- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Distinct signatures of the nature of phase transition in binary neutron-star mergers

Sagnik Chatterjee1,2,*, Shamim Haque1,*, Kamal Krishna Nath3, Rana Nandi4, and Ritam Mallick1,†

  • *These authors contributed equally to this work.
  • †Contact author: mallick@iiserb.ac.in
PDF

Phys. Rev. D 113, 123009 – Published 3 June, 2026

DOI: https://doi.org/10.1103/5ts1-p7t7

Abstract

Binary neutron-star mergers offer crucial insights into the matter properties of neutron stars. We present the possible imprints in the gravitational wave signal from the nature of phase transition from such events. Our study employs a one-parameter family of equation of states built using a polytropic approach with a control parameter Δp surveying the features of hadron-quark phase transition, from Maxwell construction to the Gibbs construction. It allows us to explore the extent of mixed phases and analyze their direct impact on merger dynamics. Post-merger gravitational wave emissions reveal the expression of specific signatures in the spectrogram and power spectral density, serving as a distinct signature of equations of state with mixed phases. We found additional peaks in power spectral density that are exclusively generated from the post-merger remnant experiencing a phase transition. Additionally, the nature of phase transition leaves specific imprints on the spectrogram, leading to a twofolded signature from gravitational wave analysis. Furthermore, we establish the first correlation between Δp and the threshold mass for prompt collapse. Our analysis shows that Δp≲0.04 is required if GW170817 formed a long-lived remnant or has experienced a delayed collapse into a black hole.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (212)

  1. E. S. Fraga, A. Kurkela, and A. Vuorinen, Interacting quark matter equation of state for compact stars, Astrophys. J. 781, L25 (2014).
  2. K. B. Fadafan, J. C. Rojas, and N. Evans, Deconfined, massive quark phase at high density and compact stars: A holographic study, Phys. Rev. D 101, 126005 (2020).
  3. V. Dexheimer, L. T. T. Soethe, J. Roark, R. O. Gomes, S. O. Kepler, and S. Schramm, Phase transitions in neutron stars, Int. J. Mod. Phys. E 27, 1830008 (2018).
  4. R. Somasundaram, I. Tews, and J. Margueron, Investigating signatures of phase transitions in neutron-star cores, Phys. Rev. C 107, 025801 (2023).
  5. L. Tolos, Dense hadronic matter in neutron stars, Acta Phys. Pol. B 55, 1 (2024).
  6. C. Providência, T. Malik, M. B. Albino, and M. Ferreira, Relativistic description of the neutron star equation of state, in Nuclear Theory in the Age of Multimessenger Astronomy (CRC Press, Boca Raton, Florida, 2024), p. 111–143, 10.1201/9781003306580-5.
  7. F. Weber, Quark matter in neutron stars, J. Phys. G 25, R195 (1999).
  8. E. Annala, T. Gorda, A. Kurkela, J. Nättilä, and A. Vuorinen, Evidence for quark-matter cores in massive neutron stars, Nat. Phys. 16, 907 (2020).
  9. N. Glendenning, Compact Stars: Nuclear Physics, Particle Physics and General Relativity, Astronomy and Astrophysics Library (Springer, New York, 2012).
  10. J. Antoniadis et al., A massive pulsar in a compact relativistic binary, Science 340, 1233232 (2013).
  11. E. Fonseca et al., Refined mass and geometric measurements of the high-mass PSR J0740+6620, Astrophys. J. Lett. 915, L12 (2021).
  12. H. T. Cromartie et al., Relativistic shapiro delay measurements of an extremely massive millisecond pulsar, Nat. Astron. 4, 72 (2020).
  13. 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).
  14. T. E. Riley et al., A nicer view of PSR J0030+0451: Millisecond pulsar parameter estimation, Astrophys. J. 887, L21 (2019).
  15. M. C. Miller et al., The radius of PSR J0740+6620 from NICER and XMM-Newton data, Astrophys. J. Lett. 918, L28 (2021).
  16. T. 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).
  17. N. K. Glendenning, First-order phase transitions with more than one conserved charge: Consequences for neutron stars, Phys. Rev. D 46, 1274 (1992).
  18. M. Alford, Color-superconducting quark matter, Annu. Rev. Nucl. Part. Sci. 51, 131 (2001).
  19. M. Alford, M. Braby, M. Paris, and S. Reddy, Hybrid stars that masquerade as neutron stars, Astrophys. J. 629, 969 (2005).
  20. S. Benić, D. Blaschke, D. E. Alvarez-Castillo, T. Fischer, and S. Typel, A new quark-hadron hybrid equation of state for astrophysics—I. High-mass twin compact stars, Astron. Astrophys. 577, A40 (2015).
  21. A. V. Olinto, On the conversion of neutron stars into strange stars, Phys. Lett. B 192, 71 (1987).
  22. A. Bhattacharyya, S. K. Ghosh, P. S. Joarder, R. Mallick, and S. Raha, Conversion of a neutron star to a strange star: A two-step process, Phys. Rev. C 74, 065804 (2006).
  23. A. Bhattacharyya, S. K. Ghosh, R. Mallick, and S. Raha, General relativistic effects on the conversion of nuclear to two-flavor quark matter in compact stars, Phys. Rev. C 76, 052801(R) (2007).
  24. A. Drago, A. Lavagno, and I. Parenti, Burning of a hadronic star into a quark or a hybrid star, Astrophys. J. 659, 1519 (2007).
  25. M. Baldo, M. Buballa, G. Burgio, F. Neumann, M. Oertel, and H.-J. Schulze, Neutron stars and the transition to color superconducting quark matter, Phys. Lett. B 562, 153 (2003).
  26. D. Blaschke, F. Sandin, T. Klähn, and J. Berdermann, Sequential deconfinement of quark flavors in neutron stars, Phys. Rev. C 80, 065807 (2009).
  27. V. A. Dexheimer and S. Schramm, Novel approach to modeling hybrid stars, Phys. Rev. C 81, 045201 (2010).
  28. M. Orsaria, H. Rodrigues, F. Weber, and G. A. Contrera, Quark deconfinement in high-mass neutron stars, Phys. Rev. C 89, 015806 (2014).
  29. M. Ferreira, R. C. Pereira, and C. m. c. Providência, Neutron stars with large quark cores, Phys. Rev. D 101, 123030 (2020).
  30. S. Han and M. Prakash, On the minimum radius of very massive neutron stars, Astrophys. J. 899, 164 (2020).
  31. S. Tewari, S. Chatterjee, D. Kumar, and R. Mallick, Analyzing the dense matter equation of states in the light of the compact object HESS J1731-347, Phys. Rev. D 111, 103009 (2025).
  32. D. Guha Roy, A. Venneti, T. Malik, S. Bhattacharya, and S. Banik, Bayesian evaluation of hadron-quark phase transition models through neutron star observables in light of nuclear and astrophysics data, Phys. Lett. B 859, 139128 (2024).
  33. P. Thakur, S. Chatterjee, K. K. Nath, and R. Mallick, Prospect of unraveling the first-order phase transition in neutron stars with f and p1 modes, Phys. Rev. D 110, 103045 (2024).
  34. H. Dimmelmeier, M. Bejger, P. Haensel, and J. L. Zdunik, Dynamic migration of rotating neutron stars due to a phase transition instability, Mon. Not. R. Astron. Soc. 396, 2269 (2009).
  35. B. Franzon, R. O. Gomes, and S. Schramm, Effects of the quark-hadron phase transition on highly magnetized neutron stars, Mon. Not. R. Astron. Soc. 463, 571 (2016).
  36. R. Prasad and R. Mallick, Dynamical phase transition in neutron stars, Astrophys. J. 859, 57 (2018).
  37. R. Prasad and R. Mallick, Gravitational waves from the phase transition of NS to QS, Astrophys. J. 893, 151 (2020).
  38. S. L. Liebling, C. Palenzuela, and L. Lehner, Effects of high density phase transitions on neutron star dynamics, Classical Quantum Gravity 38, 115007 (2021).
  39. S. Shashank, F. H. Nouri, and A. Gupta, f-mode oscillations of compact stars with realistic equations of state in dynamical spacetime, New Astron. 104, 102067 (2023).
  40. P. L. Espino and V. Paschalidis, Fate of twin stars on the unstable branch: Implications for the formation of twin stars, Phys. Rev. D 105, 043014 (2022).
  41. M. Naseri, G. Bozzola, and V. Paschalidis, Exploring pathways to forming twin stars, Phys. Rev. D 110, 044037 (2024).
  42. B. P. Abbott, R. Abbott et al. (The LIGO Scientific Collaboration and the Virgo Collaboration), Gw170817: Measurements of neutron star radii and equation of state, Phys. Rev. Lett. 121, 161101 (2018).
  43. 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).
  44. C. A. Raithel, F. Özel, and D. Psaltis, Tidal deformability from GW170817 as a direct probe of the neutron star radius, Astrophys. J. Lett. 857, L23 (2018).
  45. S. De, D. Finstad, J. M. Lattimer, D. A. Brown, E. Berger, and C. M. Biwer, Tidal deformabilities and radii of neutron stars from the observation of GW170817, Phys. Rev. Lett. 121, 091102 (2018).
  46. N. Sarin and P. D. Lasky, The evolution of binary neutron star post-merger remnants: A review, Gen. Relativ. Gravit. 53, 59 (2021).
  47. L. Baiotti and L. Rezzolla, Binary neutron star mergers: A review of Einstein’s richest laboratory, Rep. Prog. Phys. 80, 096901 (2017).
  48. L. Baiotti, Gravitational waves from neutron star mergers and their relation to the nuclear equation of state, Prog. Part. Nucl. Phys. 109, 103714 (2019).
  49. D. Radice, S. Bernuzzi, and A. Perego, The dynamics of binary neutron star mergers and GW170817, Annu. Rev. Nucl. Part. Sci. 70, 95 (2020).
  50. T. Dietrich, T. Hinderer, and A. Samajdar, Interpreting binary neutron star mergers: Describing the binary neutron star dynamics, modelling gravitational waveforms, and analyzing detections, Gen. Relativ. Gravit. 53, 27 (2021).
  51. A. Bauswein, R. Oechslin, and H.-T. Janka, Discriminating strange star mergers from neutron star mergers by gravitational-wave measurements, Phys. Rev. D 81, 024012 (2010).
  52. A. Bauswein and H.-T. Janka, Measuring neutron-star properties via gravitational waves from neutron-star mergers, Phys. Rev. Lett. 108, 011101 (2012).
  53. C. Ecker, T. Gorda, A. Kurkela, and L. Rezzolla, Constraining the equation of state in neutron-star cores via the long-ringdown signal, Nat. Commun. 16, 1320 (2025).
  54. R. Oechslin, G. Poghosyan, and K. Uryū, Quark matter in neutron star mergers, Nucl. Phys. A718, 706 (2003).
  55. R. Oechslin, K. Uryū, G. Poghosyan, and F. K. Thielemann, The influence of quark matter at high densities on binary neutron star mergers, Mon. Not. R. Astron. Soc. 349, 1469 (2004).
  56. R. Oechslin, S. Rosswog, and F.-K. Thielemann, Conformally flat smoothed particle hydrodynamics application to neutron star mergers, Phys. Rev. D 65, 103005 (2002).
  57. C. A. Raithel and E. R. Most, Characterizing the breakdown of quasi-universality in postmerger gravitational waves from binary neutron star mergers, Astrophys. J. Lett. 933, L39 (2022).
  58. M. Hanauske, K. Takami, L. Bovard, L. Rezzolla, J. A. Font, F. Galeazzi, and H. Stöcker, Rotational properties of hypermassive neutron stars from binary mergers, Phys. Rev. D 96, 043004 (2017).
  59. L. Rezzolla and K. Takami, Gravitational-wave signal from binary neutron stars: A systematic analysis of the spectral properties, Phys. Rev. D 93, 124051 (2016).
  60. K. Takami, L. Rezzolla, and L. Baiotti, Spectral properties of the post-merger gravitational-wave signal from binary neutron stars, Phys. Rev. D 91, 064001 (2015).
  61. K. Takami, L. Rezzolla, and L. Baiotti, Constraining the equation of state of neutron stars from binary mergers, Phys. Rev. Lett. 113, 091104 (2014).
  62. J. S. Read et al., Matter effects on binary neutron star waveforms, Phys. Rev. D 88, 044042 (2013).
  63. S. D. Tootle, L. J. Papenfort, E. R. Most, and L. Rezzolla, Quasi-universal behavior of the threshold mass in unequal-mass, spinning binary neutron star mergers, Astrophys. J. Lett. 922, L19 (2021).
  64. Y. Sekiguchi, K. Kiuchi, K. Kyutoku, and M. Shibata, Effects of hyperons in binary neutron star mergers, Phys. Rev. Lett. 107, 211101 (2011).
  65. V. Vijayan, N. Rahman, A. Bauswein, G. Martínez-Pinedo, and I. L. Arbina, Impact of pions on binary neutron star mergers, Phys. Rev. D 108, 023020 (2023).
  66. A. Bauswein, H.-T. Janka, K. Hebeler, and A. Schwenk, Equation-of-state dependence of the gravitational-wave signal from the ring-down phase of neutron-star mergers, Phys. Rev. D 86, 063001 (2012).
  67. A. Bauswein, N. Stergioulas, and H.-T. Janka, Revealing the high-density equation of state through binary neutron star mergers, Phys. Rev. D 90, 023002 (2014).
  68. A. Bauswein and N. Stergioulas, Unified picture of the post-merger dynamics and gravitational wave emission in neutron star mergers, Phys. Rev. D 91, 124056 (2015).
  69. C. A. Raithel and E. R. Most, Tidal deformability doppelgänger: Implications of a low-density phase transition in the neutron star equation of state, Phys. Rev. D 108, 023010 (2023).
  70. E. R. Most and A. A. Philippov, Electromagnetic precursor flares from the late inspiral of neutron star binaries, Mon. Not. R. Astron. Soc. 515, 2710 (2022).
  71. E. R. Most and A. A. Philippov, Electromagnetic precursors to gravitational-wave events: Numerical simulations of flaring in pre-merger binary neutron star magnetospheres, Astrophys. J. Lett. 893, L6 (2020).
  72. E. R. Most and E. Quataert, Flares, jets, and quasiperiodic outbursts from neutron star merger remnants, Astrophys. J. Lett. 947, L15 (2023).
  73. M. Hanauske et al., Neutron star mergers: Probing the eos of hot, dense matter by gravitational waves,, Particles 2, 44 (2019).
  74. B. Giacomazzo, L. Rezzolla, and L. Baiotti, Accurate evolutions of inspiralling and magnetized neutron stars: Equal-mass binaries, Phys. Rev. D 83, 044014 (2011).
  75. L. Rezzolla, B. Giacomazzo, L. Baiotti, J. Granot, C. Kouveliotou, and M. A. Aloy, The missing link: Merging neutron stars naturally produce jet-like structures and can power short gamma-ray bursts, Astrophys. J. Lett. 732, L6 (2011).
  76. K. Kiuchi, K. Kyutoku, Y. Sekiguchi, M. Shibata, and T. Wada, High resolution numerical relativity simulations for the merger of binary magnetized neutron stars, Phys. Rev. D 90, 041502(R) (2014).
  77. Y. Sekiguchi, K. Kiuchi, K. Kyutoku, and M. Shibata, Gravitational waves and neutrino emission from the merger of binary neutron stars, Phys. Rev. Lett. 107, 051102 (2011).
  78. K. Kiuchi, K. Kyutoku, Y. Sekiguchi, and M. Shibata, Global simulations of strongly magnetized remnant massive neutron stars formed in binary neutron star mergers, Phys. Rev. D 97, 124039 (2018).
  79. F. Foucart, Monte Carlo closure for moment-based transport schemes in general relativistic radiation hydrodynamic simulations, Mon. Not. R. Astron. Soc. 475, 4186 (2018).
  80. F. Foucart, M. D. Duez, F. Hebert, L. E. Kidder, H. P. Pfeiffer, and M. A. Scheel, Monte-Carlo neutrino transport in neutron star merger simulations, Astrophys. J. Lett. 902, L27 (2020).
  81. S. Blacker, H. Kochankovski, A. Bauswein, A. Ramos, and L. Tolos, Thermal behavior as indicator for hyperons in binary neutron star merger remnants, Phys. Rev. D 109, 043015 (2024).
  82. S. Blacker, A. Bauswein, and S. Typel, Exploring thermal effects of the hadron-quark matter transition in neutron star mergers, Phys. Rev. D 108, 063032 (2023).
  83. O. Just, V. Vijayan, Z. Xiong, S. Goriely, T. Soultanis, A. Bauswein, J. Guilet, H.-T. Janka, and G. Martínez-Pinedo, End-to-end kilonova models of neutron star mergers with delayed black hole formation, Astrophys. J. Lett. 951, L12 (2023).
  84. H. Gieg, T. Dietrich, and M. Ujevic, Simulating binary neutron stars with hybrid equation of states: Gravitational waves, electromagnetic signatures and challenges for numerical relativity, Particles 2, 365 (2019).
  85. K. Kiuchi, A. Reboul-Salze, M. Shibata, and Y. Sekiguchi, A large-scale magnetic field produced by a solar-like dynamo in binary neutron star mergers, Nat. Astron. 8, 298 (2024).
  86. C. Palenzuela, S. L. Liebling, D. Neilsen, L. Lehner, O. L. Caballero, E. O’Connor, and M. Anderson, Effects of the microphysical equation of state in the mergers of magnetized neutron stars with neutrino cooling, Phys. Rev. D 92, 044045 (2015).
  87. M. Anderson et al., Magnetized neutron-star mergers and gravitational-wave signals, Phys. Rev. Lett. 100, 191101 (2008).
  88. Y.-J. Huang et al., Merger and postmerger of binary neutron stars with a quark-hadron crossover equation of state, Phys. Rev. Lett. 129, 181101 (2022).
  89. M. Hanauske et al., Detecting the hadron-quark phase transition with gravitational waves, Universe 5, 156 (2019).
  90. E. R. Most, L. J. Papenfort, V. Dexheimer, M. Hanauske, S. Schramm, H. Stöcker, and L. Rezzolla, Signatures of quark-hadron phase transitions in general-relativistic neutron-star mergers, Phys. Rev. Lett. 122, 061101 (2019).
  91. E. R. Most, L. Jens Papenfort, V. Dexheimer, M. Hanauske, H. Stoecker, and L. Rezzolla, On the deconfinement phase transition in neutron-star mergers, Eur. Phys. J. A 56, 59 (2020).
  92. L. R. Weih, M. Hanauske, and L. Rezzolla, Postmerger gravitational-wave signatures of phase transitions in binary mergers, Phys. Rev. Lett. 124, 171103 (2020).
  93. S. Tootle, C. Ecker, K. Topolski, T. Demircik, M. Järvinen, and L. Rezzolla, Quark formation and phenomenology in binary neutron-star mergers using V-QCD, SciPost Phys. 13, 109 (2022).
  94. A. Kedia, H. I. Kim, I.-S. Suh, and G. J. Mathews, Binary neutron star mergers as a probe of quark-hadron crossover equations of state, Phys. Rev. D 106, 103027 (2022).
  95. A. Prakash et al., Signatures of deconfined quark phases in binary neutron star mergers, Phys. Rev. D 104, 083029 (2021).
  96. Y. Fujimoto, K. Fukushima, K. Hotokezaka, and K. Kyutoku, Gravitational wave signal for quark matter with realistic phase transition, Phys. Rev. Lett. 130, 091404 (2023).
  97. S. Haque, R. Mallick, and S. K. Thakur, Effects of onset of phase transition on binary neutron star mergers, Mon. Not. R. Astron. Soc. 527, 11575–11586 (2023).
  98. M. Ujevic, H. Gieg, F. Schianchi, S. V. Chaurasia, I. Tews, and T. Dietrich, Reverse phase transitions in binary neutron-star systems with exotic-matter cores, Phys. Rev. D 107, 024025 (2023).
  99. Y. Fujimoto, K. Fukushima, K. Hotokezaka, and K. Kyutoku, Signature of hadron-quark crossover in binary-neutron-star mergers, Phys. Rev. D 111, 063054 (2025).
  100. A. Bauswein and S. Blacker, Impact of quark deconfinement in neutron star mergers and hybrid star mergers, Eur. Phys. J. Spec. Top. 229, 3595 (2020).
  101. S. Blacker et al., Constraining the onset density of the hadron-quark phase transition with gravitational-wave observations, Phys. Rev. D 102, 123023 (2020).
  102. A. Bauswein, N.-U. F. Bastian, D. B. Blaschke, K. Chatziioannou, J. A. Clark, T. Fischer, and M. Oertel, Identifying a first-order phase transition in neutron-star mergers through gravitational waves, Phys. Rev. Lett. 122, 061102 (2019).
  103. R. Nandi and P. Char, Hybrid stars in the light of GW170817, Astrophys. J. 857, 12 (2018).
  104. R. Nandi, P. Char, and S. Pal, Constraining the relativistic mean-field model equations of state with gravitational wave observations, Phys. Rev. C 99, 052802(R) (2019).
  105. R. Nandi and S. Pal, Finding quark content of neutron stars in light of GW170817, Eur. Phys. J. ST 230, 551 (2021).
  106. R. Mallick, D. Kuzur, and R. Nandi, Semi-empirical relation to understand matter properties at neutron star interiors, Eur. Phys. J. C 82, 512 (2022).
  107. A. Kumar, V. B. Thapa, and M. Sinha, Hybrid stars are compatible with recent astrophysical observations, Phys. Rev. D 107, 063024 (2023).
  108. J. J. Li, A. Sedrakian, and M. Alford, Relativistic hybrid stars with sequential first-order phase transitions in light of multimessenger constraints, Astrophys. J. 944, 206 (2023).
  109. G. A. Contrera, D. Blaschke, J. P. Carlomagno, A. G. Grunfeld, and S. Liebing, Quark-nuclear hybrid equation of state for neutron stars under modern observational constraints, Phys. Rev. C 105, 045808 (2022).
  110. P. Qin, Z. Bai, S. Wang, C. Wang, and S.-x. Qin, Hadron-quark phase transition in neutron star by combining the relativistic Brueckner-Hartree-Fock theory and Dyson-Schwinger equation approach, Phys. Rev. D 107, 103009 (2023).
  111. D. Sen, H. Gil, and C. H. Hyun, Hadron-quark phase transition in the neutron star with vector mit bag model and Korea-Ibs-Daegu-Skku functional, Front. Astron. Space Sci. 11, 1421839 (2024).
  112. L. Brandes and W. Weise, Constraints on phase transitions in neutron star matter, Symmetry 16, 111 (2024).
  113. S. Han, M. A. A. Mamun, S. Lalit, C. Constantinou, and M. Prakash, Treating quarks within neutron stars, Phys. Rev. D 100, 103022 (2019).
  114. I. A. Rather, A. Kumar, H. C. Das, M. Imran, A. A. Usmani, and S. K. Patra, Constraining bag constant for hybrid neutron stars, Int. J. Mod. Phys. E 29, 2050044 (2020).
  115. X. H. Wu and H. Shen, Finite-size effects on the hadron-quark phase transition in neutron stars, Phys. Rev. C 96, 025802 (2017).
  116. C. Constantinou, T. Zhao, S. Han, and M. Prakash, Framework for phase transitions between the Maxwell and Gibbs constructions, Phys. Rev. D 107, 074013 (2023).
  117. K. Maslov et al., Hybrid equation of state with pasta phases, and third family of compact stars, Phys. Rev. C 100, 025802 (2019).
  118. M. Ju, J. Hu, and H. Shen, Hadron-quark pasta phase in massive neutron stars, Astrophys. J. 923, 250 (2021).
  119. H. Dinh Thi, T. Carreau, A. F. Fantina, and F. Gulminelli, Uncertainties in the pasta-phase properties of catalysed neutron stars, Astron. Astrophys. 654, A114 (2021).
  120. D. N. Voskresensky, M. Yasuhira, and T. Tatsumi, Charge screening at first order phase transitions and hadron quark mixed phase, Nucl. Phys. A723, 291 (2003).
  121. T. Tatsumi, M. Yasuhira, and D. Voskresensky, Hadron-quark mixed phase in neutron stars, Nucl. Phys. A718, 359 (2003).
  122. T. Endo, Charge screening effect on hadron-quark mixed phase in compact stars, in 29th Johns Hopkins Workshop on Current Problems in Particle Theory: Strong Matter in the Heavens, edited by G. Domokos (2006), p. 19.1, arXiv:astro-ph/0601017.
  123. T. Noda, M.-a. Hashimoto, N. Yasutake, T. Maruyama, T. Tatsumi, and M. Fujimoto, Cooling of compact stars with color superconducting phase in quark-hadron mixed phase, Astrophys. J. 765, 1 (2013).
  124. N. Yasutake, R. Łastowiecki, S. Benić, D. Blaschke, T. Maruyama, and T. Tatsumi, Finite-size effects at the hadron-quark transition and heavy hybrid stars, Phys. Rev. C 89, 065803 (2014).
  125. A. Ayriyan and H. Grigorian, Model of the phase transition mimicking the pasta phase in cold and dense quark-hadron matter, EPJ Web Conf. 173, 03003 (2018).
  126. V. Abgaryan, D. Alvarez-Castillo, A. Ayriyan, D. Blaschke, and H. Grigorian, Two novel approaches to the hadron-quark mixed phase in compact stars, Universe 4, 94 (2018).
  127. D. Blaschke and D. Alvarez-Castillo, A mixing interpolation method to mimic pasta phases in compact star matter, Eur. Phys. J. A 56, 124 (2020).
  128. D. E. Alvarez-Castillo and D. B. Blaschke, High-mass twin stars with a multipolytrope equation of state, Phys. Rev. C 96, 045809 (2017).
  129. M. Shahrbaf, D. Blaschke, and S. Khanmohamadi, Mixed phase transition from hypernuclear matter to deconfined quark matter fulfilling mass-radius constraints of neutron stars, J. Phys. G 47, 115201 (2020).
  130. J. P. Pereira, M. Bejger, J. L. Zdunik, and P. Haensel, Differentiating between sharp and smoother phase transitions in neutron stars, Phys. Rev. D 105, 123015 (2022).
  131. B. K. Pradhan, D. Chatterjee, and D. E. Alvarez-Castillo, Probing hadron–quark phase transition in twin stars using f-modes, Mon. Not. R. Astron. Soc. 531, 4640 (2024).
  132. F. Özel, D. Psaltis, S. Ransom, P. Demorest, and M. Alford, The massive pulsar PSR J1614-2230: Linking quantum chromodynamics, gamma-ray bursts, and gravitational wave astronomy, Astrophys. J. Lett. 724, L199 (2010).
  133. 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).
  134. E. Annala, T. Gorda, A. Kurkela, and A. Vuorinen, Gravitational-wave constraints on the neutron-star-matter equation of state, Phys. Rev. Lett. 120, 172703 (2018).
  135. A. Bauswein, O. Just, H.-T. Janka, and N. Stergioulas, Neutron-star radius constraints from GW170817 and future detections, Astrophys. J. Lett. 850, L34 (2017).
  136. L. Rezzolla, E. R. Most, and L. R. Weih, Using gravitational-wave observations and quasi-universal relations to constrain the maximum mass of neutron stars, Astrophys. J. Lett. 852, L25 (2018).
  137. J. M. Lattimer, M. Prakash, D. Masak, and A. Yahil, Rapidly rotating pulsars and the equation of state, Astrophys. J. 355, 241 (1990).
  138. J. M. Lattimer and M. Prakash, Neutron star structure and the equation of state, Astrophys. J. 550, 426 (2001).
  139. L. Rezzolla and O. Zanotti, Relativistic Hydrodynamics (Oxford University Press, New York, 2013), 10.1093/acprof:oso/9780198528906.001.0001.
  140. J. S. Read, B. D. Lackey, B. J. Owen, and J. L. Friedman, Constraints on a phenomenologically parametrized neutron-star equation of state, Phys. Rev. D 79, 124032 (2009).
  141. J. A. Font, J. M. Ibanez, A. Marquina, and J. M. Marti, Multidimensional relativistic hydrodynamics: Characteristic fields and modern high-resolution shock-capturing schemes, Astron. Astrophys. 282, 304 (1994), https://ui.adsabs.harvard.edu/abs/1994A%26A...282..304F/abstract.
  142. H. T. Janka, T. Zwerger, and R. Moenchmeyer, Does artificial viscosity destroy prompt type-II supernova explosions?, Astron. Astrophys. 268, 360 (1993), https://ui.adsabs.harvard.edu/abs/1993A%26A...268..360J/abstract.
  143. Radice, D. and Rezzolla, L., Thc: A new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics, Astron. Astrophys. 547, A26 (2012).
  144. D. Radice, L. Rezzolla, and F. Galeazzi, Beyond second-order convergence in simulations of binary neutron stars in full general relativity, Mon. Not. R. Astron. Soc.: Lett. 437, L46 (2013).
  145. D. Radice, L. Rezzolla, and F. Galeazzi, High-order fully general-relativistic hydrodynamics: New approaches and tests, Classical Quantum Gravity 31, 075012 (2014).
  146. F. Banyuls, J. A. Font, J. M. Ibáñez, J. M. Martí, and J. A. Miralles, Numerical 3+1 general relativistic hydrodynamics: A local characteristic approach, Astrophys. J. 476, 221 (1997).
  147. B. D. Metzger, Kilonovae, Living Rev. Relativity 23, 1 (2019).
  148. M. Hanauske, L. R. Weih, H. Stöcker, and L. Rezzolla, Metastable hypermassive hybrid stars as neutron-star merger remnants, Eur. Phys. J. Spec. Top. 230, 543 (2021).
  149. E. Capote et al., Advanced LIGO detector performance in the fourth observing run, Phys. Rev. D 111, 062002 (2025).
  150. S. Hild et al., Sensitivity studies for third-generation gravitational wave observatories, Classical Quantum Gravity 28, 094013 (2011).
  151. A. Bauswein, S. Blacker, G. Lioutas, T. Soultanis, V. Vijayan, and N. Stergioulas, Systematics of prompt black-hole formation in neutron star mergers, Phys. Rev. D 103, 123004 (2021).
  152. A. Bauswein et al., Equation of state constraints from the threshold binary mass for prompt collapse of neutron star mergers, Phys. Rev. Lett. 125, 141103 (2020).
  153. K. Hotokezaka, K. Kyutoku, H. Okawa, M. Shibata, and K. Kiuchi, Binary neutron star mergers: Dependence on the nuclear equation of state, Phys. Rev. D 83, 124008 (2011).
  154. S. Köppel, L. Bovard, and L. Rezzolla, A general-relativistic determination of the threshold mass to prompt collapse in binary neutron star mergers, Astrophys. J. Lett. 872, L16 (2019).
  155. A. Bauswein, T. W. Baumgarte, and H.-T. Janka, Prompt merger collapse and the maximum mass of neutron stars, Phys. Rev. Lett. 111, 131101 (2013).
  156. C. Ecker, K. Topolski, M. Järvinen, and A. Stehr, Prompt black hole formation in binary neutron star mergers, Phys. Rev. D 111, 023001 (2025).
  157. S. Chatterjee and K. K. Nath, Insights into neutron stars from gravitational redshifts and universal relations, Eur. Phys. J. C 85, 862 (2025).
  158. L. Piro et al., A long-lived neutron star merger remnant in GW170817: constraints and clues from x-ray observations, Mon. Not. R. Astron. Soc. 483, 1912 (2018).
  159. R. Gill, A. Nathanail, and L. Rezzolla, When did the remnant of GW170817 collapse to a black hole?, Astrophys. J. 876, 139 (2019).
  160. B. Margalit and B. D. Metzger, Constraining the maximum mass of neutron stars from multi-messenger observations of GW170817, Astrophys. J. Lett. 850, L19 (2017).
  161. Y.-W. Yu, L.-D. Liu, and Z.-G. Dai, A long-lived remnant neutron star after GW170817 inferred from its associated kilonova, Astrophys. J. 861, 114 (2018).
  162. S. Ai, H. Gao, Z.-G. Dai, X.-F. Wu, A. Li, B. Zhang, and M.-Z. Li, The allowed parameter space of a long-lived neutron star as the merger remnant of GW170817, Astrophys. J. 860, 57 (2018).
  163. A. Murguia-Berthier et al., A neutron star binary merger model for GW170817/GRB 170817A/SSS17A, Astrophys. J. Lett. 848, L34 (2017).
  164. M. Agathos et al., Inferring prompt black-hole formation in neutron star mergers from gravitational-wave data, Phys. Rev. D 101, 044006 (2020).
  165. L. Rezzolla, E. R. Most, and L. R. Weih, Using gravitational-wave observations and quasi-universal relations to constrain the maximum mass of neutron stars, Astrophys. J. 852, L25 (2018).
  166. M. Mould, C. J. Moore, and D. Gerosa, Calibrating signal-to-noise ratio detection thresholds using gravitational-wave catalogs, Phys. Rev. D 109, 063013 (2024).
  167. P. Petrov, L. P. Singer, M. W. Coughlin, V. Kumar, M. Almualla, S. Anand, M. Bulla, T. Dietrich, F. Foucart, and N. Guessoum, Data-driven expectations for electromagnetic counterpart searches based on LIGO/Virgo public alerts, Astrophys. J. 924, 54 (2022).
  168. F. Iacovelli, M. Mancarella, S. Foffa, and M. Maggiore, Forecasting the detection capabilities of third-generation gravitational-wave detectors using GWFAST, Astrophys. J. 941, 208 (2022).
  169. S. Ronchini, M. Branchesi, G. Oganesyan, B. Banerjee, U. Dupletsa, G. Ghirlanda, J. Harms, M. Mapelli, and F. Santoliquido, Perspectives for multimessenger astronomy with the next generation of gravitational-wave detectors and high-energy satellites, Astron. Astrophys. 665, A97 (2022).
  170. A. Bauswein, S. Goriely, and H.-T. Janka, Systematics of dynamical mass ejection, nucleosynthesis, and radioactively powered electromagnetic signals from neutron-star mergers, Astrophys. J. 773, 78 (2013).
  171. L. Lehner, S. L. Liebling, C. Palenzuela, O. L. Caballero, E. O’Connor, M. Anderson, and D. Neilsen, Unequal mass binary neutron star mergers and multimessenger signals, Classical Quantum Gravity 33, 184002 (2016).
  172. D. Radice, A. Perego, K. Hotokezaka, S. Bernuzzi, S. A. Fromm, and L. F. Roberts, Viscous-dynamical ejecta from binary neutron star mergers, Astrophys. J. Lett. 869, L35 (2018).
  173. R. Ciolfi, W. Kastaun, B. Giacomazzo, A. Endrizzi, D. M. Siegel, and R. Perna, General relativistic magnetohydrodynamic simulations of binary neutron star mergers forming a long-lived neutron star, Phys. Rev. D 95, 063016 (2017).
  174. C. R. Harris et al., Array programming with numpy, Nature (London) 585, 357 (2020).
  175. P. Virtanen et al., scipy1.0: Fundamental algorithms for scientific computing in python, Nat. Methods 17, 261 (2020).
  176. J. D. Hunter, Matplotlib: A 2d graphics environment, Comput. Sci. Eng. 9, 90 (2007).
  177. M. L. Waskom, seaborn: Statistical data visualization, J. Open Source Software 6, 3021 (2021).
  178. Wes McKinney, data structures for statistical computing in python, in Proceedings of the 9th python in Conference, edited by Stéfan van der Walt and Jarrod Millman (2010), pp. 56–61, 10.25080/Majora-92bf1922-00a.
  179. G. Bozzola, kuibit: Analyzing Einstein toolkit simulations with python, J. Open Source Software 6, 3099 (2021).
  180. Kuibit, https://sbozzolo.github.io/kuibit/.
  181. T. Kluyver et al., Jupyter notebooks—a publishing format for reproducible computational workflows, in Positioning and Power in Academic Publishing: Players, Agents and Agendas, edited by F. Loizides and B. Schmidt (IOS Press, Göttingen, Germany, 2016), pp. 87–90, https://ebooks.iospress.nl/publication/42900.
  182. Z. F. Seidov, The stability of a star with a phase change in general relativity theory, Sov. Astron. 15, 347 (1971), https://ui.adsabs.harvard.edu/scan/manifest/1971SvA....15..347S.
  183. A. Bauswein, H.-T. Janka, and R. Oechslin, Testing approximations of thermal effects in neutron star merger simulations, Phys. Rev. D 82, 084043 (2010).
  184. C. A. Raithel, V. Paschalidis, and F. Özel, Realistic finite-temperature effects in neutron star merger simulations, Phys. Rev. D 104, 063016 (2021).
  185. A. Figura, J.-J. Lu, G. F. Burgio, Z.-H. Li, and H.-J. Schulze, Hybrid equation of state approach in binary neutron-star merger simulations, Phys. Rev. D 102, 043006 (2020).
  186. A. Kurganov and E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection–diffusion equations, J. Comput. Phys. 160, 241 (2000).
  187. B. Einfeldt, On Godunov-type methods for gas dynamics, SIAM J. Numer. Anal. 25, 294 (1988).
  188. A. Suresh and H. T. Huynh, Accurate monotonicity-preserving schemes with runge kutta time stepping, J. Comput. Phys. 136, 83 (1997).
  189. A. Mignone, P. Tzeferacos, and G. Bodo, High-order conservative finite difference GLM–MHD schemes for cell-centered MHD, J. Comput. Phys. 229, 5896 (2010).
  190. A. Harten, P. D. Lax, and B. v. Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev. 25, 35 (1983).
  191. S. Bernuzzi and D. Hilditch, Constraint violation in free evolution schemes: Comparing the bssnok formulation with a conformal decomposition of the z4 formulation, Phys. Rev. D 81, 084003 (2010).
  192. D. Hilditch, S. Bernuzzi, M. Thierfelder, Z. Cao, W. Tichy, and B. Brügmann, Compact binary evolutions with the z4c formulation, Phys. Rev. D 88, 084057 (2013).
  193. D. Pollney, C. Reisswig, E. Schnetter, N. Dorband, and P. Diener, High accuracy binary black hole simulations with an extended wave zone, Phys. Rev. D 83, 044045 (2011).
  194. C. Reisswig, R. Haas, C. D. Ott, E. Abdikamalov, P. Mösta, D. Pollney, and E. Schnetter, Three-dimensional general-relativistic hydrodynamic simulations of binary neutron star coalescence and stellar collapse with multipatch grids, Phys. Rev. D 87, 064023 (2013).
  195. F. Löffler et al., The Einstein toolkit: A community computational infrastructure for relativistic astrophysics, Classical Quantum Gravity 29, 115001 (2012).
  196. Einstein toolkit: Open software for relativistic astrophysics, http://Einsteintoolkit.org/.
  197. T. Goodale et al., The cactus framework and toolkit: Design and applications, in High Performance Computing for Computational Science—VECPAR 2002 (Springer, Berlin, Heidelberg, 2003), 10.1007/3-540-36569-9_13.
  198. cactus computational toolkit, http://cactuscode.org/.
  199. E. Schnetter, P. Diener, E. N. Dorband, and M. Tiglio, A multi-block infrastructure for three-dimensional time-dependent numerical relativity, Classical Quantum Gravity 23, S553 (2006).
  200. E. Schnetter, S. H. Hawley, and I. Hawke, Evolutions in 3d numerical relativity using fixed mesh refinement, Classical Quantum Gravity 21, 1465 (2004).
  201. H.-O. Kreiss, Methods for the Approximate Solution of Time Dependent Problems (World Meteorological Organization and International Council of Scientific Unions, Geneva, 1973), https://test.nypl.org/research/research-catalog/bib/pb994409033506421.
  202. S. Gottlieb, D. I. Ketcheson, and C.-W. Shu, High order strong stability preserving time discretizations, J. Sci. Comput. 38, 251 (2009).
  203. R. De Pietri, A. Feo, F. Maione, and F. Löffler, Modeling equal and unequal mass binary neutron star mergers using public codes, Phys. Rev. D 93, 064047 (2016).
  204. S. Bernuzzi, D. Radice, C. D. Ott, L. F. Roberts, P. Mösta, and F. Galeazzi, How loud are neutron star mergers?, Phys. Rev. D 94, 024023 (2016).
  205. Lorene: Langage objet pour la relativité numérique, https://lorene.obspm.fr/.
  206. E. Gourgoulhon, P. Grandclément, K. Taniguchi, J.-A. Marck, and S. Bonazzola, Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity: Method and tests, Phys. Rev. D 63, 064029 (2001).
  207. J. W. York, Conformal, “thin-sandwich” data for the initial-value problem of general relativity, Phys. Rev. Lett. 82, 1350 (1999).
  208. K. Kyutoku, M. Shibata, and K. Taniguchi, Reducing orbital eccentricity in initial data of binary neutron stars, Phys. Rev. D 90, 064006 (2014).
  209. E. Newman and R. Penrose, Errata: An approach to gravitational radiation by a method of spin coefficients, J. Math. Phys. (N.Y.) 4, 998 (1963).
  210. S. A. Teukolsky, Perturbations of a rotating black hole. I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations, Astrophys. J. 185, 635 (1973).
  211. J. N. Goldberg, A. J. Macfarlane, E. T. Newman, F. Rohrlich, and E. C. G. Sudarshan, Spin-s spherical harmonics, J. Math. Phys. (N.Y.) 8, 2155 (1967).
  212. R. Abbott et al. (LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration), Population of merging compact binaries inferred using gravitational waves through GWTC-3, Phys. Rev. X 13, 011048 (2023).

Outline

Information

Phys. Rev. D 113, 123009– Published 3 June, 2026
  • Received 21 April 2025
  • Accepted 27 April 2026
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation