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

Physical Review Letters

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Pitching Cosmic Curveballs: Environmental Effects on Extreme-Mass-Ratio Inspirals with Spinning Secondaries

Leif Lui1, Lisa V. Drummond2, and Alejandro Torres-Orjuela1,*

  • *Contact author: atorreso@bimsa.cn
PDF

Phys. Rev. Lett. 137, 121403 – Published 16 September, 2026

DOI: https://doi.org/10.1103/dy3h-65ty

Abstract

Much like the aerodynamic deflection of a spinning curveball, a rotating secondary in an extreme-mass-ratio inspiral (EMRI) experiences Magnus and lift forces, in addition to the standard drag force, when traversing a gaseous environment. We present the first framework that incorporates these specific spin-coupled environmental effects (EEs) into the evolution of EMRI. Over the multiyear observation windows of space-based gravitational wave (GW) detectors, these interactions imprint a unique, distinguishable dephasing signature on the signal. Crucially, a Fisher matrix analysis reveals that gas drag breaks the fundamental vacuum-projection degeneracy between the secondary’s spin magnitude and inclination, thereby tightening parameter constraints. Thus, accounting for EEs is not merely a modeling necessity, but could potentially be a powerful tool for enhancing the detectability of the secondary’s intrinsic spin, and could serve as a novel probe of accretion flows harboring massive black holes.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (136)

  1. S. Chandrasekhar, Astrophys. J. 97, 255 (1943).
  2. E. C. Ostriker, Astrophys. J. 513, 252 (1999).
  3. A. Escala, R. B. Larson, P. S. Coppi, and D. Mardones, Astrophys. J. 607, 765 (2004).
  4. H. Kim and W.-T. Kim, Astrophys. J. 665, 432 (2007).
  5. E. Barausse and L. Rezzolla, Phys. Rev. D 77, 104027 (2008).
  6. B. Kocsis, N. Yunes, and A. Loeb, Phys. Rev. D 84, 024032 (2011).
  7. N. Yunes, B. Kocsis, A. Loeb, and Z. Haiman, Phys. Rev. Lett. 107, 171103 (2011).
  8. A. Derdzinski, D. D’Orazio, P. Duffell, Z. Haiman, and A. MacFadyen, Mon. Not. R. Astron. Soc. 501, 3540 (2021).
  9. D. Traykova, K. Clough, T. Helfer, E. Berti, P. G. Ferreira, and L. Hui, Phys. Rev. D 104, 103014 (2021).
  10. D. Traykova, R. Vicente, K. Clough, T. Helfer, E. Berti, P. G. Ferreira, and L. Hui, Phys. Rev. D 108, L121502 (2023).
  11. L. Zwick, K. Hendriks, D. O’Neill, J. Takátsy, P. Kirkeberg, C. Tiede, J. Stegmann, J. Samsing, and D. J. D’Orazio, Phys. Rev. D 112, 063005 (2025).
  12. L. F. O. Costa, R. Franco, and V. Cardoso, Phys. Rev. D 98, 024026 (2018).
  13. Z. Wang, T. Helfer, D. Traykova, K. Clough, and E. Berti, Phys. Rev. D 110, 024009 (2024).
  14. C. Dyson, J. Redondo-Yuste, M. van de Meent, and V. Cardoso, Phys. Rev. D 109, 104038 (2024).
  15. T. K. Karydas, R. Vicente, and G. Bertone, Phys. Rev. D 113, 043057 (2026).
  16. P. Amaro-Seoane, H. Audley, S. Babak, J. Baker, E. Barausse, P. Bender, E. Berti, P. Binetruy, M. Born, D. Bortoluzzi et al., arXiv:1702.00786.
  17. S. Babak, J. Gair, A. Sesana, E. Barausse, C. F. Sopuerta, C. P. L. Berry, E. Berti, P. Amaro-Seoane, A. Petiteau, and A. Klein, Phys. Rev. D 95, 103012 (2017).
  18. L. Barack and C. Cutler, Phys. Rev. D 75, 042003 (2007).
  19. P. Amaro-Seoane, Living Rev. Relativity 21, 4 (2018).
  20. P. A. Seoane et al. (LISA Collaboration), Living Rev. Relativity 26, 2 (2023).
  21. K. G. Arun et al. (LISA Collaboration), Living Rev. Relativity 25, 4 (2022).
  22. N. Afshordi, S. Akçay, P. A. Seoane, A. Antonelli, J. C. Aurrekoetxea, L. Barack, E. Barausse, R. Benkel, L. Bernard et al. (LISA Consortium Waveform Working Group), Living Rev. Relativity 28, 9 (2025).
  23. M. Colpi, K. Danzmann, M. Hewitson, K. Holley-Bockelmann, P. Jetzer, G. Nelemans, A. Petiteau, D. Shoemaker, C. Sopuerta, R. Stebbins et al., arXiv:2402.07571.
  24. J. Luo et al. (TianQin Collaboration), Classical Quantum Gravity 33, 035010 (2016).
  25. J. Mei et al., Prog. Theor. Exp. Phys. 2021, 05A107 (2021).
  26. E.-K. Li et al., Rep. Prog. Phys. 88, 056901 (2025).
  27. A. Torres-Orjuela, S.-J. Huang, Z.-C. Liang, S. Liu, H.-T. Wang, C.-Q. Ye, Y.-M. Hu, and J. Mei, Sci. China Phys. Mech. Astron. 67, 259511 (2024).
  28. X. Gong et al., J. Phys. Conf. Ser. 610, 012011 (2015).
  29. W.-H. Ruan, Z.-K. Guo, R.-G. Cai, and Y.-Z. Zhang, Int. J. Mod. Phys. A 35, 2050075 (2020).
  30. S. A. Teukolsky, Phys. Rev. Lett. 29, 1114 (1972).
  31. S. A. Teukolsky, Astrophys. J. 185, 635 (1973).
  32. S. A. Teukolsky and W. H. Press, Astrophys. J. 193, 443 (1974).
  33. S. Chandrasekhar and S. Detweiler, Proc. R. Soc. A 344, 441 (1975).
  34. E. Poisson, Phys. Rev. D 47, 1497 (1993).
  35. C. Cutler, L. S. Finn, E. Poisson, and G. J. Sussman, Phys. Rev. D 47, 1511 (1993).
  36. T. Apostolatos, D. Kennefick, A. Ori, and E. Poisson, Phys. Rev. D 47, 5376 (1993).
  37. E. Poisson, Phys. Rev. D 48, 1860 (1993).
  38. E. Poisson and M. Sasaki, Phys. Rev. D 51, 5753 (1995).
  39. S. Mano, H. Suzuki, and E. Takasugi, Prog. Theor. Phys. 95, 1079 (1996).
  40. S. Mano and E. Takasugi, Prog. Theor. Phys. 97, 213 (1997).
  41. M. Campanelli and C. O. Lousto, Phys. Rev. D 56, 6363 (1997).
  42. S. A. Hughes, Phys. Rev. D 62, 044029 (2000).
  43. R. K. L. Lo, Phys. Rev. D 110, 124070 (2024).
  44. L. V. Drummond, P. Lynch, A. G. Hanselman, D. R. Becker, and S. A. Hughes, Phys. Rev. D 109, 064030 (2024).
  45. L. V. Drummond, P. Lynch, A. G. Hanselman, D. R. Becker, and S. A. Hughes, Phys. Rev. D 109, 064030 (2024).
  46. V. Skoupý and V. Witzany, Phys. Rev. Lett. 134, 171401 (2025).
  47. G. A. Piovano, Phys. Rev. D 113, 064024 (2026).
  48. V. Skoupý, G. Lukes-Gerakopoulos, L. V. Drummond, and S. A. Hughes, Phys. Rev. D 108, 044041 (2023).
  49. G. A. Piovano, C. Pantelidou, J. Mac Uilliam, and V. Witzany, Phys. Rev. D 111, 044009 (2025).
  50. L. V. Drummond, S. A. Hughes, V. Skoupý, P. Lynch, and G. A. Piovano, arXiv:2603.12189.
  51. V. Skoupý, arXiv:2603.13482.
  52. E. A. Huerta, J. R. Gair, and D. A. Brown, Phys. Rev. D 85, 064023 (2012).
  53. G. A. Piovano, R. Brito, A. Maselli, and P. Pani, Phys. Rev. D 104, 124019 (2021).
  54. Q. Cui, W.-B. Han, and Z. Pan, Phys. Rev. D 111, 103044 (2025).
  55. O. Burke, G. A. Piovano, N. Warburton, P. Lynch, L. Speri, C. Kavanagh, B. Wardell, A. Pound, L. Durkan, and J. Miller, Phys. Rev. D 109, 124048 (2024).
  56. V. Skoupý, G. A. Piovano, and V. Witzany, Phys. Rev. D 112, 124054 (2025).
  57. N. Dai, Y. Gong, T. Jiang, and D. Liang, Phys. Rev. D 106, 064003 (2022).
  58. N. Dai, Y. Gong, Y. Zhao, and T. Jiang, Phys. Rev. D 110, 084080 (2024).
  59. S. Mitra, N. Speeney, S. Chakraborty, and E. Berti, Phys. Rev. D 112, 044030 (2025).
  60. R. Vicente, T. K. Karydas, and G. Bertone, Phys. Rev. Lett. 135, 211401 (2025).
  61. L. Lui, A. Torres-Orjuela, R. K. Chowdhury, and L. Dai, Astrophys. J. 1004, 221 (2026).
  62. A. Hegade K. R., C. F. Gammie, and N. Yunes, Phys. Rev. D 112, 124012 (2025).
  63. A. Hegade K. R., C. F. Gammie, and N. Yunes, Phys. Rev. D 112, 124068 (2025).
  64. A. Papapetrou, Proc. R. Soc. A 209, 248 (1951).
  65. W. G. Dixon, Proc. R. Soc. A 319, 509 (1970).
  66. M. Mathisson, Gen. Relativ. Gravit. 42, 1011 (2010).
  67. V. Witzany, J. Steinhoff, and G. Lukes-Gerakopoulos, Classical Quantum Gravity 36, 075003 (2019).
  68. V. Witzany and G. A. Piovano, Phys. Rev. Lett. 132, 171401 (2024).
  69. V. Witzany, V. Skoupý, L. C. Stein, and S. Tanay, Phys. Rev. D 111, 044032 (2025).
  70. P. Ramond and S. Isoyama, Phys. Rev. D 111, 064027 (2025).
  71. R. P. Kerr, Phys. Rev. Lett. 11, 237 (1963).
  72. A. Pound and E. Poisson, Phys. Rev. D 77, 044013 (2008).
  73. J. R. Gair, É. É. Flanagan, S. Drasco, T. Hinderer, and S. Babak, Phys. Rev. D 83, 044037 (2011).
  74. V. Skoupý and G. Lukes-Gerakopoulos, Phys. Rev. D 103, 104045 (2021).
  75. B. Carter, Phys. Rev. 174, 1559 (1968).
  76. Y. Mino, Phys. Rev. D 67, 084027 (2003).
  77. S. Drasco and S. A. Hughes, Phys. Rev. D 69, 044015 (2004).
  78. S. Drasco and S. A. Hughes, Phys. Rev. D 73, 024027 (2006).
  79. S. Isoyama, R. Fujita, H. Nakano, N. Sago, and T. Tanaka, Prog. Theor. Exp. Phys. 2019, 013E01 (2019).
  80. N. Sago, R. Fujita, S. Isoyama, and H. Nakano, Prog. Theor. Exp. Phys. 2026, 073E04 (2026).
  81. Y. Yin, R. K. L. Lo, and X. Chen, Phys. Rev. D 113, 124007 (2026).
  82. M. van de Meent, Phys. Rev. D 97, 104033 (2018).
  83. A. Pound, Phys. Rev. D 95, 104056 (2017).
  84. N. Warburton, A. Pound, B. Wardell, J. Miller, and L. Durkan, Phys. Rev. Lett. 127, 151102 (2021).
  85. B. Wardell, A. Pound, N. Warburton, J. Miller, L. Durkan, and A. Le Tiec, Phys. Rev. Lett. 130, 241402 (2023).
  86. A. Spiers, A. Pound, and B. Wardell, Phys. Rev. D 110, 064030 (2024).
  87. Y.-X. Wei, X.-L. Zhu, J.-d. Zhang, and J. Mei, Phys. Rev. D 112, 064048 (2025).
  88. J. Mathews, B. Wardell, A. Pound, and N. Warburton, Phys. Rev. D 113, 064034 (2026).
  89. J. Lewis, T. Kakehi, A. Pound, and T. Tanaka, Phys. Rev. D 113, 064046 (2026).
  90. S. D. Upton, B. Wardell, A. Pound, N. Warburton, and L. Barack, Phys. Rev. D 113, 064013 (2026).
  91. A. J. K. Chua, C. R. Galley, and M. Vallisneri, Phys. Rev. Lett. 122, 211101 (2019).
  92. A. J. K. Chua, M. L. Katz, N. Warburton, and S. A. Hughes, Phys. Rev. Lett. 126, 051102 (2021).
  93. M. L. Katz, A. J. K. Chua, L. Speri, N. Warburton, and S. A. Hughes, Phys. Rev. D 104, 064047 (2021).
  94. C. E. A. Chapman-Bird, L. Speri, Z. Nasipak, O. Burke, M. L. Katz, A. Santini, S. Kejriwal, P. Lynch, J. Mathews, H. Khalvati et al., Phys. Rev. D 112, 104023 (2025).
  95. Z. Nasipak, Phys. Rev. D 106, 064042 (2022).
  96. Z. Nasipak, Phys. Rev. D 109, 044020 (2024).
  97. C. Dyson, T. F. M. Spieksma, R. Brito, M. van de Meent, and S. Dolan, Phys. Rev. Lett. 134, 211403 (2025).
  98. L. Mallick, W. N. Alston, M. L. Parker, A. C. Fabian, C. Pinto, G. C. Dewangan, A. Markowitz, P. Gandhi, A. K. Kembhavi, and R. Misra, Mon. Not. R. Astron. Soc. 479, 615 (2018).
  99. J. A. Tomsick, M. L. Parker, J. A. García, K. Yamaoka, D. Barret, J.-L. Chiu, M. Clavel, A. Fabian, F. Fürst, P. Gandhi et al., Astrophys. J. 855, 3 (2018).
  100. J. Jiang, A. C. Fabian, T. Dauser, L. Gallo, J. A. García, E. Kara, M. L. Parker, J. A. Tomsick, D. J. Walton, and C. S. Reynolds, Mon. Not. R. Astron. Soc. 489, 3436 (2019).
  101. A. C. Fabian, C. S. Reynolds, J. Jiang, C. Pinto, L. C. Gallo, M. L. Parker, A. N. Lasenby, W. N. Alston, D. J. K. Buisson, E. M. Cackett et al., Mon. Not. R. Astron. Soc. 493, 2518 (2020).
  102. Y. Xu, J. A. García, D. J. Walton, R. M. T. Connors, K. Madsen, and F. A. Harrison, Astrophys. J. 913, 13 (2021).
  103. J. Jiang, T. Dauser, A. C. Fabian, W. N. Alston, L. C. Gallo, M. L. Parker, and C. S. Reynolds, Mon. Not. R. Astron. Soc. 514, 1107 (2022).
  104. L. Mallick, A. C. Fabian, J. A. García, J. A. Tomsick, M. L. Parker, T. Dauser, D. R. Wilkins, B. De Marco, J. F. Steiner, R. M. T. Connors et al., Mon. Not. R. Astron. Soc. 513, 4361 (2022).
  105. Y. Ding, J. A. García, T. R. Kallman, C. Mendoza, M. Bautista, F. A. Harrison, J. A. Tomsick, and J. Dong, Astrophys. J. 974, 280 (2024).
  106. A. Madathil-Pottayil et al., Mon. Not. R. Astron. Soc. 534, 608 (2024).
  107. P. Peng and X. Chen, Astrophys. J. 950, 3 (2023).
  108. P. Peng, A. Franchini, M. Bonetti, A. Sesana, and X. Chen, Astrophys. J. 989, 122 (2025).
  109. F. Duque, L. Sberna, A. Spiers, and R. Vicente, Phys. Rev. D 113, 084028 (2026).
  110. Y. Zeng and Z. Pan, Phys. Rev. D 113, 123002 (2026).
  111. L. Lindblom, B. J. Owen, and D. A. Brown, Phys. Rev. D 78, 124020 (2008).
  112. C. Dyson and D. J. D’Orazio, arXiv:2601.19123.
  113. P. Mach, M. Momennia, and O. Sarbach, Phys. Rev. D 113, 044068 (2026).
  114. N. J. Cornish and L. J. Rubbo, Phys. Rev. D 67, 022001 (2003).
  115. S. Babak, H. Fang, J. R. Gair, K. Glampedakis, and S. A. Hughes, Phys. Rev. D 75, 024005 (2007).
  116. A. Klein, E. Barausse, A. Sesana, A. Petiteau, E. Berti, S. Babak, J. Gair, S. Aoudia, I. Hinder, F. Ohme, and B. Wardell, Phys. Rev. D 93, 024003 (2016).
  117. P. Amaro-Seoane, J. Andrews, M. Arca Sedda, A. Askar, Q. Baghi, R. Balasov, I. Bartos, S. S. Bavera, J. Bellovary et al., Living Rev. Relativity 26, 2 (2023).
  118. L. S. Finn, Phys. Rev. D 46, 5236 (1992).
  119. C. Cutler and E. E. Flanagan, Phys. Rev. D 49, 2658 (1994).
  120. M. Vallisneri, Phys. Rev. D 77, 042001 (2008).
  121. J. Veitch and A. Vecchio, Phys. Rev. D 81, 062003 (2010).
  122. J. Veitch, V. Raymond, B. Farr, W. Farr, P. Graff, S. Vitale, B. Aylott, K. Blackburn, N. Christensen, M. Coughlin et al., Phys. Rev. D 91, 042003 (2015).
  123. J. Meidam, K. W. Tsang, J. Goldstein, M. Agathos, A. Ghosh, C.-J. Haster, V. Raymond, A. Samajdar, P. Schmidt, R. Smith et al., Phys. Rev. D 97, 044033 (2018).
  124. W.-F. Feng, H.-T. Wang, X.-C. Hu, Y.-M. Hu, and Y. Wang, Phys. Rev. D 99, 123002 (2019).
  125. E. Pizzati, S. Sachdev, A. Gupta, and B. S. Sathyaprakash, Phys. Rev. D 105, 104016 (2022).
  126. P. Lynch, M. van de Meent, and N. Warburton, Classical Quantum Gravity 39, 145004 (2022).
  127. M. L. Katz, A. J. K. Chua, L. Speri, N. Warburton, and S. A. Hughes, Phys. Rev. D 104, 064047 (2021).
  128. E. Poisson and C. M. Will, Phys. Rev. D 52, 848 (1995).
  129. G. A. Piovano, A. Maselli, and P. Pani, Phys. Rev. D 102, 024041 (2020).
  130. S. Datta, R. Brito, S. A. Hughes, T. Klinger, and P. Pani, Phys. Rev. D 110, 024048 (2024).
  131. Y. Yang, L. Lui, A. Torres-Orjuela, and X. Chen, Phys. Rev. D 114, 023028 (2026).
  132. V. Witzany and V. Skoupý, arXiv:2606.25792.
  133. M. Van De Meent and N. Warburton, Classical Quantum Gravity 35, 144003 (2018).
  134. P. Lynch, M. van de Meent, and N. Warburton, Phys. Rev. D 109, 084072 (2024).
  135. P. Lynch, V. Witzany, M. van de Meent, and N. Warburton, Classical Quantum Gravity 41, 225002 (2024).
  136. T. K. Karydas and G. Bertone, Phys. Rev. D 114, 023054 (2026).

Outline

Information

Phys. Rev. Lett. 137, 121403– Published 16 September, 2026
  • Received 31 May 2026
  • Revised 23 July 2026
  • Accepted 31 August 2026
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation