Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Millihertz oscillations near the innermost orbit of a supermassive black hole

Nature volume 638, pages 370–375 (2025)Cite this article

Subjects

Abstract

Recent discoveries from time-___domain surveys are defying our expectations for how matter accretes onto supermassive black holes (SMBHs). The increased rate of short-timescale, repetitive events around SMBHs, including the recently discovered quasi-periodic eruptions1,2,3,4,5, are garnering further interest in stellar-mass companions around SMBHs and the progenitors to millihertz-frequency gravitational-wave events. Here we report the discovery of a highly significant millihertz quasi-periodic oscillation (QPO) in an actively accreting SMBH, 1ES 1927+654, which underwent a major optical, ultraviolet and X-ray outburst beginning in 20186,7. The QPO was detected in 2022 with a roughly 18-minute period, corresponding to coherent motion on a scale of less than 10 gravitational radii, much closer to the SMBH than typical quasi-periodic eruptions. The period decreased to 7.1 minutes over 2 years with a decelerating period evolution (\(\ddot{P}\) greater than zero). To our knowledge, this evolution has never been seen in SMBH QPOs or high-frequency QPOs in stellar-mass black holes. Models invoking orbital decay of a stellar-mass companion struggle to explain the period evolution without stable mass transfer to offset angular-momentum losses, and the lack of a direct analogue to stellar-mass black-hole QPOs means that many instability models cannot explain all of the observed properties of the QPO in 1ES 1927+654. Future X-ray monitoring will test these models, and if it is a stellar-mass orbiter, the Laser Interferometer Space Antenna (LISA) should detect its low-frequency gravitational-wave emission.

Access through your institution
Buy or subscribe

This is a preview of subscription content, access via your institution

Access options

Access through your institution

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: X-ray spectral-timing overview of 1ES 1927+654.
Fig. 2: XMM-Newton light curves and PSDs in the 2–10 keV band for observations that show a QPO.
Fig. 3: Evolution of the QPO frequency over time.

Similar content being viewed by others

Data availability

All the data used in this work are publicly available through XMM-SAS.

Code availability

The spectra, light curves and code used to analyse the data and produce all figures have been made publicly available on CodeOcean and GitHub (https://github.com/memasterson/1ES1927_mHzQPO/).

References

  1. Miniutti, G. et al. Nine-hour X-ray quasi-periodic eruptions from a low-mass black hole galactic nucleus. Nature 573, 381–384 (2019).

    ADS  CAS  PubMed  MATH  Google Scholar 

  2. Giustini, M., Miniutti, G. & Saxton, R. D. X-ray quasi-periodic eruptions from the galactic nucleus of RX J1301.9+2747. Astron. Astrophys. 636, L2 (2020).

    ADS  Google Scholar 

  3. Arcodia, R. et al. X-ray quasi-periodic eruptions from two previously quiescent galaxies. Nature 592, 704–707 (2021).

    ADS  CAS  PubMed  PubMed Central  MATH  Google Scholar 

  4. Chakraborty, J. et al. Possible X-ray quasi-periodic eruptions in a tidal disruption event candidate. Astrophys. J. Lett. 921, L40 (2021).

    ADS  CAS  MATH  Google Scholar 

  5. Arcodia, R. et al. The more the merrier: SRG/eROSITA discovers two further galaxies showing X-ray quasi-periodic eruptions. Astron. Astrophys. 684, A64 (2024).

    CAS  MATH  Google Scholar 

  6. Trakhtenbrot, B. et al. 1ES 1927+654: an AGN caught changing look on a timescale of months. Astrophys. J. 883, 94 (2019).

    ADS  CAS  MATH  Google Scholar 

  7. Ricci, C. et al. The destruction and recreation of the X-ray corona in a changing-look active galactic nucleus. Astrophys. J. Lett. 898, L1 (2020).

    ADS  MATH  Google Scholar 

  8. Li, R. et al. The host galaxy and rapidly evolving broad-line region in the changing-look active galactic nucleus 1ES 1927+654. Astrophys. J. 933, 70 (2022).

    ADS  MATH  Google Scholar 

  9. Boller, T. et al. 1ES 1927+654: persistent and rapid X-ray variability in an AGN with low intrinsic neutral X-ray absorption and narrow optical emission lines. Astron. Astrophys. 397, 557–564 (2003).

    ADS  CAS  MATH  Google Scholar 

  10. Tran, H. D., Lyke, J. E. & Mader, J. A. Indecent exposure in Seyfert 2 galaxies: a close look. Astrophys. J. Lett. 726, L21 (2011).

    ADS  Google Scholar 

  11. Gallo, L. C. et al. 1ES 1927+654: a bare Seyfert 2. Mon. Not. R. Astron. Soc. 433, 421–433 (2013).

    ADS  MATH  Google Scholar 

  12. Ricci, C. et al. The 450 day X-ray monitoring of the changing-look AGN 1ES 1927+654. Astrophys. J. Suppl. Ser. 255, 7 (2021).

    ADS  CAS  MATH  Google Scholar 

  13. Masterson, M. et al. Evolution of a relativistic outflow and X-ray corona in the extreme changing-look AGN 1ES 1927+654. Astrophys. J. 934, 35 (2022).

    ADS  MATH  Google Scholar 

  14. Laha, S. et al. A radio, optical, UV, and X-ray view of the enigmatic changing-look active galactic nucleus 1ES 1927+654 from its pre- to postflare states. Astrophys. J. 931, 5 (2022).

    ADS  Google Scholar 

  15. Ghosh, R. et al. A reemerging bright soft X-ray state of the changing-look active galactic nucleus 1ES 1927+654: a multiwavelength view. Astrophys. J. 955, 3 (2023).

    ADS  CAS  Google Scholar 

  16. Liu, Z. et al. X-ray spectral properties of the AGN sample in the northern XMM-XXL field. Mon. Not. R. Astron. Soc. 459, 1602–1625 (2016).

    ADS  CAS  MATH  Google Scholar 

  17. Vaughan, S. & Uttley, P. Where are the X-ray quasi-periodic oscillations in active galaxies? Mon. Not. R. Astron. Soc. 362, 235–244 (2005).

    ADS  CAS  MATH  Google Scholar 

  18. Gierliński, M., Middleton, M., Ward, M. & Done, C. A periodicity of ~1 hour in X-ray emission from the active galaxy RE J1034+396. Nature 455, 369–371 (2008).

    ADS  PubMed  Google Scholar 

  19. Alston, W. N., Markeviciute, J., Kara, E., Fabian, A. C. & Middleton, M. Detection of a QPO in five XMM-Newton observations of RE J1034+396. Mon. Not. R. Astron. Soc. 445, L16–L20 (2014).

    ADS  CAS  Google Scholar 

  20. Pasham, D. R. et al. A loud quasi-periodic oscillation after a star is disrupted by a massive black hole. Science 363, 531–534 (2019).

    ADS  CAS  PubMed  Google Scholar 

  21. Lin, D., Irwin, J. A., Godet, O., Webb, N. A. & Barret, D. A ~3.8 hr periodicity from an ultrasoft active galactic nucleus candidate. Astrophys. J. Lett. 776, L10 (2013).

    ADS  Google Scholar 

  22. Lin, D. et al. Large decay of X-ray flux in 2XMM J123103.2+110648: evidence for a tidal disruption event. Mon. Not. R. Astron. Soc. 468, 783–789 (2017).

    ADS  CAS  MATH  Google Scholar 

  23. Webbe, R. & Young, A. J. Variability in a low-mass active galactic nucleus: oscillation or eruption? Mon. Not. R. Astron. Soc. 518, 3428–3440 (2023).

    ADS  MATH  Google Scholar 

  24. Timmer, J. & König, M. On generating power law noise. Astron. Astrophys. 300, 707 (1995).

    ADS  MATH  Google Scholar 

  25. Akaike, H. A new look at the statistical model identification. IEEE Trans. Automat. Contr. 19, 716–723 (1974).

    ADS  MathSciNet  MATH  Google Scholar 

  26. Xia, R., Liu, H. & Xue, Y. First observational evidence for an interconnected evolution between time lag and QPO frequency among AGNs. Astrophys. J. Lett. 961, L32 (2024).

    ADS  MATH  Google Scholar 

  27. Remillard, R. A. & McClintock, J. E. X-ray properties of black-hole binaries. Annu. Rev. Astron. Astrophys. 44, 49–92 (2006).

    ADS  MATH  Google Scholar 

  28. Ingram, A. R. & Motta, S. E. A review of quasi-periodic oscillations from black hole X-ray binaries: observation and theory. New Astron. Rev. 85, 101524 (2019).

    MATH  Google Scholar 

  29. Wevers, T., Pasham, D. R., Jalan, P., Rakshit, S. & Arcodia, R. Host galaxy properties of quasi-periodically erupting X-ray sources. Astron. Astrophys. 659, L2 (2022).

    ADS  CAS  Google Scholar 

  30. Terashima, Y., Kamizasa, N., Awaki, H., Kubota, A. & Ueda, Y. A candidate active galactic nucleus with a pure soft thermal X-ray spectrum. Astrophys. J. 752, 154 (2012).

    ADS  Google Scholar 

  31. Miniutti, G. et al. A high Eddington-ratio, true Seyfert 2 galaxy candidate: implications for broad-line region models. Mon. Not. R. Astron. Soc. 433, 1764–1777 (2013).

    ADS  MATH  Google Scholar 

  32. Sun, L., Shu, X. & Wang, T. RX J1301.9+2747: a highly variable Seyfert galaxy with extremely soft X-ray emission. Astrophys. J. 768, 167 (2013).

    ADS  Google Scholar 

  33. Franchini, A. et al. Quasi-periodic eruptions from impacts between the secondary and a rigidly precessing accretion disc in an extreme mass-ratio inspiral system. Astron. Astrophys. 675, A100 (2023).

    MATH  Google Scholar 

  34. Linial, I. & Metzger, B. D. EMRI + TDE = QPE: periodic X-ray flares from star-disk collisions in galactic nuclei. Astrophys. J. 957, 34 (2023).

    ADS  CAS  Google Scholar 

  35. Lu, W. & Quataert, E. Quasi-periodic eruptions from mildly eccentric unstable mass transfer in galactic nuclei. Mon. Not. R. Astron. Soc. 524, 6247–6266 (2023).

    ADS  MATH  Google Scholar 

  36. King, A. Quasi-periodic eruptions from galaxy nuclei. Mon. Not. R. Astron. Soc. 515, 4344–4349 (2022).

    ADS  MATH  Google Scholar 

  37. Marsh, T. R., Nelemans, G. & Steeghs, D. Mass transfer between double white dwarfs. Mon. Not. R. Astron. Soc. 350, 113–128 (2004).

    ADS  MATH  Google Scholar 

  38. Remillard, R. A., Muno, M. P., McClintock, J. E. & Orosz, J. A. Evidence for harmonic relationships in the high-frequency quasi-periodic oscillations of XTE J1550−564 and GRO J1655−40. Astrophys. J. 580, 1030–1042 (2002).

    ADS  Google Scholar 

  39. Remillard, R. A., McClintock, J. E., Orosz, J. A. & Levine, A. M. The X-ray outburst of H1743−322 in 2003: high-frequency QPOs with a 3:2 frequency ratio. Astrophys. J. 637, 1002–1009 (2006).

    ADS  CAS  MATH  Google Scholar 

  40. Belloni, T. M., Sanna, A. & Méndez, M. High-frequency quasi-periodic oscillations in black hole binaries. Mon. Not. R. Astron. Soc. 426, 1701–1709 (2012).

    ADS  MATH  Google Scholar 

  41. Vignarca, F., Migliari, S., Belloni, T., Psaltis, D. & van der Klis, M. Tracing the power-law component in the energy spectrum of black hole candidates as a function of the QPO frequency. Astron. Astrophys. 397, 729–738 (2003).

    ADS  Google Scholar 

  42. Stella, L., Vietri, M., & Morsink, S. M. Correlations in the quasi-periodic oscillation frequencies of low-mass X-ray binaries and the relativistic precession model. Astrophys. J. Lett. 524, L63–L66 (1999).

    ADS  MATH  Google Scholar 

  43. Ingram, A., Done, C. & Fragile, P. C. Low-frequency quasi-periodic oscillations spectra and Lense–Thirring precession. Mon. Not. R. Astron. Soc. 397, L101–L105 (2009).

    ADS  MATH  Google Scholar 

  44. Nixon, C., King, A., Price, D. & Frank, J. Tearing up the disk: how black holes accrete. Astrophys. J. Lett. 757, L24 (2012).

    ADS  MATH  Google Scholar 

  45. Liska, M. et al. Disc tearing and Bardeen–Petterson alignment in GRMHD simulations of highly tilted thin accretion discs. Mon. Not. R. Astron. Soc. 507, 983–990 (2021).

    ADS  CAS  MATH  Google Scholar 

  46. Musoke, G., Liska, M., Porth, O., van der Klis, M. & Ingram, A. Disc tearing leads to low and high frequency quasi-periodic oscillations in a GRMHD simulation of a thin accretion disc. Mon. Not. R. Astron. Soc. 518, 1656–1671 (2023).

    ADS  Google Scholar 

  47. Kaaz, N. et al. Nozzle shocks, disk tearing, and streamers drive rapid accretion in 3D GRMHD simulations of warped thin disks. Astrophys. J. 955, 72 (2023).

    ADS  CAS  MATH  Google Scholar 

  48. Meyer, E. T. et al. Emergence of a radio jet in the changing-look AGN 1ES 1927+654. Preprint at https://arxiv.org/abs/2406.18061 (2024).

  49. Cabanac, C. et al. Variability of X-ray binaries from an oscillating hot corona. Mon. Not. R. Astron. Soc. 404, 738–748 (2010).

    ADS  CAS  MATH  Google Scholar 

  50. Buisson, D. J. K. et al. MAXI J1820+070 with NuSTAR I. An increase in variability frequency but a stable reflection spectrum: coronal properties and implications for the inner disc in black hole binaries. Mon. Not. R. Astron. Soc. 490, 1350–1362 (2019).

    ADS  CAS  MATH  Google Scholar 

  51. Jansen, F. et al. XMM-Newton observatory. I. The spacecraft and operations. Astron. Astrophys. 365, L1–L6 (2001).

    ADS  MATH  Google Scholar 

  52. Gendreau, K. C. et al. The Neutron star Interior Composition Explorer (NICER): design and development. In Space Telescopes and Instrumentation 2016: Ultraviolet to Gamma Ray, Society of Photo-Optical Instrumentation Engineers Conference Series Vol 9905 (eds den Herder, J.-W. A. et al.) 99051H (SPIE, 2016).

  53. Remillard, R. A. et al. An empirical background model for the NICER X-ray timing instrument. Astron. J. 163, 130 (2022).

    ADS  CAS  MATH  Google Scholar 

  54. Vaughan, S., Edelson, R., Warwick, R. S. & Uttley, P. On characterizing the variability properties of X-ray light curves from active galaxies. Mon. Not. R. Astron. Soc. 345, 1271–1284 (2003).

    ADS  Google Scholar 

  55. Wilkins, D. R. Low-frequency X-ray timing with Gaussian processes and reverberation in the radio-loud AGN 3C 120. Mon. Not. R. Astron. Soc. 489, 1957–1972 (2019).

    ADS  CAS  MATH  Google Scholar 

  56. Vaughan, S. A simple test for periodic signals in red noise. Astron. Astrophys. 431, 391–403 (2005).

    ADS  CAS  MATH  Google Scholar 

  57. González-Martín, O. & Vaughan, S. X-ray variability of 104 active galactic nuclei. XMM-Newton power-spectrum density profiles. Astron. Astrophys. 544, A80 (2012).

    ADS  MATH  Google Scholar 

  58. Uttley, P., McHardy, I. M. & Papadakis, I. E. Measuring the broad-band power spectra of active galactic nuclei with RXTE. Mon. Not. R. Astron. Soc. 332, 231–250 (2002).

    ADS  Google Scholar 

  59. Markowitz, A. et al. X-ray fluctuation power spectral densities of Seyfert 1 galaxies. Astrophys. J. 593, 96–114 (2003).

    ADS  MATH  Google Scholar 

  60. McHardy, I. M., Papadakis, I. E., Uttley, P., Page, M. J. & Mason, K. O. Combined long and short time-scale X-ray variability of NGC 4051 with RXTE and XMM-Newton. Mon. Not. R. Astron. Soc. 348, 783–801 (2004).

    ADS  Google Scholar 

  61. McHardy, I. M., Koerding, E., Knigge, C., Uttley, P. & Fender, R. P. Active galactic nuclei as scaled-up Galactic black holes. Nature 444, 730–732 (2006).

    ADS  CAS  PubMed  Google Scholar 

  62. Belloni, T., Psaltis, D. & van der Klis, M. A unified description of the timing features of accreting X-ray binaries. Astrophys. J. 572, 392–406 (2002).

    ADS  CAS  MATH  Google Scholar 

  63. Vaughan, S. A Bayesian test for periodic signals in red noise. Mon. Not. R. Astron. Soc. 402, 307–320 (2010).

    ADS  CAS  MATH  Google Scholar 

  64. Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. emcee: the MCMC hammer. Publ. Astron. Soc. Pac. 125, 306 (2013).

    ADS  MATH  Google Scholar 

  65. Sugiura, N. Further analysis of the data by akaike’s information criterion and the finite corrections. Commun. Stat. Theory Methods 7, 13–26 (1978).

    MATH  Google Scholar 

  66. Emmanoulopoulos, D. et al. A search for X-ray reprocessing echoes in the power spectral density functions of AGN. Mon. Not. R. Astron. Soc. 461, 1642–1655 (2016).

    ADS  CAS  MATH  Google Scholar 

  67. Ashton, D. I. & Middleton, M. J. Searching for energy-resolved quasi-periodic oscillations in AGN. Mon. Not. R. Astron. Soc. 501, 5478–5499 (2021).

    ADS  CAS  MATH  Google Scholar 

  68. Li, R. et al. The interplay between the disk and corona of the changing-look active galactic nucleus 1ES 1927+654. Astrophys. J. 975, 140 (2024).

  69. Heil, L. M., Uttley, P. & Klein-Wolt, M. Inclination-dependent spectral and timing properties in transient black hole X-ray binaries. Mon. Not. R. Astron. Soc. 448, 3348–3353 (2015).

    ADS  MATH  Google Scholar 

  70. Motta, S. E. et al. Geometrical constraints on the origin of timing signals from black holes. Mon. Not. R. Astron. Soc. 447, 2059–2072 (2015).

    ADS  MATH  Google Scholar 

  71. van den Eijnden, J. et al. Inclination dependence of QPO phase lags in black hole X-ray binaries. Mon. Not. R. Astron. Soc. 464, 2643–2659 (2017).

    ADS  MATH  Google Scholar 

  72. Ingram, A. et al. A quasi-periodic modulation of the iron line centroid energy in the black hole binary H1743−322. Mon. Not. R. Astron. Soc. 461, 1967–1980 (2016).

    ADS  CAS  MATH  Google Scholar 

  73. Nathan, E. et al. Phase-resolved spectroscopy of a quasi-periodic oscillation in the black hole X-ray binary GRS 1915+105 with NICER and NuSTAR. Mon. Not. R. Astron. Soc. 511, 255–279 (2022).

    ADS  CAS  MATH  Google Scholar 

  74. Soleri, P., Belloni, T. & Casella, P. A transient low-frequency quasi-periodic oscillation from the black hole binary GRS 1915+105. Mon. Not. R. Astron. Soc. 383, 1089–1102 (2008).

    ADS  CAS  MATH  Google Scholar 

  75. Homan, J. et al. A rapid change in X-ray variability and a jet ejection in the black hole transient MAXI J1820+070. Astrophys. J. Lett. 891, L29 (2020).

    ADS  CAS  MATH  Google Scholar 

  76. Motta, S., Muñoz-Darias, T., Casella, P., Belloni, T. & Homan, J. Low-frequency oscillations in black holes: a spectral-timing approach to the case of GX 339−4. Mon. Not. R. Astron. Soc. 418, 2292–2307 (2011).

    ADS  Google Scholar 

  77. Morgan, E. H., Remillard, R. A. & Greiner, J. RXTE observations of QPOs in the black hole candidate GRS 1915+105. Astrophys. J. 482, 993–1010 (1997).

    ADS  Google Scholar 

  78. Remillard, R. A., Morgan, E. H., McClintock, J. E., Bailyn, C. D. & Orosz, J. A. RXTE observations of 0.1-300 Hz quasi-periodic oscillationsin the microquasar GRO J1655−40. Astrophys. J. 522, 397–412 (1999).

    ADS  Google Scholar 

  79. Remillard, R. A. et al. X-ray nova XTE J1550−564: discovery of a quasi-periodic oscillation near 185 Hz. Astrophys. J. Lett. 517, L127–L130 (1999).

    ADS  MATH  Google Scholar 

  80. Homan, J. et al. Correlated X-ray spectral and timing behavior of the black hole candidate XTE J1550−564: a new interpretation of black hole states. Astrophys. J. Suppl. Ser. 132, 377–402 (2001).

    ADS  CAS  MATH  Google Scholar 

  81. Miller, J. M. et al. High-frequency quasi-periodic oscillations in the 2000 outburst of the galactic microquasar XTE J1550−564. Astrophys. J. 563, 928–933 (2001).

    ADS  MATH  Google Scholar 

  82. Strohmayer, T. E. Discovery of a 450 Hz quasi-periodic oscillation from the microquasar GRO J1655−40 with the Rossi X-ray timing explorer. Astrophys. J. Lett. 552, L49–L53 (2001).

    ADS  MATH  Google Scholar 

  83. Motta, S. E. et al. Black hole spin measurements through the relativistic precession model: XTE J1550−564. Mon. Not. R. Astron. Soc. 439, L65–L69 (2014).

    ADS  MATH  Google Scholar 

  84. Abramowicz, M. A. & Kluźniak, W. A precise determination of black hole spin in GRO J1655−40. Astron. Astrophys. 374, L19–L20 (2001).

    ADS  MATH  Google Scholar 

  85. Abramowicz, M. A., Karas, V., Kluzniak, W., Lee, W. H. & Rebusco, P. Non-linear resonance in nearly geodesic motion in low-mass X-ray binaries. Publ. Astron. Soc. Jpn 55, 467–466 (2003).

    ADS  CAS  MATH  Google Scholar 

  86. Rezzolla, L., Yoshida, S., Maccarone, T. J. & Zanotti, O. A new simple model for high-frequency quasi-periodic oscillations in black hole candidates. Mon. Not. R. Astron. Soc. 344, L37–L41 (2003).

    ADS  MATH  Google Scholar 

  87. Alston, W. N. et al. Discovery of an ~2-h high-frequency X-ray QPO and iron Kα reverberation in the active galaxy MS 2254.9−3712. Mon. Not. R. Astron. Soc. 449, 467–476 (2015).

    ADS  CAS  MATH  Google Scholar 

  88. Raj, A. & Nixon, C. J. Disk tearing: implications for black hole accretion and AGN variability. Astrophys. J. 909, 82 (2021).

    ADS  CAS  MATH  Google Scholar 

  89. Pan, X., Li, S.-L., Cao, X., Miniutti, G. & Gu, M. A disk instability model for the quasi-periodic eruptions of GSN 069. Astrophys. J. Lett. 928, L18 (2022).

    ADS  Google Scholar 

  90. Kaur, K., Stone, N. C. & Gilbaum, S. Magnetically dominated discs in tidal disruption events and quasi-periodic eruptions. Mon. Not. R. Astron. Soc. 524, 1269–1290 (2023).

    ADS  MATH  Google Scholar 

  91. Pan, X., Li, S.-L. & Cao, X. Application of the disk instability model to all quasiperiodic eruptions. Astrophys. J. 952, 32 (2023).

    ADS  MATH  Google Scholar 

  92. Śniegowska, M., Grzȩdzielski, M., Czerny, B. & Janiuk, A. Modified models of radiation pressure instability applied to 10, 105, and 107 M⊙ accreting black holes. Astron. Astrophys. 672, A19 (2023).

    ADS  Google Scholar 

  93. Dai, L. & Blandford, R. Roche accretion of stars close to massive black holes. Mon. Not. R. Astron. Soc. 434, 2948–2960 (2013).

    ADS  MATH  Google Scholar 

  94. Suková, P., Zajaček, M., Witzany, V. & Karas, V. Stellar transits across a magnetized accretion torus as a mechanism for plasmoid ejection. Astrophys. J. 917, 43 (2021).

    ADS  Google Scholar 

  95. Xian, J., Zhang, F., Dou, L., He, J. & Shu, X. X-ray quasi-periodic eruptions driven by star-disk collisions: application to GSN069 and probing the spin of massive black holes. Astrophys. J. Lett. 921, L32 (2021).

    ADS  CAS  Google Scholar 

  96. Tagawa, H. & Haiman, Z. Flares from stars crossing active galactic nucleus discs on low-inclination orbits. Mon. Not. R. Astron. Soc. 526, 69–79 (2023).

    ADS  MATH  Google Scholar 

  97. King, A. GSN 069—a tidal disruption near miss. Mon. Not. R. Astron. Soc. 493, L120–L123 (2020).

    ADS  Google Scholar 

  98. Krolik, J. H. & Linial, I. Quasiperiodic erupters: a stellar mass-transfer model for the radiation. Astrophys. J. 941, 24 (2022).

    ADS  MATH  Google Scholar 

  99. Metzger, B. D., Stone, N. C. & Gilbaum, S. Interacting stellar EMRIs as sources of quasi-periodic eruptions in galactic nuclei. Astrophys. J. 926, 101 (2022).

    ADS  MATH  Google Scholar 

  100. Zhao, Z. Y., Wang, Y. Y., Zou, Y. C., Wang, F. Y. & Dai, Z. G. Quasi-periodic eruptions from the helium envelope of hydrogen-deficient stars stripped by supermassive black holes. Astron. Astrophys. 661, A55 (2022).

    ADS  CAS  MATH  Google Scholar 

  101. King, A. QPE or QPO?—Quasiperiodic activity in low-mass galaxy nuclei. Mon. Not. R. Astron. Soc. 523, L26–L29 (2023).

    ADS  Google Scholar 

  102. Arcodia, R. et al. The complex time and energy evolution of quasi-periodic eruptions in eRO-QPE1. Astron. Astrophys. 662, A49 (2022).

    CAS  MATH  Google Scholar 

  103. Miniutti, G. et al. Repeating tidal disruptions in GSN 069: long-term evolution and constraints on quasi-periodic eruptions’ models. Astron. Astrophys. 670, A93 (2023).

    MATH  Google Scholar 

  104. Chakraborty, J. et al. Testing EMRI models for quasi-periodic eruptions with 3.5 yr of monitoring eRO-QPE1. Astrophys. J. 965, 12 (2024).

    ADS  CAS  MATH  Google Scholar 

  105. Miniutti, G. et al. Alive and kicking: a new QPE phase in GSN 069 revealing a quiescent luminosity threshold for QPEs. Astron. Astrophys. 674, L1 (2023).

    ADS  MATH  Google Scholar 

  106. Song, J. R. et al. Possible ~0.4 h X-ray quasi-periodicity from an ultrasoft active galactic nucleus. Astron. Astrophys. 644, L9 (2020).

    ADS  MATH  Google Scholar 

  107. Arcodia, R. et al. Cosmic hide and seek: the volumetric rate of X-ray quasi-periodic eruptions. Astron. Astrophys. 684, L14 (2024).

    ADS  MATH  Google Scholar 

  108. Peters, P. C. Gravitational radiation and the motion of two point masses. Phys. Rev. 136, 1224–1232 (1964).

    ADS  MATH  Google Scholar 

  109. Pan, Z., Lyu, Z. & Yang, H. Wet extreme mass ratio inspirals may be more common for spaceborne gravitational wave detection. Phys. Rev. D 104, 063007 (2021).

    ADS  CAS  MATH  Google Scholar 

  110. Eggleton, P. P. Aproximations to the radii of Roche lobes. Astrophys. J. 268, 368–369 (1983).

    ADS  MATH  Google Scholar 

  111. Verbunt, F. & Rappaport, S. Mass transfer instabilities due to angular momentum flows in close binaries. Astrophys. J. 332, 193 (1988).

    ADS  MATH  Google Scholar 

  112. Ramsay, G. et al. Physical properties of AM CVn stars: new insights from Gaia DR2. Astron. Astrophys. 620, A141 (2018).

    CAS  MATH  Google Scholar 

  113. Strohmayer, T. E. A real-time view of orbital evolution in HM Cancri. Astrophys. J. Lett. 912, L8 (2021).

    ADS  CAS  MATH  Google Scholar 

  114. Linial, I. & Quataert, E. Period evolution of repeating transients in galactic nuclei. Mon. Not. R. Astron. Soc. 527, 4317–4329 (2024).

    ADS  MATH  Google Scholar 

  115. Peng, P. & Chen, X. The last migration trap of compact objects in AGN accretion disc. Mon. Not. R. Astron. Soc. 505, 1324–1333 (2021).

    ADS  CAS  MATH  Google Scholar 

  116. Payne, A. V. et al. ASASSN-14ko is a periodic nuclear transient in ESO 253−G003. Astrophys. J. 910, 125 (2021).

    ADS  CAS  MATH  Google Scholar 

  117. Wevers, T. et al. Live to die another day: the rebrightening of AT 2018fyk as a repeating partial tidal disruption event. Astrophys. J. Lett. 942, L33 (2023).

    ADS  MATH  Google Scholar 

  118. Somalwar, J. J. et al. The first systematically identified repeating partial tidal disruption event. Preprint at https://arxiv.org/abs/2310.03782 (2023).

  119. Gafton, E., Tejeda, E., Guillochon, J., Korobkin, O. & Rosswog, S. Relativistic effects on tidal disruption kicks of solitary stars. Mon. Not. R. Astron. Soc. 449, 771–780 (2015).

    ADS  CAS  Google Scholar 

  120. Cufari, M., Nixon, C. J. & Coughlin, E. R. Tidal capture of stars by supermassive black holes: implications for periodic nuclear transients and quasi-periodic eruptions. Mon. Not. R. Astron. Soc. 520, L38–L41 (2023).

    ADS  Google Scholar 

  121. Cufari, M., Coughlin, E. R. & Nixon, C. J. Using the Hills mechanism to generate repeating partial tidal disruption events and ASASSN-14ko. Astrophys. J. Lett. 929, L20 (2022).

    ADS  Google Scholar 

  122. Ryu, T. et al. In-plane tidal disruption of stars in discs of active galactic nuclei. Mon. Not. R. Astron. Soc. 527, 8103–8117 (2024).

    ADS  MATH  Google Scholar 

  123. Wang, Y., Lin, D. N. C., Zhang, B. & Zhu, Z. Changing-look active galactic nuclei behavior induced by disk-captured tidal disruption events. Astrophys. J. Lett. 962, L7 (2024).

    ADS  CAS  Google Scholar 

  124. Amaro-Seoane, P. et al. Laser Interferometer Space Antenna. Preprint at https://arxiv.org/abs/1702.00786 (2017).

  125. Burdge, K. B. et al. A systematic search of Zwicky Transient Facility data for ultracompact binary LISA-detectable gravitational-wave sources. Astrophys. J. 905, 32 (2020).

    ADS  CAS  Google Scholar 

  126. Stella, L. & Vietri, M. Lense–Thirring precession and quasi-periodic oscillations in low-mass X-ray binaries. Astrophys. J. Lett. 492, L59–L62 (1998).

    ADS  MATH  Google Scholar 

  127. Motta, S. E., Belloni, T. M., Stella, L., Muñoz-Darias, T. & Fender, R. Precise mass and spin measurements for a stellar-mass black hole through X-ray timing: the case of GRO J1655−40. Mon. Not. R. Astron. Soc. 437, 2554–2565 (2014).

    ADS  Google Scholar 

  128. Motta, S. E., Franchini, A., Lodato, G. & Mastroserio, G. On the different flavours of Lense–Thirring precession around accreting stellar mass black holes. Mon. Not. R. Astron. Soc. 473, 431–439 (2018).

    ADS  CAS  Google Scholar 

  129. Franchini, A., Lodato, G. & Facchini, S. Lense–Thirring precession around supermassive black holes during tidal disruption events. Mon. Not. R. Astron. Soc. 455, 1946–1956 (2016).

    ADS  CAS  Google Scholar 

  130. Ogilvie, G. I. The non-linear fluid dynamics of a warped accretion disc. Mon. Not. R. Astron. Soc. 304, 557–578 (1999).

    ADS  MATH  Google Scholar 

  131. Doǧan, S., Nixon, C. J., King, A. R. & Pringle, J. E. Instability of warped discs. Mon. Not. R. Astron. Soc. 476, 1519–1531 (2018).

    ADS  Google Scholar 

  132. Nixon, C. J. & King, A. R. Broken discs: warp propagation in accretion discs. Mon. Not. R. Astron. Soc. 421, 1201–1208 (2012).

    ADS  MATH  Google Scholar 

  133. Nealon, R., Price, D. J. & Nixon, C. J. On the Bardeen–Petterson effect in black hole accretion discs. Mon. Not. R. Astron. Soc. 448, 1526–1540 (2015).

    ADS  Google Scholar 

  134. Liska, M., Tchekhovskoy, A., Ingram, A. & van der Klis, M. Bardeen–Petterson alignment, jets, and magnetic truncation in GRMHD simulations of tilted thin accretion discs. Mon. Not. R. Astron. Soc. 487, 550–561 (2019).

    ADS  Google Scholar 

  135. Bollimpalli, D. A., Fragile, P. C., Dewberry, J. W. & Kluźniak, W. Truncated, tilted discs as a possible source of quasi-periodic oscillations. Mon. Not. R. Astron. Soc. 528, 1142–1157 (2024).

    ADS  Google Scholar 

  136. Kara, E. et al. A global look at X-ray time lags in Seyfert galaxies. Mon. Not. R. Astron. Soc. 462, 511–531 (2016).

    ADS  CAS  MATH  Google Scholar 

  137. Kara, E. et al. The corona contracts in a black-hole transient. Nature 565, 198–201 (2019).

    ADS  CAS  PubMed  MATH  Google Scholar 

  138. Axelsson, M. & Veledina, A. Accretion geometry of the black hole binary MAXI J1820+070 probed by frequency-resolved spectroscopy. Mon. Not. R. Astron. Soc. 507, 2744–2754 (2021).

    ADS  CAS  MATH  Google Scholar 

  139. De Marco, B. et al. The inner flow geometry in MAXI J1820+070 during hard and hard-intermediate states. Astron. Astrophys. 654, A14 (2021).

    MATH  Google Scholar 

  140. Wang, J. et al. Disk, corona, jet connection in the intermediate state of MAXI J1820+070 revealed by NICER spectral-timing analysis. Astrophys. J. Lett. 910, L3 (2021).

    ADS  CAS  MATH  Google Scholar 

  141. Markoff, S., Falcke, H. & Fender, R. A jet model for the broadband spectrum of XTE J1118+480. Synchrotron emission from radio to X-rays in the low/hard spectral state. Astron. Astrophys. 372, L25–L28 (2001).

    ADS  CAS  MATH  Google Scholar 

  142. Falcke, H., Körding, E. & Markoff, S. A scheme to unify low-power accreting black holes. Jet-dominated accretion flows and the radio/X-ray correlation. Astron. Astrophys. 414, 895–903 (2004).

    ADS  MATH  Google Scholar 

  143. Markoff, S., Nowak, M. A. & Wilms, J. Going with the flow: can the base of jets subsume the role of compact accretion disk coronae? Astrophys. J. 635, 1203–1216 (2005).

    ADS  Google Scholar 

Download references

Acknowledgements

We thank XMM-Newton principal investigator, N. Schartel, for approving the target-of-opportunity requests. M.M. thanks M. Ng for discussions regarding X-ray timing; L. Drummond for discussions about extreme-mass-ratio models; and the organizers and participants of the UCSB KITP TDE Workshop, including, but not limited to, J. Dai, G. Lodato, C. Nixon, A. Mummery, A. Franchini, I. Linial and D. Pasham for their comments, questions and discussions regarding these results. E.K. thanks A. Dittmann and D. Wilkins for discussions. R.A. was supported by NASA through the NASA Hubble Fellowship grant HST-HF2-51499.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. A.I. acknowledges support from the Royal Society. M.G. is supported by the ‘Programa de Atracción de Talento’ of the Comunidad de Madrid, grant number 2022-5A/TIC-24235. C. Pinto is supported by PRIN MUR SEAWIND funded by NextGenerationEU. B.T. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 950533) and from the Israel Science Foundation (grant number 1849/19). J.W. acknowledges support from the NASA FINESST Graduate Fellowship, under grant 80NSSC22K1596. This research was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP).

Author information

Authors and Affiliations

  1. MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA, USA

    Megan Masterson, Erin Kara, Christos Panagiotou, Joheen Chakraborty, Kevin Burdge, Riccardo Arcodia, Ronald A. Remillard & Jingyi Wang

  2. Centre for Astrophysics Research, Department of Physics, Astronomy and Mathematics, University of Hertfordshire, Hatfield, UK

    William N. Alston

  3. Núcleo de Astronomía de la Facultad de Ingeniería, Universidad Diego Portales, Santiago, Chile

    Claudio Ricci

  4. Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing, People’s Republic of China

    Claudio Ricci

  5. Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD, USA

    Sibasish Laha, S. Bradley Cenko, Michael Loewenstein & Dev R. Sadaula

  6. Center for Space Science and Technology, University of Maryland Baltimore County, Baltimore, MD, USA

    Sibasish Laha & Dev R. Sadaula

  7. Center for Research and Exploration in Space Science and Technology, NASA/GSFC, Greenbelt, Maryland, USA

    Sibasish Laha & Dev R. Sadaula

  8. School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel

    Iair Arcavi & Benny Trakhtenbrot

  9. Joint Space-Science Institute, University of Maryland, College Park, MD, USA

    S. Bradley Cenko

  10. Institute of Astronomy, University of Cambridge, Cambridge, UK

    Andrew C. Fabian

  11. X-ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD, USA

    Javier A. García

  12. Cahill Center for Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA, USA

    Javier A. García

  13. Centro de Astrobiología (CAB), CSIC-INTA, Madrid, Spain

    Margherita Giustini & Giovanni Miniutti

  14. School of Mathematics, Statistics, and Physics, Newcastle University, Newcastle upon Tyne, UK

    Adam Ingram

  15. Center for Astrophysics ∣ Harvard & Smithsonian, Cambridge, MA, USA

    Peter Kosec

  16. Department of Astronomy, University of Maryland, College Park, MD, USA

    Michael Loewenstein

  17. Department of Physics, University of Maryland Baltimore County, Baltimore, MD, USA

    Eileen T. Meyer & Onic I. Shuvo

  18. INAF - IASF Palermo, Palermo, Italy

    Ciro Pinto

Authors
  1. Megan Masterson
    View author publications

    Search author on:PubMed Google Scholar

  2. Erin Kara
    View author publications

    Search author on:PubMed Google Scholar

  3. Christos Panagiotou
    View author publications

    Search author on:PubMed Google Scholar

  4. William N. Alston
    View author publications

    Search author on:PubMed Google Scholar

  5. Joheen Chakraborty
    View author publications

    Search author on:PubMed Google Scholar

  6. Kevin Burdge
    View author publications

    Search author on:PubMed Google Scholar

  7. Claudio Ricci
    View author publications

    Search author on:PubMed Google Scholar

  8. Sibasish Laha
    View author publications

    Search author on:PubMed Google Scholar

  9. Iair Arcavi
    View author publications

    Search author on:PubMed Google Scholar

  10. Riccardo Arcodia
    View author publications

    Search author on:PubMed Google Scholar

  11. S. Bradley Cenko
    View author publications

    Search author on:PubMed Google Scholar

  12. Andrew C. Fabian
    View author publications

    Search author on:PubMed Google Scholar

  13. Javier A. García
    View author publications

    Search author on:PubMed Google Scholar

  14. Margherita Giustini
    View author publications

    Search author on:PubMed Google Scholar

  15. Adam Ingram
    View author publications

    Search author on:PubMed Google Scholar

  16. Peter Kosec
    View author publications

    Search author on:PubMed Google Scholar

  17. Michael Loewenstein
    View author publications

    Search author on:PubMed Google Scholar

  18. Eileen T. Meyer
    View author publications

    Search author on:PubMed Google Scholar

  19. Giovanni Miniutti
    View author publications

    Search author on:PubMed Google Scholar

  20. Ciro Pinto
    View author publications

    Search author on:PubMed Google Scholar

  21. Ronald A. Remillard
    View author publications

    Search author on:PubMed Google Scholar

  22. Dev R. Sadaula
    View author publications

    Search author on:PubMed Google Scholar

  23. Onic I. Shuvo
    View author publications

    Search author on:PubMed Google Scholar

  24. Benny Trakhtenbrot
    View author publications

    Search author on:PubMed Google Scholar

  25. Jingyi Wang
    View author publications

    Search author on:PubMed Google Scholar

Contributions

M.M. and E.K. led the analysis, interpretation and preparation of the paper, and requested a subset of the XMM-Newton and NICER data. C. Panagiotou and W.N.A. assisted with X-ray timing analysis. J.C. and K.B. contributed to the white-dwarf accretion modelling and computed the expected LISA signal. J.C., R.A., M.G. and G.M. provided information about QPEs, their models and connections to 1ES 1927+654. S.L., S.B.C., E.T.M., D.R.S. and O.I.S. triggered two of the XMM-Newton target-of-opportunity observations in this work. A.C.F. suggested the idea of coronal oscillations. A.I. and J.W. provided feedback on the timing analysis and relativistic precession model. R.A.R. assisted with the comparison with BHXB QPOs and NICER observations. C.R., P.K., C. Pinto and B.T. provided feedback on the analysis. C.R., I.A., A.C.F., J.A.G., P.K., M.L., C. Pinto, R.A.R. and B.T. assisted with the associated XMM-Newton proposal. All authors contributed to the scientific interpretation of the results and provided feedback on the paper.

Corresponding author

Correspondence to Megan Masterson.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks Gregoire Marcel, Richard Saxton and Yuhan Yao for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Unbinned PSDs from the 2–10 keV light curves with 20s binning for ObsIDs 0915390701, 0931791401, 0932392001, and 0932392101.

The resulting MCMC fit to a power-law or Lorentzian broadband noise model is shown in orange or purple, respectively. The shaded regions show a 1σ confidence region. The bottom two panels show the data divided by the power-law and Lorentzian models, highlighting the strong QPO feature at roughly 1.7 mHz (ObsIDs 0915390701), 2.2 mHz (ObsID 0931791401), and 2.3 mHz (ObsIDs 0932392001, 0932392101). These broadband noise models were used to simulate power spectra for estimating the statistical significance of the QPOs.

Extended Data Fig. 2 2–10 keV PSDs for the 4 observations taken in July-August 2022.

Left Four Panels: Unbinned PSDs from the 2–10 keV light curves with 20s binning for the 4 observations taken in July-August 2022 (ObsIDs 0902590201, 0902590301, 0902590401, 0902590501). The resulting MCMC fit to a power-law or Lorentzian broadband noise model is shown in orange or purple, respectively, with the 1σ confidence intervals shown as shaded regions. This model is fit simultaneously to all of these observations with all parameters tied. The bottom two panels show the data divided by the power-law and Lorentzian models. All four observations show an excess near 0.9 mHz. Rightmost Panel: Binned PSD created by averaging the individual PSDs at each frequency and then binning n = 6 neighbouring frequency bins. The resulting simultaneous fits to the broad band noise are shown again, solely for visual purposes. There is a clear, but broad, excess around 0.9 mHz.

Extended Data Fig. 3 Binned PSDs (n = 6 frequencies per bin, standard error uncertainties) for each of the observations showing evidence for a QPO.

The yellow, orange, and purple data shows the 0.3–2 keV, 1–4 keV, and 2–10 keV PSDs, respectively. Each column corresponds to a single epoch in time. Note that the July-August 2022 (March 2024) data contains 4 (2) observations taken within roughly 1 week of each other. The lower energy PSDs all show a weaker QPO than the higher energy (2–10 keV) PSDs, and thus, we use the 2–10 keV PSDs for analysis of the QPO.

Extended Data Fig. 4 Fractional RMS of the QPO in February 2023, August 2023, and March 2024 (first observation only) in two different energy bands – 0.3–2 keV and 2–10 keV.

The fractional RMS was estimated using the normalization of the best-fitting Lorentzian for the QPO, and the error bars represent 1σ confidence intervals from the MCMCs. As in BHXBs, the fraction RMS increases with energy, suggesting that the Comptonized component is what is being modulated on the QPO frequency.

Extended Data Fig. 5 Location of the QPO in terms of the ISCO, assuming that the QPO corresponds to the orbital frequency.

The solid lines show the best mass estimate (1.38 × 106 M⊙; ref. 8), which gives rise to the grey dotted line as a lower limit on the spin of the SMBH. However, the spin constraint is highly sensitive to the mass, which has significant uncertainty. The shaded regions show the effects of this (1σ) uncertainty8.

Extended Data Fig. 6 Frequency dependence of the QPO on the spectral shape and X-ray flux, all of which show positive correlations.

Error bars represent 1σ uncertainty. a, Photon index of the power-law component versus QPO frequency. The photon index was measured by fitting the 0.3–10 keV spectrum with the XSPEC model tbabs × ztbabs × (zpower + zbbody). b, Hard X-ray flux (2–10 keV) versus QPO frequency. c, Soft X-ray flux (0.3–2 keV) versus QPO frequency.

Extended Data Fig. 7 Mass versus spin contours assuming that the most rapid QPO (f = 2.34 mHz, March 2024) is the associated with the radial epicyclic frequency at various radii from the black hole.

The best mass estimate, from host galaxy scaling relations, is shown in grey, with the shaded regions showing the 1σ uncertainty region. The QPO can only be associated with the radial epicyclic frequency if the SMBH mass is on the low end of the uncertainty range, the SMBH is rapidly spinning, and the tearing radius is small. Even if the SMBH mass is an order of magnitude lower than the estimate from host galaxy scaling relations, the QPO would still need to be produced within 10 Rg if it is related to the radial epicyclic frequency.

Extended Data Table 1 XMM-Newton Observation Details
Full size table
Extended Data Table 2 Details of the QPO in 2–10 keV XMM-Newton Data
Full size table

Supplementary information

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Masterson, M., Kara, E., Panagiotou, C. et al. Millihertz oscillations near the innermost orbit of a supermassive black hole. Nature 638, 370–375 (2025). https://doi.org/10.1038/s41586-024-08385-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-024-08385-x

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing