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Inference on inner galaxy structure via gravitational waves from supermassive binaries

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Abstract

The detection of a stochastic gravitational wave background by pulsar-timing arrays indicates the presence of a population of supermassive black hole binaries. Although the observed spectrum generally matches predictions for orbital evolution driven by gravitational-wave emission in circular orbits, there is a preference for a spectral turnover at the lowest observed frequencies, which may point to substantial hardening during a transition from early environmental influences to later stages dominated by emission. In the vicinity of these binaries, the ejection of stars or dark matter particles through gravitational three-body slingshots efficiently extracts orbital energy, leading to a low-frequency turnover in the spectrum. Here we model how the gravitational-wave spectrum depends on the initial inner galactic profile before scouring by binary ejections while accounting for a range of initial binary eccentricities. By analysing the NANOGrav 15-year data, we find that a parsec-scale galactic-centre density of around 106 M⊙ pc−3 is favoured across most of the parameter space, thus shedding light on the environmental effects that shape black hole evolution and the combined matter density near galaxy centres.

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Fig. 1: Illustrative SGWB spectra from a simplified SMBHB population.
Fig. 2: Posterior constraints on eccentricity and environmental parameters.
Fig. 3: Constraints and corresponding SGWB spectra for fixed initial eccentricities.
Fig. 4: Posterior constraints from alternative eccentricity and density-profile parameterizations.

Data availability

The NANOGrav 15-year dataset is described in and available through ref. 7.

Code availability

All methods required to evaluate the conclusions in this paper are provided in the main text, Methods and Supplementary Information. The holodeck and PTArcade codes used in this work are publicly available via GitHub at https://github.com/nanograv/holodeck and https://github.com/andrea-mitridate/PTArcade, respectively. The code supporting the findings of this study is available via GitHub at https://github.com/XueXiao-Physics/NG15_Galactic_Tomography.

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Acknowledgements

We are grateful to K. Blum, V. Cardoso, G. Carullo, S. Chen, J. Cline, H. Kim, B. Liu, Y. Ma, Z. Pan, S. Tiruvaskar and R. Vicente for useful discussions. The NANOGrav Collaboration receives support from National Science Foundation (NSF) Physics Frontiers Center (Award Nos. 1430284 and 2020265), the Gordon and Betty Moore Foundation, NSF AccelNet (Award No. 2114721), an NSERC Discovery Grant and CIFAR. The Arecibo Observatory is a facility of the NSF operated under a cooperative agreement (Agreement No. AST-1744119) by the University of Central Florida in alliance with Universidad Ana G. Méndez and Yang Enterprises, Inc. The Green Bank Observatory is a facility of the NSF operated under cooperative agreement by Associated Universities, Inc. The National Radio Astronomy Observatory is a facility of the NSF operated under cooperative agreement by Associated Universities, Inc. Part of this research was performed at the Jet Propulsion Laboratory, under contract with NASA. Y.C. is supported by the Villum Foundation (Grant No. 37766), by the Danish Research Foundation and by the European Union’s H2020 ERC Advanced Grant ‘Black holes: gravitational engines of discovery’ (Grant Agreement No. Gravitas-101052587). The views and opinions expressed here are, however, those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. D.J.D. acknowledges support from the Danish Independent Research Fund through a Sapere Aude Starting Grant (No. 121587). A. Mitridate and X.X. are supported by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy (EXC 2121 Quantum Universe – 390833306). IFAE is partially funded by the CERCA programme of the Generalitat de Catalunya. X.X. is funded by Grant No. CNS2023-143767 through MICIU/AEI/10.13039/501100011033 and by European Union NextGenerationEU/PRTR. Y.C. and X.X. acknowledge the support of the Rosenfeld Foundation and the European Consortium for Astroparticle Theory in the form of an exchange travel grant. L.B. acknowledges support from the NSF (Award No. AST-1909933) and from the Research Corporation for Science Advancement under Cottrell Scholar Award No. 27553. P.R.B. is supported by the Science and Technology Facilities Council (Grant No. ST/W000946/1). S.B.-S. gratefully acknowledges the support of a Sloan Fellowship, and the support of the NSF (Award No. 1815664). The work of R.B., N. Laal, X.S., J.T. and D.W. is partly supported by the George and Hannah Bolinger Memorial Fund managed by the College of Science at Oregon State University. M.C., P.P. and S.R.T. acknowledge support from the NSF (Award No. AST-2007993). M.C. was supported by the Vanderbilt Initiative in Data Intensive Astrophysics Fellowship. Support for this work was provided by the NSF through the Grote Reber Fellowship Program administered by Associated Universities, Inc./National Radio Astronomy Observatory. Pulsar research at UBC is supported by an NSERC Discovery Grant and by CIFAR. K.C. is supported by a UBC Four Year Fellowship (6456). M.E.D. acknowledges support from the Naval Research Laboratory through NASA (Contract No. S-15633Y). T.D. and M.T.L. are supported by an NSF Astronomy and Astrophysics Grant (Award No. 2009468). E.C.F. is supported by NASA (Award No. 80GSFC24M0006). G.E.F., S.C.S. and S.J.V. are supported by the NSF (Award No. PHY-2011772). K.A.G. and S.R.T. acknowledge support from an NSF CAREER award (Award No. 2146016). A.D.J. and M.V. acknowledge support from the Caltech and Jet Propulsion Laboratory President’s and Director’s Research and Development Fund. A.D.J. acknowledges support from the Sloan Foundation. N. Laal acknowledges support from a Larry W. Martin and Joyce B. O’Neill Endowed Fellowship in the College of Science at Oregon State University. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA (Contract No. 80NM0018D0004). D.R.L. and M.A.M. are supported by the NSF (Grant No. 1458952). M.A.M. is supported by the NSF (Grant No. 2009425). C.M.F.M. was supported in part by the NSF (Grant Nos. NSF PHY-1748958 and AST-2106552). The Dunlap Institute is funded by an endowment established by the David Dunlap family and the University of Toronto. K.D.O. was supported in part by the NSF (Grant No. 2207267). T.T.P. acknowledges support from the Extragalactic Astrophysics Research Group at Eötvös Loránd University, funded by the Eötvös Loránd Research Network, which was used during the development of this research. H.A.R. is supported by NSF Partnerships for Research and Education in Physics (Award No. 2216793). S.M.R. and I.H.S. are CIFAR fellows. Portions of this work performed at NRL were supported by ONR 6.1 basic research funding. J.D.R. also acknowledges support from start-up funds from Texas Tech University. J.S. is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship (Award No. AST-2202388) and acknowledges previous support from the NSF (Award No. 1847938). C.U. acknowledges support from BGU (Kreitman fellowship), and the Council for Higher Education and Israel Academy of Sciences and Humanities (Excellence fellowship). C.A.W. acknowledges support from CIERA, the Adler Planetarium and the Brinson Foundation through a CIERA-Adler postdoctoral fellowship. O.Y. is supported by a NSF Graduate Research Fellowship (Grant No. DGE-2139292).

Author information

Authors and Affiliations

  1. State Key Laboratory of Dark Matter Physics, Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China

    Yifan Chen

  2. Key Laboratory for Particle Astrophysics and Cosmology (MOE) & Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai, China

    Yifan Chen

  3. Center of Gravity, Niels Bohr Institute, Copenhagen, Denmark

    Yifan Chen

  4. Institute for Theoretical Physics, Goethe University, Frankfurt am Main, Germany

    Matthias Daniel & Laura Sagunski

  5. Space Telescope Science Institute, Baltimore, MD, USA

    Daniel J. D’Orazio

  6. Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD, USA

    Daniel J. D’Orazio

  7. Niels Bohr International Academy, Niels Bohr Institute, Copenhagen, Denmark

    Daniel J. D’Orazio

  8. Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA

    Xuanye Fan

  9. Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany

    Andrea Mitridate & Xiao Xue

  10. Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, Bellaterra (Barcelona), Spain

    Xiao Xue

  11. II. Institute of Theoretical Physics, Universität Hamburg, Hamburg, Germany

    Xiao Xue

  12. Center for Gravitation, Cosmology and Astrophysics, Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, WI, USA

    Gabriella Agazie, Akash Anumarlapudi, Gabriel E. Freedman, Aaron D. Johnson, Megan L. Jones, David L. Kaplan, Alexander McEwen, Shashwat C. Sardesai, Xavier Siemens & Sarah J. Vigeland

  13. Newcastle University, Newcastle upon Tyne, UK

    Anne M. Archibald

  14. X-Ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD, USA

    Zaven Arzoumanian

  15. Department of Physics, Oregon State University, Corvallis, OR, USA

    Jeremy G. Baier, Bence Bécsy, Rand Burnette, Heling Deng, Jeffrey S. Hazboun, Nima Laal, Xavier Siemens, Jacob Taylor & David Wright

  16. Department of Physics and Astronomy, Widener University, Chester, PA, USA

    Paul T. Baker

  17. Physics Department, University of Florida, Gainesville, FL, USA

    Laura Blecha

  18. Cornell Center for Astrophysics and Planetary Science and Department of Astronomy, Cornell University, Ithaca, NY, USA

    Adam Brazier, Shami Chatterjee & James M. Cordes

  19. Cornell Center for Advanced Computing, Cornell University, Ithaca, NY, USA

    Adam Brazier

  20. Institute for Gravitational Wave Astronomy and School of Physics and Astronomy, University of Birmingham, Birmingham, UK

    Paul R. Brook

  21. Department of Physics and Astronomy, West Virginia University, Morgantown, WV, USA

    Sarah Burke-Spolaor, Lankeswar Dey, William Fiore, Emmanuel Fonseca, Nate Garver-Daniels, Peter A. Gentile, Joseph Glaser, Ross J. Jennings, Tingting Liu, Duncan R. Lorimer, Maura A. McLaughlin, Brent J. Shapiro-Albert & Haley M. Wahl

  22. Center for Gravitational Waves and Cosmology, West Virginia University, Morgantown, WV, USA

    Sarah Burke-Spolaor, Lankeswar Dey, William Fiore, Emmanuel Fonseca, Nate Garver-Daniels, Peter A. Gentile, Joseph Glaser, Ross J. Jennings, Tingting Liu, Duncan R. Lorimer, Maura A. McLaughlin, Brent J. Shapiro-Albert & Haley M. Wahl

  23. Department of Physics, University of Connecticut, Storrs, CT, USA

    J. Andrew Casey-Clyde

  24. Department of Physics and Astronomy, Vanderbilt University, Nashville, TN, USA

    Maria Charisi, Kyle A. Gersbach, William G. Lamb, Natasha McMann, Polina Petrov, Jessie C. Runnoe & Stephen R. Taylor

  25. Department of Physics, New Mexico Institute of Mining and Technology, Socorro, NM, USA

    Tyler Cohen

  26. Department of Physics, Montana State University, Bozeman, MT, USA

    Neil J. Cornish

  27. Department of Physics and Astronomy, Franklin & Marshall College, Lancaster, PA, USA

    Fronefield Crawford

  28. National Academy of Sciences, Washington, DC, USA

    H. Thankful Cromartie

  29. US Naval Research Laboratory, Washington, DC, USA

    H. Thankful Cromartie, Megan E. DeCesar, Bradley W. Meyers & Ingrid H. Stairs

  30. Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada

    Kathryn Crowter

  31. George Mason University, Fairfax, VA, USA

    Megan E. DeCesar

  32. National Radio Astronomy Observatory, Socorro, NM, USA

    Paul B. Demorest & Kevin Stovall

  33. Department of Physics, Hillsdale College, Hillsdale, MI, USA

    Timothy Dolch

  34. Eureka Scientific, Oakland, CA, USA

    Timothy Dolch

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

    Elizabeth C. Ferrara

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

    Elizabeth C. Ferrara

  37. NASA Goddard Space Flight Center, Greenbelt, MD, USA

    Elizabeth C. Ferrara

  38. Department of Astronomy, University of California, Berkeley, Berkeley, CA, USA

    Emiko C. Gardiner, Luke Zoltan Kelley & Chung-Pei Ma

  39. Department of Physics and Astronomy, University of Montana, Missoula, MT, USA

    Deborah C. Good

  40. Department of Astronomy and Astrophysics, University of Michigan, Ann Arbor, MI, USA

    Kayhan Gültekin

  41. Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, CA, USA

    Aaron D. Johnson, Patrick M. Meyers, Stella Koch Ocker & Michele Vallisneri

  42. Space Science Division, Naval Research Laboratory, Washington, DC, USA

    Matthew Kerr & Paul S. Ray

  43. University of Washington Bothell, Bothell, WA, USA

    Joey S. Key

  44. SETI Institute, Mountain View, CA, USA

    Michael T. Lam

  45. School of Physics and Astronomy, Rochester Institute of Technology, Rochester, NY, USA

    Michael T. Lam, Sophia V. Sosa Fiscella & Olivia Young

  46. Laboratory for Multiwavelength Astrophysics, Rochester Institute of Technology, Rochester, NY, USA

    Michael T. Lam, Sophia V. Sosa Fiscella & Olivia Young

  47. Department of Physics, Yale University, New Haven, CT, USA

    Bjorn Larsen & Chiara M. F. Mingarelli

  48. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA

    T. Joseph W. Lazio & Michele Vallisneri

  49. Department of Physics and Astronomy, State University of New York at Oswego, Oswego, NY, USA

    Natalia Lewandowska

  50. Department of Astronomy & Astrophysics, University of Toronto, Toronto, Ontario, Canada

    Jing Luo

  51. Green Bank Observatory, Green Bank, WV, USA

    Ryan S. Lynch & Jacob E. Turner

  52. Department of Physics, University of California, Berkeley, CA, USA

    Chung-Pei Ma

  53. Department of Physics, University of the Pacific, Stockton, CA, USA

    Dustin R. Madison

  54. Department of Physics and Astronomy, Union College, Schenectady, NY, USA

    James W. McKee

  55. International Centre for Radio Astronomy Research, Curtin University, Bentley, Western Australia, Australia

    Bradley W. Meyers

  56. Dunlap Institute for Astronomy and Astrophysics, University of Toronto, Toronto, Ontario, Canada

    Cherry Ng

  57. Department of Physics, Lafayette College, Easton, PA, USA

    David J. Nice & Joseph K. Swiggum

  58. The Observatories of the Carnegie Institution for Science, Pasadena, CA, USA

    Stella Koch Ocker

  59. Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, MA, USA

    Ken D. Olum

  60. Institute of Physics and Astronomy, Eötvös Loránd University, Budapest, Hungary

    Timothy T. Pennucci

  61. Arecibo Observatory, Arecibo, PR, USA

    Benetge B. P. Perera

  62. Department of Physics, Texas Tech University, Lubbock, TX, USA

    Nihan S. Pol & Joseph D. Romano

  63. Department of Physics, University of Puerto Rico, Mayagüez, PR, USA

    Henri A. Radovan

  64. National Radio Astronomy Observatory, Charlottesville, VA, USA

    Scott M. Ransom & Alexander Saffer

  65. Department of Physics, Penn State Abington, Abington, PA, USA

    Ann Schmiedekamp & Carl Schmiedekamp

  66. Institute for Theoretical Physics, University of Münster, Münster, Germany

    Kai Schmitz

  67. Giant Army, Seattle, WA, USA

    Brent J. Shapiro-Albert

  68. Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO, USA

    Joseph Simon

  69. Center for Astrophysics, Harvard University, Cambridge, MA, USA

    Magdalena S. Siwek

  70. Department of Physics and Astronomy, Oberlin College, Oberlin, OH, USA

    Daniel R. Stinebring

  71. Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Hannover, Germany

    Abhimanyu Susobhanan & Rutger van Haasteren

  72. Department of Physics, Middle East Technical University, Ankara, Turkey

    Caner Ünal

  73. Department of Physics, Ben-Gurion University of the Negev, Be’er Sheva, Israel

    Caner Ünal

  74. Feza Gursey Institute, Bogazici University, Kandilli, Istanbul, Turkey

    Caner Ünal

  75. Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University, Evanston, IL, USA

    Caitlin A. Witt

  76. Adler Planetarium, Chicago, IL, USA

    Caitlin A. Witt

Authors
  1. Yifan Chen
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  2. Matthias Daniel
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  3. Daniel J. D’Orazio
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  4. Xuanye Fan
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  5. Andrea Mitridate
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  6. Laura Sagunski
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  7. Xiao Xue
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Consortia

The NANOGrav Collaboration

  • Gabriella Agazie
  • , Akash Anumarlapudi
  • , Anne M. Archibald
  • , Zaven Arzoumanian
  • , Jeremy G. Baier
  • , Paul T. Baker
  • , Bence Bécsy
  • , Laura Blecha
  • , Adam Brazier
  • , Paul R. Brook
  • , Sarah Burke-Spolaor
  • , Rand Burnette
  • , J. Andrew Casey-Clyde
  • , Maria Charisi
  • , Shami Chatterjee
  • , Tyler Cohen
  • , James M. Cordes
  • , Neil J. Cornish
  • , Fronefield Crawford
  • , H. Thankful Cromartie
  • , Kathryn Crowter
  • , Megan E. DeCesar
  • , Paul B. Demorest
  • , Heling Deng
  • , Lankeswar Dey
  • , Timothy Dolch
  • , Elizabeth C. Ferrara
  • , William Fiore
  • , Emmanuel Fonseca
  • , Gabriel E. Freedman
  • , Emiko C. Gardiner
  • , Nate Garver-Daniels
  • , Peter A. Gentile
  • , Kyle A. Gersbach
  • , Joseph Glaser
  • , Deborah C. Good
  • , Kayhan Gültekin
  • , Jeffrey S. Hazboun
  • , Ross J. Jennings
  • , Aaron D. Johnson
  • , Megan L. Jones
  • , David L. Kaplan
  • , Luke Zoltan Kelley
  • , Matthew Kerr
  • , Joey S. Key
  • , Nima Laal
  • , Michael T. Lam
  • , William G. Lamb
  • , Bjorn Larsen
  • , T. Joseph W. Lazio
  • , Natalia Lewandowska
  • , Tingting Liu
  • , Duncan R. Lorimer
  • , Jing Luo
  • , Ryan S. Lynch
  • , Chung-Pei Ma
  • , Dustin R. Madison
  • , Alexander McEwen
  • , James W. McKee
  • , Maura A. McLaughlin
  • , Natasha McMann
  • , Bradley W. Meyers
  • , Patrick M. Meyers
  • , Chiara M. F. Mingarelli
  • , Cherry Ng
  • , David J. Nice
  • , Stella Koch Ocker
  • , Ken D. Olum
  • , Timothy T. Pennucci
  • , Benetge B. P. Perera
  • , Polina Petrov
  • , Nihan S. Pol
  • , Henri A. Radovan
  • , Scott M. Ransom
  • , Paul S. Ray
  • , Joseph D. Romano
  • , Jessie C. Runnoe
  • , Alexander Saffer
  • , Shashwat C. Sardesai
  • , Ann Schmiedekamp
  • , Carl Schmiedekamp
  • , Kai Schmitz
  • , Brent J. Shapiro-Albert
  • , Xavier Siemens
  • , Joseph Simon
  • , Magdalena S. Siwek
  • , Sophia V. Sosa Fiscella
  • , Ingrid H. Stairs
  • , Daniel R. Stinebring
  • , Kevin Stovall
  • , Abhimanyu Susobhanan
  • , Joseph K. Swiggum
  • , Jacob Taylor
  • , Stephen R. Taylor
  • , Jacob E. Turner
  • , Caner Ünal
  • , Michele Vallisneri
  • , Rutger van Haasteren
  • , Sarah J. Vigeland
  • , Haley M. Wahl
  • , Caitlin A. Witt
  • , David Wright
  •  & Olivia Young

Contributions

This paper uses a decade’s worth of pulsar-timing observations and is the product of the work of many people. Y.C., L.S. and X.X. initiated the project and developed the core idea, with D.J.D. contributing to its development. Y.C., M.D., D.J.D., X.F., A. Mitridate, L.S., and X.X. participated in discussions, provided critical feedback, and shaped the research and analysis. Y.C. coordinated the project and wrote the paper. M.D., X.F. and X.X. developed the analysis code, created the figures and edited the text. X.F. performed the analysis using alternative parameterizations, under the guidance of Y.C. and X.X. D.J.D. offered guidance on the SMBHB population model and the holodeck code, wrote the discussion on the environmental effects from gas and edited the text. A. Mitridate provided guidance on the PTArcade code and the presentation of NANOGrav 15-year data. G.A., A.A, A.M.A., Z.A., P.T.B., P.R.B., H.T.C., K.C., M.E.D., P.B.D., T.D., E.C.F., W.F., E.F., G.E.F., N.G.-D., D.C.G., P.A.G., J.G., R.J.J., M.L.J., D.L.K., M.K., M.T.L., D.R.L., J.L., R.S.L., A. McEwen, M.A.M., N.M., B.W.M., C.N., D.J.N., B.B.P.P., N.S.P., H.A.R., S.M.R., P.S.R., A.S., C.S., B.J.S.-A., I.H.S., K.S., A.S., J.K.S. and H.M.W. developed timing models and ran observations for the NANOGrav 15-year dataset. Development of the holodeck population modelling framework was led by L.Z.K., with contributions from J.A.C-C., D.W., E.C.G., K.G., M.S.S. and S.C. PTArcade, which was used in this analysis, was mainly developed by A. Mitridate, with help from D.W., K.D.O. G.A., A.A., A.M.A., Z.A., J.G.B., P.T.B., B.B., L.B., A.B., P.R.B., S.B.-S., R.B., J.A.C.-C., M.C., S.C., T.C., J.M.C., N.J.C., F.C., H.T.C., K.C., M.E.D., P.B.D., H.D., L.D., T.D., E.C.F., W.F., E.F., G.E.F., N.G.-D., P.A.G., K.A.G., J.G., D.C.G., K.G., J.S.H., R.J.J., A.D.J., M.L.J., L.Z.K., M.K., J.S.K., N. Laal, M.T.L., W.G.L., B.L., T.J.W.L., N. Lewandowska, T.L., D.R.L., J.L., R.S.L., C.-P.M., D.R.M., A. McEwen, J.W.M., M.A.M., N.M., B.W.M., P.M.M., C.M.F.M., A. Mitridate, C.N., D.J.N., S.K.O., K.D.O., T.T.P., B.B.P.P., P.P., N.S.P., H.A.R., S.M.R., P.S.R., J.D.R., J.C.R., A. Saffer, S.C.S., A. Schmiedekamp, C.S., K. Schmitz, B.J.S.-A., X.S., J.S., M.S.S., S.V.S.F., I.H.S., D.R.S., K. Stovall, A. Susobhanan, J.K.S., J.T., S.R.T., J.E.T., C.U., M.V., R.V.H., S.J.V., H.M.W., C.A.W., D.W. and O.Y. developed and validated the NANOGrav 15-year data.

Corresponding authors

Correspondence to Yifan Chen, Xuanye Fan or Xiao Xue.

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Supplementary Information

Supplementary Table 1 and Figs. 1 and 2.

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Chen, Y., Daniel, M., D’Orazio, D.J. et al. Inference on inner galaxy structure via gravitational waves from supermassive binaries. Nat Astron (2026). https://doi.org/10.1038/s41550-026-02782-0

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