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Sharpening the dark matter signature in gravitational waveforms I: Accretion and eccentricity evolution (2402.13053v2)

Published 20 Feb 2024 in gr-qc, astro-ph.CO, and hep-ph

Abstract: Dark matter overdensities around black holes can alter the dynamical evolution of a companion object orbiting around it, and cause a dephasing of the gravitational waveform. Here, we present a refined calculation of the co-evolution of the binary and the dark matter distribution, taking into account the accretion of dark matter particles on the companion black hole, and generalizing previous quasi-circular calculations to the general case of eccentric orbits. These calculations are validated by dedicated N-body simulations. We show that accretion can lead to a large dephasing, and therefore cannot be neglected in general. We also demonstrate that dark matter spikes tend to circularize eccentric orbits faster than previously thought.

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References (65)
  1. Pau Amaro-Seoane et al. (LISA), “Laser Interferometer Space Antenna,”  (2017), arXiv:1702.00786 [astro-ph.IM] .
  2. Wen-Rui Hu and Yue-Liang Wu, “The Taiji Program in Space for gravitational wave physics and the nature of gravity,” Natl. Sci. Rev. 4, 685–686 (2017).
  3. David Shoemaker (LIGO Scientific), ‘‘Gravitational wave astronomy with LIGO and similar detectors in the next decade,”  (2019), arXiv:1904.03187 [gr-qc] .
  4. F. Acernese et al. (VIRGO), “Advanced Virgo: a second-generation interferometric gravitational wave detector,” Class. Quant. Grav. 32, 024001 (2015), arXiv:1408.3978 [gr-qc] .
  5. T. Akutsu et al. (KAGRA), “Overview of KAGRA : KAGRA science,”  (2020), arXiv:2008.02921 [gr-qc] .
  6. Caio F. B. Macedo, Paolo Pani, Vitor Cardoso,  and Luís C. B. Crispino, “Into the lair: gravitational-wave signatures of dark matter,” Astrophys. J. 774, 48 (2013), arXiv:1302.2646 [gr-qc] .
  7. Enrico Barausse, Vitor Cardoso,  and Paolo Pani, “Can environmental effects spoil precision gravitational-wave astrophysics?” Phys. Rev. D 89, 104059 (2014), arXiv:1404.7149 [gr-qc] .
  8. Enrico Barausse, Vitor Cardoso,  and Paolo Pani, “Environmental Effects for Gravitational-wave Astrophysics,” J. Phys. Conf. Ser. 610, 012044 (2015), arXiv:1404.7140 [astro-ph.CO] .
  9. Lorenz Zwick, Pedro R. Capelo,  and Lucio Mayer, “Priorities in gravitational waveforms for future space-borne detectors: vacuum accuracy or environment?” Mon. Not. Roy. Astron. Soc. 521, 4645–4651 (2023), arXiv:2209.04060 [gr-qc] .
  10. Philippa S. Cole, Gianfranco Bertone, Adam Coogan, Daniele Gaggero, Theophanes Karydas, Bradley J. Kavanagh, Thomas F. M. Spieksma,  and Giovanni Maria Tomaselli, “Distinguishing environmental effects on binary black hole gravitational waveforms,” Nature Astron. 7, 943–950 (2023a), arXiv:2211.01362 [gr-qc] .
  11. Ramin G. Daghigh and Gabor Kunstatter, “Who knows what dark matter lurks in the heart of M87: The shadow knows, and so does the ringdown,”  (2023), arXiv:2308.15682 [gr-qc] .
  12. Paolo Gondolo and Joseph Silk, “Dark matter annihilation at the galactic center,” Phys. Rev. Lett. 83, 1719–1722 (1999), arXiv:astro-ph/9906391 [astro-ph] .
  13. Piero Ullio, HongSheng Zhao,  and Marc Kamionkowski, “A Dark matter spike at the galactic center?” Phys. Rev. D 64, 043504 (2001), arXiv:astro-ph/0101481 .
  14. Hong-Sheng Zhao and Joseph Silk, “Mini-dark halos with intermediate mass black holes,” Phys. Rev. Lett. 95, 011301 (2005), arXiv:astro-ph/0501625 .
  15. Gianfranco Bertone, Andrew R. Zentner,  and Joseph Silk, “A new signature of dark matter annihilations: gamma-rays from intermediate-mass black holes,” Phys. Rev. D 72, 103517 (2005), arXiv:astro-ph/0509565 .
  16. Otto A. Hannuksela, Kenny C. Y. Ng,  and Tjonnie G. F. Li, “Extreme dark matter tests with extreme mass ratio inspirals,” Phys. Rev. D 102, 103022 (2020), arXiv:1906.11845 [astro-ph.CO] .
  17. Kazunari Eda, Yousuke Itoh, Sachiko Kuroyanagi,  and Joseph Silk, “New Probe of Dark-Matter Properties: Gravitational Waves from an Intermediate-Mass Black Hole Embedded in a Dark-Matter Minispike,” Phys. Rev. Lett.  110, 221101 (2013), arXiv:1301.5971 [gr-qc] .
  18. Bradley J. Kavanagh, David A. Nichols, Gianfranco Bertone,  and Daniele Gaggero, “Detecting dark matter around black holes with gravitational waves: Effects of dark-matter dynamics on the gravitational waveform,” Phys. Rev. D 102, 083006 (2020), arXiv:2002.12811 [gr-qc] .
  19. Kazunari Eda, Yousuke Itoh, Sachiko Kuroyanagi,  and Joseph Silk, “Gravitational waves as a probe of dark matter minispikes,” Phys. Rev. D 91, 044045 (2015), arXiv:1408.3534 [gr-qc] .
  20. Xiao-Jun Yue and Wen-Biao Han, ‘‘Gravitational waves with dark matter minispikes: the combined effect,” Phys. Rev. D 97, 064003 (2018), arXiv:1711.09706 [gr-qc] .
  21. Xiao-Jun Yue, Wen-Biao Han,  and Xian Chen, “Dark matter: an efficient catalyst for intermediate-mass-ratio-inspiral events,” Astrophys. J. 874, 34 (2019), arXiv:1802.03739 [gr-qc] .
  22. Thomas D. P. Edwards, Marco Chianese, Bradley J. Kavanagh, Samaya M. Nissanke,  and Christoph Weniger, “Unique Multimessenger Signal of QCD Axion Dark Matter,” Phys. Rev. Lett. 124, 161101 (2020), arXiv:1905.04686 [hep-ph] .
  23. Chao Zhang, Guoyang Fu,  and Ning Dai, “Detecting dark matter with extreme mass-ratio inspirals,”   (2024), arXiv:2401.04467 [gr-qc] .
  24. Nicholas Speeney, Andrea Antonelli, Vishal Baibhav,  and Emanuele Berti, “Impact of relativistic corrections on the detectability of dark-matter spikes with gravitational waves,” Phys. Rev. D 106, 044027 (2022), arXiv:2204.12508 [gr-qc] .
  25. Diego Montalvo, Adam Smith-Orlik, Saeed Rastgoo, Laura Sagunski, Niklas Becker,  and Hazkeel Khan, “Post-Newtonian effects in compact binaries with a dark matter spike: A Lagrangian approach,”   (2024), arXiv:2401.06084 [gr-qc] .
  26. Adam Coogan, Gianfranco Bertone, Daniele Gaggero, Bradley J. Kavanagh,  and David A. Nichols, “Measuring the dark matter environments of black hole binaries with gravitational waves,” Phys. Rev. D 105, 043009 (2022), arXiv:2108.04154 [gr-qc] .
  27. Philippa S. Cole, Adam Coogan, Bradley J. Kavanagh,  and Gianfranco Bertone, “Measuring dark matter spikes around primordial black holes with Einstein Telescope and Cosmic Explorer,” Phys. Rev. D 107, 083006 (2023b), arXiv:2207.07576 [astro-ph.CO] .
  28. Xiao-Jun Yue and Zhoujian Cao, “Dark matter minispike: A significant enhancement of eccentricity for intermediate-mass-ratio inspirals,” Phys. Rev. D 100, 043013 (2019), arXiv:1908.10241 [astro-ph.HE] .
  29. Niklas Becker, Laura Sagunski, Lukas Prinz,  and Saeed Rastgoo, “Circularization versus eccentrification in intermediate mass ratio inspirals inside dark matter spikes,” Phys. Rev. D 105, 063029 (2022), arXiv:2112.09586 [gr-qc] .
  30. Gen-Liang Li, Yong Tang,  and Yue-Liang Wu, “Probing dark matter spikes via gravitational waves of extreme-mass-ratio inspirals,” Sci. China Phys. Mech. Astron. 65, 100412 (2022), arXiv:2112.14041 [astro-ph.CO] .
  31. David A. Nichols, Benjamin A. Wade,  and Alexander M. Grant, “Secondary accretion of dark matter in intermediate mass-ratio inspirals: Dark-matter dynamics and gravitational-wave phase,” Phys. Rev. D 108, 124062 (2023), arXiv:2309.06498 [gr-qc] .
  32. Bradley J. Kavanagh, Theophanes K. Karydas, Gianfranco Bertone, Pierfrancesco Di Cintio,  and Mario Pasquato, “Sharpening the dark matter signature in gravitational waveforms II: Numerical results with the NbodyIMRI code,”  (2024), to appear.
  33. Bradley J. Kavanagh, “NbodyIMRI [Code, v1.0],” https://github.com/bradkav/NbodyIMRI, DOI:10.5281/zenodo.10641173 (2024).
  34. Gerardo Alvarez and Hai-Bo Yu, “Density spikes near black holes in self-interacting dark matter halos and indirect detection constraints,” Phys. Rev. D 104, 043013 (2021), arXiv:2012.15050 [hep-ph] .
  35. Stuart L. Shapiro and Jessie Shelton, “Weak annihilation cusp inside the dark matter spike about a black hole,” Phys. Rev. D 93, 123510 (2016), arXiv:1606.01248 [astro-ph.HE] .
  36. Hyungjin Kim, Alessandro Lenoci, Isak Stomberg,  and Xiao Xue, “Adiabatically compressed wave dark matter halo and intermediate-mass-ratio inspirals,” Phys. Rev. D 107, 083005 (2023), arXiv:2212.07528 [astro-ph.GA] .
  37. Gianfranco Bertone and David Merritt, “Time-dependent models for dark matter at the Galactic Center,” Phys. Rev. D72, 103502 (2005), arXiv:astro-ph/0501555 [astro-ph] .
  38. Stuart L. Shapiro and Douglas C. Heggie, “Effect of stars on the dark matter spike around a black hole: A tale of two treatments,” Phys. Rev. D 106, 043018 (2022), arXiv:2209.08105 [astro-ph.GA] .
  39. Laleh Sadeghian, Francesc Ferrer,  and Clifford M. Will, “Dark matter distributions around massive black holes: A general relativistic analysis,” Phys. Rev. D 88, 063522 (2013), arXiv:1305.2619 [astro-ph.GA] .
  40. Katherine J. Mack, Jeremiah P. Ostriker,  and Massimo Ricotti, “Growth of structure seeded by primordial black holes,” Astrophys. J. 665, 1277–1287 (2007), arXiv:astro-ph/0608642 .
  41. Yu. N. Eroshenko, “Dark matter density spikes around primordial black holes,” Astron. Lett. 42, 347–356 (2016), arXiv:1607.00612 [astro-ph.HE] .
  42. Julian Adamek, Christian T. Byrnes, Mateja Gosenca,  and Shaun Hotchkiss, “WIMPs and stellar-mass primordial black holes are incompatible,” Phys. Rev. D 100, 023506 (2019), arXiv:1901.08528 [astro-ph.CO] .
  43. Yu. N. Eroshenko, “Dark matter around primordial black hole at the radiation-dominated stage,” Int. J. Mod. Phys. A 35, 2040046 (2020), arXiv:1910.01564 [astro-ph.CO] .
  44. Mathieu Boudaud, Thomas Lacroix, Martin Stref, Julien Lavalle,  and Pierre Salati, “In-depth analysis of the clustering of dark matter particles around primordial black holes. Part I. Density profiles,” JCAP 08, 053 (2021), arXiv:2106.07480 [astro-ph.CO] .
  45. Ning Dai, Yungui Gong, Tong Jiang,  and Dicong Liang, “Intermediate mass-ratio inspirals with dark matter minispikes,” Phys. Rev. D 106, 064003 (2022), arXiv:2111.13514 [gr-qc] .
  46. David Merritt, Stefan Harfst,  and Gianfranco Bertone, “Collisionally Regenerated Dark Matter Structures in Galactic Nuclei,” Phys. Rev. D75, 043517 (2007), arXiv:astro-ph/0610425 [astro-ph] .
  47. Michele Maggiore, Gravitational Waves. Vol. 1: Theory and Experiments, Oxford Master Series in Physics (Oxford University Press, 2007).
  48. S. Chandrasekhar, ‘‘Dynamical Friction. I. General Considerations: the Coefficient of Dynamical Friction.” apj 97, 255 (1943a).
  49. S. Chandrasekhar, “Dynamical Friction. II. The Rate of Escape of Stars from Clusters and the Evidence for the Operation of Dynamical Friction.” Astrophys. J.  97, 263 (1943b).
  50. S. Chandrasekhar, “Dynamical Friction. III. a More Exact Theory of the Rate of Escape of Stars from Clusters.” Astrophys. J.  98, 54 (1943c).
  51. Pau Amaro-Seoane, Jonathan R. Gair, Marc Freitag, M. Coleman Miller, Ilya Mandel, Curt J. Cutler,  and Stanislav Babak, “Astrophysics, detection and science applications of intermediate- and extreme mass-ratio inspirals,” Class. Quant. Grav. 24, R113–R169 (2007), arXiv:astro-ph/0703495 .
  52. Fani Dosopoulou, “Dynamical friction in dark matter spikes: corrections to Chandrasekhar’s formula,”   (2023), arXiv:2305.17281 [astro-ph.HE] .
  53. Bradley J. Kavanagh, “HaloFeedback [Code, v0.9],” https://github.com/bradkav/HaloFeedback, DOI:10.5281/zenodo.3688813 (2020).
  54. Angel R. Plastino and Juan C. Muzzio, “On the Use and Abuse of Newton’s Second Law for Variable Mass Problems,” Celestial Mechanics and Dynamical Astronomy 53, 227–232 (1992).
  55. Steven B. Giddings and Michelangelo L. Mangano, “Astrophysical implications of hypothetical stable TeV-scale black holes,” Phys. Rev. D 78, 035009 (2008), arXiv:0806.3381 [hep-ph] .
  56. W. G. Unruh, “Absorption cross section of small black holes,” Phys. Rev. D 14, 3251–3259 (1976).
  57. Fani Dosopoulou and Fabio Antonini, “Dynamical friction and the evolution of Supermassive Black hole Binaries: the final hundred-parsec problem,” Astrophys. J. 840, 31 (2017), arXiv:1611.06573 [astro-ph.GA] .
  58. Diego J. Muñoz, Ryan Miranda,  and Dong Lai, “Hydrodynamics of circumbinary accretion: Angular momentum transfer and binary orbital evolution,” Astrophys. J. 871, 84 (2019), arXiv:1810.04676 [astro-ph.HE] .
  59. Daniel J. D’Orazio and Paul C. Duffell, “Orbital Evolution of Equal-mass Eccentric Binaries due to a Gas Disk: Eccentric Inspirals and Circular Outspirals,” Astrophys. J. Lett. 914, L21 (2021), arXiv:2103.09251 [astro-ph.HE] .
  60. Magdalena Siwek, Rainer Weinberger,  and Lars Hernquist, “Orbital evolution of binaries in circumbinary discs,” Mon. Not. Roy. Astron. Soc. 522, 2707–2717 (2023), arXiv:2302.01785 [astro-ph.HE] .
  61. Daniel Baumann, Gianfranco Bertone, John Stout,  and Giovanni Maria Tomaselli, “Ionization of gravitational atoms,” Phys. Rev. D 105, 115036 (2022), arXiv:2112.14777 [gr-qc] .
  62. Alexis Boudon, Philippe Brax,  and Patrick Valageas, “Subsonic accretion and dynamical friction for a black hole moving through a self-interacting scalar dark matter cloud,” Phys. Rev. D 106, 043507 (2022), arXiv:2204.09401 [astro-ph.CO] .
  63. Stuart L. Shapiro, “Spikes and accretion of unbound, collisionless matter around black holes,”  (2023), arXiv:2310.13739 [astro-ph.GA] .
  64. Pau Amaro Seoane et al., “The effect of mission duration on LISA science objectives,” Gen. Rel. Grav. 54, 3 (2022), arXiv:2107.09665 [astro-ph.IM] .
  65. Vitor Cardoso, Caio F. B. Macedo,  and Rodrigo Vicente, “Eccentricity evolution of compact binaries and applications to gravitational-wave physics,” Phys. Rev. D 103, 023015 (2021), arXiv:2010.15151 [gr-qc] .
Citations (4)

Summary

  • The paper provides a refined theoretical model for dark matter accretion in binary systems, demonstrating its significant impact on inspiral dynamics.
  • The paper reveals that dark matter spikes influence eccentricity evolution, leading to faster circularization than previous models predicted.
  • The paper employs N-body simulations to validate dynamic friction feedback mechanisms, highlighting observable phase shifts in gravitational waveforms.

Accretion and Eccentricity in Binary Systems within Dark Matter Spikes: A Detailed Analysis

The paper "Sharpening the dark matter signature in gravitational waveforms I: Accretion and eccentricity evolution" presents an in-depth exploration of the effects of dark matter (DM) surrounding black holes on gravitational waveforms. It explores the dynamical interactions between binary systems and dark matter spikes, placing particular emphasis on the processes of dark matter accretion onto black holes and the evolution of orbital eccentricity. These phenomena have crucial implications for the paper of gravitational waves, especially in preparation for future space-based detectors such as LISA and Taiji.

Key Contributions

  1. Accretion of Dark Matter: The paper provides a refined theoretical framework to account for the accretion of DM particles by a black hole within a binary system. It presents a nuanced model considering the increase in mass of the orbiting companion due to accretion, directly affecting the inspiral dynamics. This model, validated via NN-body simulations, incorporates the accretion cross-section and interaction details, painting a comprehensive picture of particle capture by black holes.
  2. Eccentricity Evolution: Contrary to some previous assumptions that gravitational interactions simplify to near-circular orbits, this paper tackles the general case of eccentric orbits. It sheds light on how dark matter spikes influence the orbit's trajectory, correcting earlier models that did not adequately account for phase-space distributions. The paper highlights that while gravitational radiation typically circularizes orbits, dark matter interactions can modify this evolution, leading to faster circularization than previously expected.
  3. Feedback Mechanisms: Incorporating dynamical friction feedback, the authors extend their analysis to account for the redistribution of DM particles due to gravitational scattering. This feedback influences both the density profile of the DM spike and the gravitational waveform's phase, offering potential observational signatures detectable by advanced gravitational wave detectors.

Numerical Validation and Results

The authors utilize sophisticated NN-body simulations to validate their theoretical models of accretion and gravitational interactions within DM spikes. Their results underscore the significant phase shift in gravitational waveforms arising from dark matter dynamics. Accretion alone could induce a large dephasing, greatly impacting waveform analyses.

They further demonstrate that dynamic friction, traditionally assumed to eccentrify orbits based on simplistic models, may instead promote more rapid circularization when viewed through the lens of a dynamically evolving DM distribution. The paper finds these interactions also alter the gravitational wave signals in ways that depend sensitively on initial orbital conditions and the properties of the DM spike.

Theoretical and Practical Implications

The refined models of accretion and eccentricity evolution have substantial implications for both theory and observational astronomy. On a theoretical level, they challenge the assumption that intermediate and extreme mass ratio inspirals (IMRIs and EMRIs) within DM spikes can be simplified to quasi-circular dynamics. Practically, these findings suggest that future gravitational wave detectors can utilize waveform dephasing to probe the properties of dark matter around black holes, offering a unique window into the elusive nature of dark matter distribution and dynamics.

The proposed advancements in understanding the interplay between DM and binary systems validate the need for accounting for these factors in accurately modeling and interpreting gravitational wave signals. Ultimately, these insights provide a stepping stone towards employing gravitational wave astronomy as a tool for exploring the dark matter landscapes surrounding black holes, further enriching our understanding of the cosmos. Future work will need to integrate these findings into detector sensitivity models to refine the search for DM signatures in observed gravitational wave events.