidal Love Numbers of Neutron and Self-Bound Quark Stars

    Postnikov, Sergey and Prakash, Madappa and Lattimer, James M. Tidal Love Numbers of Neutron and Self-Bound Quark Stars. Phys. Rev. D. 2010. doi:10.1103/PhysRevD.82.024016. arXiv:1004.5098

    2010 doi arXiv

  11. [19]

    Relativistic tidal properties of neutron stars

    Damour, Thibault and Nagar, Alessandro. Relativistic tidal properties of neutron stars. Phys. Rev. D. 2009. doi:10.1103/PhysRevD.80.084035. arXiv:0906.0096

    2009 doi arXiv

  12. [20]

    and Lang, Ryan N

    Hinderer, Tanja and Lackey, Benjamin D. and Lang, Ryan N. and Read, Jocelyn S. Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral. Phys. Rev. D. 2010. doi:10.1103/PhysRevD.81.123016. arXiv:0911.3535

    2010 doi arXiv

  13. [21]

    Tidal effects in gravitational waves from neutron stars in scalar-tensor theories of gravity

    Creci, Gast \'o n and van Gemeren, Iris and Hinderer, Tanja and Steinhoff, Jan. Tidal effects in gravitational waves from neutron stars in scalar-tensor theories of gravity. SciPost Phys. Core. 2025. doi:10.21468/SciPostPhysCore.8.2.042. arXiv:2412.06620

    2025 doi arXiv

  14. [22]

    Torsional oscillations of crystalline color-superconducting hybrid stars: Possible sources for Advanced LIGO?

    Lin, Lap-Ming. Torsional oscillations of crystalline color-superconducting hybrid stars: Possible sources for Advanced LIGO?. Phys. Rev. D. 2013. doi:10.1103/PhysRevD.88.124002. arXiv:1311.2654

    2013 doi arXiv

  15. [23]

    Role of crustal physics in the tidal deformation of a neutron star

    Biswas, Bhaskar and Nandi, Rana and Char, Prasanta and Bose, Sukanta. Role of crustal physics in the tidal deformation of a neutron star. Phys. Rev. D. 2019. doi:10.1103/PhysRevD.100.044056. arXiv:1905.00678

    2019 doi arXiv

  16. [24]

    Penner, A. J. and Andersson, N. and Samuelsson, L. and Hawke, I. and Jones, D. I. Tidal deformations of neutron stars: The role of stratification and elasticity. Phys. Rev. D. 2011. doi:10.1103/PhysRevD.84.103006. arXiv:1107.0669

    2011 doi arXiv

  17. [25]

    and Schmitt, Andreas and Rajagopal, Krishna and Sch

    Alford, Mark G. and Schmitt, Andreas and Rajagopal, Krishna and Sch. Color superconductivity in dense quark matter. Rev. Mod. Phys. 2008. doi:10.1103/RevModPhys.80.1455. arXiv:0709.4635

    2008 doi arXiv

  18. [26]

    Tidal Love numbers of neutron stars

    Hinderer, Tanja. Tidal Love numbers of neutron stars. Astrophys. J. 2008. doi:10.1086/533487. arXiv:0711.2420

    2008 doi arXiv

  19. [27]

    and Brown, Duncan A

    De, Soumi and Finstad, Daniel and Lattimer, James M. and Brown, Duncan A. and Berger, Edo and Biwer, Christopher M. Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817. Phys. Rev. Lett. 2018. doi:10.1103/PhysRevLett.121.091102. arXiv:1804.08583

    2018 doi arXiv

  20. [28]

    Abbott, B. P. and others. GW170817: Measurements of neutron star radii and equation of state. Phys. Rev. Lett. 2018. doi:10.1103/PhysRevLett.121.161101. arXiv:1805.11581

    2018 doi arXiv

  21. [29]

    Gravitational-wave constraints on the neutron-star-matter Equation of State

    Annala, Eemeli and Gorda, Tyler and Kurkela, Aleksi and Vuorinen, Aleksi. Gravitational-wave constraints on the neutron-star-matter Equation of State. Phys. Rev. Lett. 2018. doi:10.1103/PhysRevLett.120.172703. arXiv:1711.02644

    2018 doi arXiv

  22. [30]

    and Sedrakian, Armen

    Paschalidis, Vasileios and Yagi, Kent and Alvarez-Castillo, David and Blaschke, David B. and Sedrakian, Armen. Implications from GW170817 and I-Love-Q relations for relativistic hybrid stars. Phys. Rev. D. 2018. doi:10.1103/PhysRevD.97.084038. arXiv:1712.00451

    2018 doi arXiv

  23. [31]

    Strange Quark stars: Observations & Speculations

    Xu, Renxin. Strange Quark stars: Observations & Speculations. J. Phys. G. 2009. doi:10.1088/0954-3899/36/6/064010. arXiv:0812.4491

    2009 doi arXiv

  24. [32]

    Constraining nonperturbative strong-field effects in scalar-tensor gravity by combining pulsar timing and laser-interferometer gravitational-wave detectors

    Shao, Lijing and Sennett, Noah and Buonanno, Alessandra and Kramer, Michael and Wex, Norbert. Constraining nonperturbative strong-field effects in scalar-tensor gravity by combining pulsar timing and laser-interferometer gravitational-wave detectors. Phys. Rev. X. 2017. doi:10...

    2017 doi arXiv

  25. [33]

    Merging Strangeon Stars

    Lai, Xiao-Yu and Yu, Yun-Wei and Zhou, En-Ping and Li, Yun-Yang and Xu, Ren-Xin. Merging Strangeon Stars. Res. Astron. Astrophys. 2018. doi:10.1088/1674-4527/18/2/24. arXiv:1710.04964

    2018 doi arXiv

  26. [34]

    Bulk strong matter: the trinity

    Lai, Xiaoyu and Xia, Chengjun and Xu, Renxin. Bulk strong matter: the trinity. Adv. Phys. X. 2022. doi:10.1080/23746149.2022.2137433. arXiv:2210.01501

    2022 doi

  27. [35]

    Strange matter

    Xia, Chengjun and Lai, Xiaoyu and Xu, Renxin. Strange matter. Int. J. Mod. Phys. A. 2025. doi:10.1142/S0217751X25501805. arXiv:2511.01146

    2025 doi arXiv

  28. [36]

    Cosmic Separation of Phases

    Witten, Edward. Cosmic Separation of Phases. Phys. Rev. D. 1984. doi:10.1103/PhysRevD.30.272

    1984 doi

  29. [37]

    Lau, S. Y. and Leung, P. T. and Lin, L. -M. Two-layer compact stars with crystalline quark matter: Screening effect on the tidal deformability. Phys. Rev. D. 2019. doi:10.1103/PhysRevD.99.023018. arXiv:1808.08107

    2019 doi arXiv

  30. [38]

    Rutherford s Atomic Nucleus versus Landau s Gigantic Nucleus: Does Nature Favor Flavor Symmetry?

    XU, Renxin. Rutherford s Atomic Nucleus versus Landau s Gigantic Nucleus: Does Nature Favor Flavor Symmetry?. Nucl. Phys. Rev. 2025. doi:10.11804/NuclPhysRev.41.QCS2023.19

    2025 doi

  31. [39]

    Solid quark matter?

    Xu, Ren-Xin. Solid quark matter?. Astrophys. J. Lett. 2003. doi:10.1086/379209. arXiv:astro-ph/0302165

    2003 doi arXiv

  32. [40]

    Strange Matter: a state before black hole

    Xu, Renxin and Guo, Yanjun. Strange Matter: a state before black hole. 11th Rencontres du Vietnam : Hot Topics in General Relativity and Gravitation. 2017. doi:10.1142/9789814699662_0004. arXiv:1601.05607

    2017 doi arXiv

  33. [41]

    Strangeon and Strangeon Star

    Lai, Xiaoyu and Xu, Renxin. Strangeon and Strangeon Star. J. Phys. Conf. Ser. 2017. doi:10.1088/1742-6596/861/1/012027. arXiv:1701.08463

    2017 doi arXiv

  34. [42]

    Quark stars composed of Lennard-Jones matter

    Lai, Xiaoyu and Xu, Renxin. Quark stars composed of Lennard-Jones matter. Mon. Not. Roy. Astron. Soc. 2009. doi:10.1111/j.1745-3933.2009.00701.x. arXiv:0905.2839

    2009 doi

  35. [43]

    Lai, X. Y. and Xu, R. X. A Polytropic Model of Quark Stars. Astropart. Phys. 2009. doi:10.1016/j.astropartphys.2008.12.007. arXiv:0804.0983

    2009 doi arXiv

  36. [44]

    Fisher forecast of finite-size effects with future gravitational wave detectors

    Shterenberg, Joshua and Zhou, Zihan. Fisher forecast of finite-size effects with future gravitational wave detectors. Phys. Rev. D. 2025. doi:10.1103/PhysRevD.111.084068. arXiv:2410.00294

    2025 doi arXiv

  37. [45]

    Solid bare strange quark stars

    Xu, Ren-Xin. Solid bare strange quark stars. IAU Symp. 2004. arXiv:astro-ph/0310050

    2004 arXiv

  38. [46]

    Shapiro Delay Measurement of A Two Solar Mass Neutron Star

    Demorest, Paul and Pennucci, Tim and Ransom, Scott and Roberts, Mallory and Hessels, Jason. Shapiro Delay Measurement of A Two Solar Mass Neutron Star. Nature. 2010. doi:10.1038/nature09466. arXiv:1010.5788

    2010 doi arXiv

  39. [47]

    Zhou, E. P. and Lu, J. G. and Tong, H. and Xu, R. X. Two types of glitches in a solid quark star model. Mon. Not. Roy. Astron. Soc. 2014. doi:10.1093/mnras/stu1370. arXiv:1404.2793

    2014 doi arXiv

  40. [48]

    The Peculiar Precursor of a Gamma-Ray Burst from a Binary Merger Involving a Magnetar

    Xiao, Shuo and others. The Peculiar Precursor of a Gamma-Ray Burst from a Binary Merger Involving a Magnetar. Astrophys. J. 2024. doi:10.3847/1538-4357/ad4ee1. arXiv:2205.02186

    2024 doi arXiv

  41. [49]

    and Kuan, Hao-Jui and Kokkotas, Kostas D

    Suvorov, Arthur G. and Kuan, Hao-Jui and Kokkotas, Kostas D. Quasi-periodic oscillations in precursor flares via seismic aftershocks from resonant shattering. Astron. Astrophys. 2022. doi:10.1051/0004-6361/202244082. arXiv:2205.11112

    2022 doi arXiv

  42. [50]

    Strangeons constitute bulk strong matter: Test using GW 170817

    Lai, Xiaoyu and Zhou, Enping and Xu, Renxin. Strangeons constitute bulk strong matter: Test using GW 170817. Eur. Phys. J. A. 2019. doi:10.1140/epja/i2019-12720-8. arXiv:1811.00193

    2019 doi arXiv

  43. [51]

    Multiple subjet model of gamma-ray bursts and possible origin of X-ray precursors and postcursors

    Nakamura, Takashi. Multiple subjet model of gamma-ray bursts and possible origin of X-ray precursors and postcursors. Astrophys. J. Lett. 2000. doi:10.1086/312663. arXiv:astro-ph/0004008

    doi arXiv

  44. [52]

    Free Energy of Anisotropic Strangeon Stars

    Chen, Shichuan and Gao, Yong and Zhou, Enping and Xu, Renxin. Free Energy of Anisotropic Strangeon Stars. Res. Astron. Astrophys. 2024. doi:10.1088/1674-4527/ad1430. arXiv:2305.19687

    2024 doi arXiv

  45. [53]

    Xu, R. X. and Qiao, G. J. and Zhang, Bing. Psr 0943+10: a bare strange star?. Astrophys. J. Lett. 1999. doi:10.1086/312226. arXiv:astro-ph/9907132

    1999 doi arXiv

  46. [54]

    The Radiation Structure of PSR B2016 + 28 Observed with FAST

    Lu, Jiguang and Peng, Bo and Xu, Renxin and Yu, Meng and Dai, Shi and Zhu, Weiwei and Yu, Ye-Zhao and Jiang, Peng and Yue, Youling and Wang, Lin. The Radiation Structure of PSR B2016 + 28 Observed with FAST. Sci. China Phys. Mech. Astron. 2019. doi:10.1007/s11433-019-9394-x. a...

    2019 doi arXiv

  47. [55]

    The Optical/UV Excess of X-Ray-dim Isolated Neutron Stars

    Wang, Weiyang and Lu, Jiguang and Tong, Hao and Ge, Mingyu and Li, Zhaosheng and Men, Yunpeng and Xu, Renxin. The Optical/UV Excess of X-Ray-dim Isolated Neutron Stars. I. Bremsstrahlung Emission from a Strangeon Star Atmosphere. Astrophys. J. 2017. doi:10.3847/1538-4357/aa5e5...

    2017 doi arXiv

  48. [56]

    Rescaling strange-cluster stars and its implications on gravitational-wave echoes

    Zhang, Chen and Gao, Yong and Xia, Cheng-Jun and Xu, Renxin. Rescaling strange-cluster stars and its implications on gravitational-wave echoes. Phys. Rev. D. 2023. doi:10.1103/PhysRevD.108.063002. arXiv:2305.13323

    2023 doi arXiv

  49. [57]

    and Link, Bennett and Epstein, Richard I

    Franco, Lucia M. and Link, Bennett and Epstein, Richard I. Quaking neutron stars. Astrophys. J. 2000. doi:10.1086/317121. arXiv:astro-ph/9911105

    2000 doi arXiv

  50. [58]

    The Precursor of GRB211211A: A Tide-induced Giant Quake?

    Zhou, Enping and others. The Precursor of GRB211211A: A Tide-induced Giant Quake?. Res. Astron. Astrophys. 2024. doi:10.1088/1674-4527/ad0825. arXiv:2305.10682

    2024 doi arXiv

  51. [59]

    Gravitational wave astronomy with TianQin

    Li, En-Kun and others. Gravitational wave astronomy with TianQin. Rept. Prog. Phys. 2025. doi:10.1088/1361-6633/adc9be. arXiv:2409.19665

    2025 doi arXiv

  52. [60]

    Quasi-periodic oscillations during magnetar giant flares in the strangeon star model

    Li, Hong-Bo and Kang, Yacheng and Hu, Zexin and Shao, Lijing and Xia, Cheng-Jun and Xu, Ren-Xin. Quasi-periodic oscillations during magnetar giant flares in the strangeon star model. Mon. Not. Roy. Astron. Soc. 2023. doi:10.1093/mnras/stad3204. arXiv:2309.09847

    2023 doi arXiv

  53. [61]

    Stability of a Schwarzschild singularity

    Regge, Tullio and Wheeler, John A. Stability of a Schwarzschild singularity. Phys. Rev. 1957. doi:10.1103/PhysRev.108.1063

    1957 doi

  54. [62]

    Rotation and deformation of strangeon stars in the Lennard-Jones model

    Gao, Yong and Lai, Xiao-Yu and Shao, Lijing and Xu, Ren-Xin. Rotation and deformation of strangeon stars in the Lennard-Jones model. Mon. Not. Roy. Astron. Soc. 2021. doi:10.1093/mnras/stab3181. arXiv:2109.13234

    2021 doi arXiv

  55. [63]

    Tidal stabilization of rigidly rotating, fully relativistic neutron stars

    Thorne, Kip S. Tidal stabilization of rigidly rotating, fully relativistic neutron stars. Phys. Rev. D. 1998. doi:10.1103/PhysRevD.58.124031. arXiv:gr-qc/9706057

    1998 doi arXiv

  56. [64]

    Constraints on interquark interaction parameters with GW170817 in a binary strange star scenario

    Zhou, En-Ping and Zhou, Xia and Li, Ang. Constraints on interquark interaction parameters with GW170817 in a binary strange star scenario. Phys. Rev. D. 2018. doi:10.1103/PhysRevD.97.083015. arXiv:1711.04312

    2018 doi arXiv

  57. [65]

    and Fantina, A

    Chamel, N. and Fantina, A. F. and Pearson, J. M. and Goriely, S. Symmetry energy from nuclear masses and neutron-star observations using generalised Skyrme functionals. J. Phys. Conf. Ser. 2016. doi:10.1088/1742-6596/665/1/012066

    2016 doi

  58. [66]

    and Chugunov, Andrey I

    Zemlyakov, Nikita A. and Chugunov, Andrey I. Constraining the shear modulus of a polycrystalline neutron star crust: Hashin-Shtrikman variational approach. Phys. Rev. D. 2025. doi:10.1103/lqd6-56zn. arXiv:2507.12266

    2025 doi arXiv

  59. [67]

    The Rigidity of crystalline color superconducting quark matter

    Mannarelli, Massimo and Rajagopal, Krishna and Sharma, Rishi. The Rigidity of crystalline color superconducting quark matter. Phys. Rev. D. 2007. doi:10.1103/PhysRevD.76.074026. arXiv:hep-ph/0702021

    2007 doi arXiv

  60. [68]

    Tidal deformations of neutron stars with elastic crusts

    Gittins, Fabian and Andersson, Nils and Pereira, Jonas P. Tidal deformations of neutron stars with elastic crusts. Phys. Rev. D. 2020. doi:10.1103/PhysRevD.101.103025. arXiv:2003.05449

    2020 doi arXiv

  61. [69]

    Modelling neutron star mountains in relativity

    Gittins, Fabian and Andersson, Nils. Modelling neutron star mountains in relativity. Mon. Not. Roy. Astron. Soc. 2021. doi:10.1093/mnras/stab2048. arXiv:2105.06493

    2021 doi arXiv

  62. [70]

    On the Energy Budget of Starquake-induced Repeating Fast Radio Bursts

    Wang, Wei-Yang and Zhang, Chen and Zhou, Enping and Liu, Xiaohui and Niu, Jiarui and Zhou, Zixuan and Gao, He and Liu, Jifeng and Xu, Renxin and Zhang, Bing. On the Energy Budget of Starquake-induced Repeating Fast Radio Bursts. Res. Astron. Astrophys. 2024. doi:10.1088/1674-4...

    2024 doi arXiv

  63. [71]

    Lau, S. Y. and Leung, P. T. and Lin, L. -M. Tidal deformations of compact stars with crystalline quark matter. Phys. Rev. D. 2017. doi:10.1103/PhysRevD.95.101302. arXiv:1705.01710

    2017 doi arXiv

  64. [72]

    A unified model of the magnetar and radio pulsar bursting phenomenology

    Perna, Rosalba and Pons, Jose A. A unified model of the magnetar and radio pulsar bursting phenomenology. Astrophys. J. Lett. 2011. doi:10.1088/2041-8205/727/2/L51. arXiv:1101.1098

    2011 doi arXiv

  65. [73]

    and Bowers, Jeffrey A

    Alford, Mark G. and Bowers, Jeffrey A. and Rajagopal, Krishna. Crystalline color superconductivity. Phys. Rev. D. 2001. doi:10.1103/PhysRevD.63.074016. arXiv:hep-ph/0008208

    2001 doi arXiv

  66. [74]

    and Campolattaro, Alfonso , title =

    Thorne, Kip S. and Campolattaro, Alfonso , title =. 1967 , month =. doi:10.1086/149288 , publisher =

    1967 doi

  67. [75]

    2019 , issn =

    The inner structure of neutron stars , journal =. 2019 , issn =. doi:10.7693/wl20190902 , url =

    2019 doi

  68. [76]

    , title =

    Ruderman, M. , title =. , year =. doi:10.1086/169558 , adsurl =

    doi

  69. [77]

    Jones, J. E. , title =. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character , volume =. 1924 , month =. doi:10.1098/rspa.1924.0082 , url =

    1924 doi

  70. [78]

    , year = 1969, month = aug, volume =

    Neutron Starquakes and Pulsar Periods. , year = 1969, month = aug, volume =. doi:10.1038/223597b0 , adsurl =

    1969 doi

  71. [79]

    Analytical Solutions of Love Numbers for a Hydrostatic Ellipsoidal Incompressible Homogeneous Earth , journal =

    Greff-Lefftz, Marianne and M. Analytical Solutions of Love Numbers for a Hydrostatic Ellipsoidal Incompressible Homogeneous Earth , journal =. 2005 , doi =

    2005

  72. [80]

    Love, A. E. H. , title =. 1911 , pages =

    1911

  73. [81]

    The rotation of the earth; a geophysical discussion

Pith tools

Reviewed July 14, 2026 · model on record in the stance chip above.