- Physical Review Journals
All JournalsPhysics Magazine

APS Open Science

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Detection of gravitational wave modes in third generation detectors

Massimo Tinto*

Sanjeev Dhurandhar†

Harshit Raj‡

  • *Contact author: massimo.tinto@gmail.com
  • †Contact author: sanjeev@iucaa.in
  • ‡Contact author: harshitrajharsh@gmail.com
PDF

APS Open Sci. 1, 000121 – Published 3 September, 2026

DOI: https://doi.org/10.1103/gk3w-ngxw

Abstract

We investigate the detectability of gravitational wave modes (emitted by black holes and neutron stars) by third-generation, ground-based gravitational wave detectors planned to be operational in the next decade. Our analysis focuses on the Cosmic Explorer and Einstein Telescope projects, which are expected to have arm lengths of tens of kilometers and to experience the amplification of a gravitational wave signal at their free spectral range frequencies. We find that both projects will also observe with good signal-to-noise ratio the elusive w-modes, which are expected to be emitted at these frequencies by spinning neutron stars.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (37)

  1. J. Aasi et al., Characterization of the LIGO detectors during their sixth science run, Class. Quantum Grav. 32, 115012 (2015).
  2. T. Accadia et al., Virgo: A laser interferometer to detect gravitational waves, J. Instrum. 7, P03012 (2012).
  3. Y. Aso, Y. Michimura, K. Somiya, M. Ando, O. Miyakawa, T. Sekiguchi, D. Tatsumi, and H. Yamamoto (The KAGRA Collaboration), Interferometer design of the KAGRA gravitational wave detector, Phys. Rev. D 88, 043007 (2013).
  4. A. G. Abac et al. (The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration), GWTC-4.0: Updating the gravitational-wave transient catalog with observations from the first part of the fourth LIGO-Virgo-KAGRA observing run, Astrophys. J. Lett. 1004, L22 (2026).
  5. A. G. Abac et al. (The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration), GWTC-5.0: Observations from the second part of the fourth LIGO-Virgo-KAGRA observing run and updates to the gravitational-wave transient catalog, arXiv:2605.27225.
  6. A. G. Abac et al. (The LIGO Scientific Collaboration, the Virgo Collaboration, the KAGRA Collaboration), Open data from LIGO, Virgo, and KAGRA through the second part of the fourth observing run, arXiv:2605.27090.
  7. E. Capote et al., Advanced LIGO detector performance in the fourth observing run, Phys. Rev. D 111, 062002 (2025).
  8. S. Afroz, S. K. Agarwalla, D. Bhattacharya, S. Bhattacharya, S. Bhattacharyya, V. Bhalerao, D. Bose, C. Borwanker, I. C. C. H., A. Chakraborty, I. Chakraborty, S. Chakraborty, D. Chatterjee, V. Chitnis, M. M. Devi, S. Dhurandhar, A. Dighe, B. Ghosal, S. Gupta, A. Hait et al., A white paper on the multi-messenger science landscape in India, arXiv:2505.24408.
  9. P. Amaro-Seoane et al., Laser interferometer space antenna, arXiv:1702.00786.
  10. W.-R. Hu and Y.-L. Wu, The Taiji program in space for gravitational wave physics and the nature of gravity, Natl. Sci. Rev. 4, 685 (2017).
  11. J. Luo, L.-S. Chen, H.-Z. Duan, Y.-G. Gong, S. Hu, J. Ji, Q. Liu, J. Mei, V. Milyukov, M. Sazhin, C.-G. Shao, V. T. Toth, H.-B. Tu, Y. Wang, Y. Wang, H.-C. Yeh, M.-S. Zhan, Y. Zhang, V. Zharov, Z.-B. Zhou, et al., TianQin: A space-borne gravitational wave detector, Class. Quantum Grav. 33, 035010 (2016).
  12. H. Yang, K. Yagi, J. Blackman, L. Lehner, V. Paschalidis, F. Pretorius, and N. Yunes, Black hole spectroscopy with coherent mode stacking, Phys. Rev. Lett. 118, 161101 (2017).
  13. H. Yang, V. Paschalidis, K. Yagi, L. Lehner, F. Pretorius, and N. Yunes, Gravitational wave spectroscopy of binary neutron star merger remnants with mode stacking, Phys. Rev. D 97, 024049 (2018).
  14. B. J. Owen and B. Rajbhandari, Multi-messenger detectability of continuous gravitational waves from the near future to next generation detectors, arXiv:2512.22938.
  15. B. J. Owen, Colloquium: Multimessenger astronomy with continuous gravitational waves and future detectors, Rev. Mod. Phys. 98, 011002 (2026).
  16. I. Gupta, C. Afle, K. G. Arun, A. Bandopadhyay, M. Baryakhtar, S. Biscoveanu, S. Borhanian, F. Broekgaarden, A. Corsi, A. Dhani, M. Evans, E. D. Hall, O. A. Hannuksela, K. Kacanja, R. Kashyap, S. Khadkikar, K. Kuns, T. G. F. Li, A. L. Miller, A. H. Nitz, et al., Characterizing gravitational wave detector networks: From A♯ to Cosmic Explorer, arXiv:2307.10421.
  17. M. Punturo, M. Abernathy, F. Acernese, B. Allen, N. Andersson, K. Arun, F. Barone, B. Barr, M. Barsuglia, M. Beker, N. Beveridge, S. Birindelli, S. Bose, L. Bosi, S. Braccini, C. Bradaschia, T. Bulik, E. Calloni, G. Cella, E. C. Mottin, et al., The Einstein Telescope: A third-generation gravitational wave observatory, Class. Quantum Grav. 27, 194002 (2010).
  18. M. Branchesi, M. Maggiore, D. Alonso, C. Badger, B. Banerjee, F. Beirnaert, E. Belgacem, S. Bhagwat, G. Boileau, S. Borhanian, D. D. Brown, M. Leong Chan, G. Cusin, S. L. Danilishin, J. Degallaix, V. De Luca, A. Dhani, T. Dietrich, U. Dupletsa, S. Foffa, et al., Science with the Einstein Telescope: A comparison of different designs, J. Cosmol. Astropart. Phys. 2023, 068 (2023).
  19. S. Hild, M. Abernathy, F. Acernese, P. Amaro-Seoane, N. Andersson, K. Arun, F. Barone, B. Barr, M. Barsuglia, M. Beker, N. Beveridge, S. Birindelli, S. Bose, L. Bosi, S. Braccini, C. Bradaschia, T. Bulik, E. Calloni, G. Cella, E. C. Mottin, et al., Sensitivity studies for third-generation gravitational wave observatories, Class. Quantum Grav. 28, 094013 (2011).
  20. M. Evans, A. Corsi, C. Afle, A. Ananyeva, K. G. Arun, S. Ballmer, A. Bandopadhyay, L. Barsotti, M. Baryakhtar, E. Berger, E. Berti, S. Biscoveanu, S. Borhanian, F. Broekgaarden, D. A. Brown, C. Cahillane, L. Campbell, H.-Y. Chen, K. J. Daniel, A. Dhani, et al., Cosmic Explorer: A submission to the NSF MPSAC NGGW subcommittee, arXiv:2306.13745.
  21. E. D. Hall, K. Kuns, J. R. Smith, Y. Bai, C. Wipf, S. Biscans, R. X. Adhikari, K. Arai, S. Ballmer, L. Barsotti, Y. Chen, M. Evans, P. Fritschel, J. Harms, B. Kamai, J. G. Rollins, D. Shoemaker, B. J. J. Slagmolen, R. Weiss, and H. Yamamoto, Gravitational-wave physics with cosmic explorer: Limits to low-frequency sensitivity, Phys. Rev. D 103, 122004 (2021).
  22. As will be shown in the following section, the amplification factor achievable by the response of a Fabry-Pérot (FP) interferometer to a GW signal at the FSR frequency depends on the reflectivities of the test-mass mirrors.
  23. K. D. Kokkotas and B. F. Schutz, W-modes: A new family of normal modes of pulsating relativistic stars, Mon. Not. R. Astron. Soc. 255, 119 (1992).
  24. N. Andersson and K. D. Kokkotas, Towards gravitational wave asteroseismology, Mon. Not. R. Astron. Soc. 299, 1059 (1998).
  25. F. Estabrook and H. Wahlquist, Response of Doppler spacecraft tracking to gravitational radiation, Gen. Relativ. Gravit. 6, 439 (1975).
  26. F. B. Estabrook, Response functions of free mass gravitational wave antennas, Gen. Relativ. Gravit. 17, 719 (1985).
  27. J. W. Armstrong, F. B. Estabrook, and M. Tinto, Time-delay interferometry for space-based gravitational wave searches, Astrophys. J. 527, 814 (1999).
  28. M. Tinto and J. W. Armstrong, Cancellation of laser noise in an unequal-arm interferometer detector of gravitational radiation, Phys. Rev. D 59, 102003 (1999).
  29. B. F. Schutz and M. Tinto, Antenna patterns of interferometric detectors of gravitational waves. I. Linearly polarized waves, Mon. Not. R. Astron. Soc. 224, 131 (1987).
  30. M. Tinto and F. B. Estabrook, Parallel beam interferometric detectors of gravitational waves, Phys. Rev. D 52, 1749 (1995).
  31. M. Rakhmanov, J. D. Romano, and J. T. Whelan, High-frequency corrections to the detector response and their effect on searches for gravitational waves, Class. Quantum Grav. 25, 184017 (2008).
  32. M. Rakhmanov, On the round-trip time for a photon propagating in the field of a plane gravitational wave, Class. Quantum Grav. 26, 155010 (2009).
  33. A. Rohatgi, WebPlotDigitizer, https://automeris.io.
  34. N. Andersson, Gravitational-Wave Astronomy: Exploring the Dark Dide of the Universe (Oxford University Press, 2019).
  35. E. E. Flanagan and S. A. Hughes, Measuring gravitational waves from binary black hole coalescences. I. Signal to noise for inspiral, merger, and ringdown, Phys. Rev. D 57, 4535 (1998).
  36. K. D. Kokkotas, T. A. Apostolatos, and N. Andersson, The inverse problem for pulsating neutron stars: A ‘fingerprint analysis’ for the supranuclear equation of state, Mon. Not. R. Astron. Soc. 320, 307 (2001).
  37. K. Kotake and T. Kuroda, Gravitational Waves from Core-Collapse Supernovae (Springer International Publishing, Cham, 2017), pp. 1671–1698.

Outline

Information

APS Open Sci. 1, 000121– Published 3 September, 2026
Vol. 1
  • Received 21 March 2026
  • Accepted 19 August 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation