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Searching accretion-enhanced dark matter annihilation signals in the Galactic Centre

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  • Published: 10 October 2024
  • Volume 2024, article number 94, (2024)
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Searching accretion-enhanced dark matter annihilation signals in the Galactic Centre
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  • Meiwen Yang1,2,
  • Zhi-Qi Guo1,2,
  • Xiao-Yi Luo1,
  • Zhao-Qiang Shen  ORCID: orcid.org/0000-0003-3722-09662,
  • Zi-Qing Xia  ORCID: orcid.org/0000-0003-4963-72752,
  • Chih-Ting Lu  ORCID: orcid.org/0000-0002-9044-62971,
  • Yue-Lin Sming Tsai  ORCID: orcid.org/0000-0002-7275-85612,3 &
  • …
  • Yi-Zhong Fan  ORCID: orcid.org/0000-0002-8966-69112,3 
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A preprint version of the article is available at arXiv.

Abstract

This study reanalyzes the detection prospects of dark matter (DM) annihilation signals in the Galactic Center, focusing on velocity-dependent dynamics within a spike density near the supermassive black hole (Sgr A⋆). We investigate three annihilation processes — p-wave, resonance, and forbidden annihilation — under semi-relativistic velocities, leveraging gamma-ray data from Fermi and DAMPE telescopes. Our analysis integrates a fermionic DM model with an electroweak axion-like particle (ALP) portal, exploring annihilation into two or four photons. Employing a comprehensive six-dimensional integration, we precisely calculate DM-induced gamma-ray fluxes near Sgr A⋆, incorporating velocity and positional dependencies in the annihilation cross-section and photon yield spectra. Our findings highlight scenarios of resonance and forbidden annihilation, where the larger ALP-DM-DM coupling constant Caχχ can affect spike density, potentially yielding detectable gamma-ray line spectra within Fermi and DAMPE energy resolution. We set upper limits for Caχχ across these scenarios, offering insights into the detectability and spectral characteristics of DM annihilation signals from the Galactic Center.

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References

  1. ATLAS collaboration, Search for Higgs bosons decaying into new spin-0 or spin-1 particles in four-lepton final states with the ATLAS detector with 139 fb−1 of pp collision data at \( \sqrt{s} \) = 13 TeV, JHEP 03 (2022) 041 [arXiv:2110.13673] [INSPIRE].

  2. CMS collaboration, Search for light bosons in decays of the 125 GeV Higgs boson in proton-proton collisions at \( \sqrt{s} \) = 8 TeV, JHEP 10 (2017) 076 [arXiv:1701.02032] [INSPIRE].

  3. BaBar collaboration, Search for Invisible Decays of a Dark Photon Produced in e+e− Collisions at BaBar, Phys. Rev. Lett. 119 (2017) 131804 [arXiv:1702.03327] [INSPIRE].

  4. XENON collaboration, First Dark Matter Search with Nuclear Recoils from the XENONnT Experiment, Phys. Rev. Lett. 131 (2023) 041003 [arXiv:2303.14729] [INSPIRE].

  5. LZ collaboration, First Dark Matter Search Results from the LUX-ZEPLIN (LZ) Experiment, Phys. Rev. Lett. 131 (2023) 041002 [arXiv:2207.03764] [INSPIRE].

  6. PandaX-4T collaboration, Dark Matter Search Results from the PandaX-4T Commissioning Run, Phys. Rev. Lett. 127 (2021) 261802 [arXiv:2107.13438] [INSPIRE].

  7. J.W. Foster et al., Search for dark matter lines at the Galactic Center with 14 years of Fermi data, Phys. Rev. D 107 (2023) 103047 [arXiv:2212.07435] [INSPIRE].

    Article  ADS  Google Scholar 

  8. Fermi-LAT collaboration, Search for 100 MeV to 10 GeV γ-ray lines in the Fermi-LAT data and implications for gravitino dark matter in μνSSM, JCAP 10 (2014) 023 [arXiv:1406.3430] [INSPIRE].

  9. MAGIC collaboration, Search for Gamma-Ray Spectral Lines from Dark Matter Annihilation up to 100 TeV toward the Galactic Center with MAGIC, Phys. Rev. Lett. 130 (2023) 061002 [arXiv:2212.10527] [INSPIRE].

  10. Planck collaboration, Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6 [Erratum ibid. 652 (2021) C4] [arXiv:1807.06209] [INSPIRE].

  11. M. Ibe, H. Murayama and T.T. Yanagida, Breit-Wigner Enhancement of Dark Matter Annihilation, Phys. Rev. D 79 (2009) 095009 [arXiv:0812.0072] [INSPIRE].

    Article  ADS  Google Scholar 

  12. W.-L. Guo and Y.-L. Wu, Enhancement of Dark Matter Annihilation via Breit-Wigner Resonance, Phys. Rev. D 79 (2009) 055012 [arXiv:0901.1450] [INSPIRE].

    Article  ADS  Google Scholar 

  13. D. Croon et al., Light dark matter through resonance scanning, Phys. Rev. D 105 (2022) L061303 [arXiv:2012.15284] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  14. Y.-C. Ding, Y.-L. Ku, C.-C. Wei and Y.-F. Zhou, Consistent explanation for the cosmic-ray positron excess in p-wave Breit-Wigner enhanced dark matter annihilation, Eur. Phys. J. C 82 (2022) 126 [arXiv:2110.10388] [INSPIRE].

    Article  ADS  Google Scholar 

  15. T. Binder, S. Chakraborti, S. Matsumoto and Y. Watanabe, A global analysis of resonance-enhanced light scalar dark matter, JHEP 01 (2023) 106 [arXiv:2205.10149] [INSPIRE].

    Article  ADS  Google Scholar 

  16. G. Bélanger, S. Chakraborti, Y. Génolini and P. Salati, GeV-scale dark matter with p-wave Breit-Wigner enhanced annihilation, Phys. Rev. D 110 (2024) 023039 [arXiv:2401.02513] [INSPIRE].

    Article  Google Scholar 

  17. R. Diamanti et al., Constraining Dark Matter Late-Time Energy Injection: Decays and P-Wave Annihilations, JCAP 02 (2014) 017 [arXiv:1308.2578] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  18. K. Bondarenko et al., Direct detection and complementary constraints for sub-GeV dark matter, JHEP 03 (2020) 118 [arXiv:1909.08632] [INSPIRE].

    Article  ADS  Google Scholar 

  19. T. Siegert, F. Calore and P.D. Serpico, Sub-GeV Dark Matter Annihilation: Limits from Milky Way observations with INTEGRAL, Mon. Not. Roy. Astron. Soc. 528 (2024) 3433 [arXiv:2401.03795] [INSPIRE].

    Article  ADS  Google Scholar 

  20. K. Griest and D. Seckel, Three exceptions in the calculation of relic abundances, Phys. Rev. D 43 (1991) 3191 [INSPIRE].

  21. R.T. D’Agnolo and J.T. Ruderman, Light Dark Matter from Forbidden Channels, Phys. Rev. Lett. 115 (2015) 061301 [arXiv:1505.07107] [INSPIRE].

    Article  ADS  Google Scholar 

  22. A. Delgado, A. Martin and N. Raj, Forbidden Dark Matter at the Weak Scale via the Top Portal, Phys. Rev. D 95 (2017) 035002 [arXiv:1608.05345] [INSPIRE].

    Article  ADS  Google Scholar 

  23. R.T. D’Agnolo, D. Liu, J.T. Ruderman and P.-J. Wang, Forbidden dark matter annihilations into Standard Model particles, JHEP 06 (2021) 103 [arXiv:2012.11766] [INSPIRE].

    Article  ADS  Google Scholar 

  24. T. Hara, S. Kanemura and T. Katayose, Is light thermal scalar dark matter possible?, Phys. Rev. D 105 (2022) 035035 [arXiv:2109.03553] [INSPIRE].

    Article  ADS  Google Scholar 

  25. G.N. Wojcik and T.G. Rizzo, Forbidden scalar dark matter and dark Higgses, JHEP 04 (2022) 033 [arXiv:2109.07369] [INSPIRE].

    Article  ADS  Google Scholar 

  26. P. Gondolo and J. Silk, Dark matter annihilation at the galactic center, Phys. Rev. Lett. 83 (1999) 1719 [astro-ph/9906391] [INSPIRE].

  27. J. Shelton, S.L. Shapiro and B.D. Fields, Black hole window into p-wave dark matter annihilation, Phys. Rev. Lett. 115 (2015) 231302 [arXiv:1506.04143] [INSPIRE].

    Article  ADS  Google Scholar 

  28. C. Johnson et al., Search for gamma-ray emission from p-wave dark matter annihilation in the Galactic Center, Phys. Rev. D 99 (2019) 103007 [arXiv:1904.06261] [INSPIRE].

    Article  ADS  Google Scholar 

  29. Fermi-LAT collaboration, Fermi Large Area Telescope Performance after 10 Years of Operation, Astrophys. J. Supp. 256 (2021) 12 [arXiv:2106.12203] [INSPIRE].

  30. DAMPE collaboration, The DArk Matter Particle Explorer mission, Astropart. Phys. 95 (2017) 6 [arXiv:1706.08453] [INSPIRE].

  31. R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].

  32. R.D. Peccei and H.R. Quinn, Constraints Imposed by CP Conservation in the Presence of Instantons, Phys. Rev. D 16 (1977) 1791 [INSPIRE].

  33. S. Weinberg, A New Light Boson?, Phys. Rev. Lett. 40 (1978) 223 [INSPIRE].

  34. F. Wilczek, Problem of Strong P and T Invariance in the Presence of Instantons, Phys. Rev. Lett. 40 (1978) 279 [INSPIRE].

  35. D.K. Ghosh, A. Ghoshal and S. Jeesun, Axion-like particle (ALP) portal freeze-in dark matter confronting ALP search experiments, JHEP 01 (2024) 026 [arXiv:2305.09188] [INSPIRE].

    Article  ADS  Google Scholar 

  36. J.-G. Cheng, Y.-F. Liang and E.-W. Liang, Search for the gamma-ray spectral lines with the DAMPE and the Fermi-LAT observations, Phys. Rev. D 108 (2023) 063015 [arXiv:2308.16762] [INSPIRE].

    Article  ADS  Google Scholar 

  37. S. Allen et al., Electroweak Axion Portal to Dark Matter, arXiv:2405.02403 [INSPIRE].

  38. A. Bharucha, F. Brümmer, N. Desai and S. Mutzel, Axion-like particles as mediators for dark matter: beyond freeze-out, JHEP 02 (2023) 141 [arXiv:2209.03932] [INSPIRE].

    Article  ADS  Google Scholar 

  39. J. Jaeckel, M. Jankowiak and M. Spannowsky, LHC probes the hidden sector, Phys. Dark Univ. 2 (2013) 111 [arXiv:1212.3620] [INSPIRE].

    Article  Google Scholar 

  40. BaBar collaboration, Search for an Axionlike Particle in B Meson Decays, Phys. Rev. Lett. 128 (2022) 131802 [arXiv:2111.01800] [INSPIRE].

  41. J.F. Navarro, C.S. Frenk and S.D.M. White, A universal density profile from hierarchical clustering, Astrophys. J. 490 (1997) 493 [astro-ph/9611107] [INSPIRE].

  42. P.J. McMillan, The mass distribution and gravitational potential of the Milky Way, Mon. Not. Roy. Astron. Soc. 465 (2016) 76 [arXiv:1608.00971] [INSPIRE].

    Article  ADS  Google Scholar 

  43. Z.-Q. Shen et al., Exploring dark matter spike distribution around the Galactic centre with stellar orbits, Mon. Not. Roy. Astron. Soc. 527 (2023) 3196 [arXiv:2303.09284] [INSPIRE].

    Article  ADS  Google Scholar 

  44. D. Yang and H.-B. Yu, Gravothermal evolution of dark matter halos with differential elastic scattering, JCAP 09 (2022) 077 [arXiv:2205.03392] [INSPIRE].

    Article  ADS  Google Scholar 

  45. T. Lacroix, M. Stref and J. Lavalle, Anatomy of Eddington-like inversion methods in the context of dark matter searches, JCAP 09 (2018) 040 [arXiv:1805.02403] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  46. L. Sadeghian, F. Ferrer and C.M. Will, Dark matter distributions around massive black holes: A general relativistic analysis, Phys. Rev. D 88 (2013) 063522 [arXiv:1305.2619] [INSPIRE].

    Article  ADS  Google Scholar 

  47. S.L. Shapiro and J. Shelton, Weak annihilation cusp inside the dark matter spike about a black hole, Phys. Rev. D 93 (2016) 123510 [arXiv:1606.01248] [INSPIRE].

    Article  ADS  Google Scholar 

  48. Y. Cheng, S.-F. Ge, X.-G. He and J. Sheng, Forbidden dark matter combusted around supermassive black hole, Phys. Lett. B 847 (2023) 138294 [arXiv:2211.05643] [INSPIRE].

    Article  Google Scholar 

  49. S.L. Shapiro and V. Paschalidis, Self-interacting dark matter cusps around massive black holes, Phys. Rev. D 89 (2014) 023506 [arXiv:1402.0005] [INSPIRE].

    Article  ADS  Google Scholar 

  50. Y. Bao, J.J. Fan and L. Li, Electroweak ALP searches at a muon collider, JHEP 08 (2022) 276 [arXiv:2203.04328] [INSPIRE].

    Article  ADS  Google Scholar 

  51. P. Lepage, gplepage/vegas: vegas version 6.1.2, (2024) [https://doi.org/10.5281/zenodo.592154].

  52. G.-W. Yuan et al., Constraints on dark matter annihilation from the Event Horizon Telescope observations of M87∗, JHEP 04 (2022) 018 [arXiv:2106.05901] [INSPIRE].

    Article  ADS  Google Scholar 

  53. Fermi-LAT collaboration, Fermi Large Area Telescope Fourth Source Catalog, Astrophys. J. Suppl. 247 (2020) 33 [arXiv:1902.10045] [INSPIRE].

  54. A.A. Abdo et al., Fermi LAT Search for Photon Lines from 30 to 200 GeV and Dark Matter Implications, Phys. Rev. Lett. 104 (2010) 091302 [arXiv:1001.4836] [INSPIRE].

    Article  ADS  Google Scholar 

  55. Fermi-LAT collaboration, Updated search for spectral lines from Galactic dark matter interactions with pass 8 data from the Fermi Large Area Telescope, Phys. Rev. D 91 (2015) 122002 [arXiv:1506.00013] [INSPIRE].

  56. T. Bringmann et al., Fermi LAT Search for Internal Bremsstrahlung Signatures from Dark Matter Annihilation, JCAP 07 (2012) 054 [arXiv:1203.1312] [INSPIRE].

    Article  ADS  Google Scholar 

  57. Y.-F. Liang et al., Search for a gamma-ray line feature from a group of nearby galaxy clusters with Fermi LAT Pass 8 data, Phys. Rev. D 93 (2016) 103525 [arXiv:1602.06527] [INSPIRE].

    Article  ADS  Google Scholar 

  58. P. De La Torre Luque, J. Smirnov and T. Linden, Gamma-ray lines in 15 years of Fermi-LAT data: New constraints on Higgs portal dark matter, Phys. Rev. D 109 (2024) L041301 [arXiv:2309.03281] [INSPIRE].

  59. Y.-Z. Fan et al., A ~ 43 GeV γ-ray line signature in the directions of a group of nearby massive galaxy clusters, arXiv:2407.11737 [INSPIRE].

  60. A. Ibarra, S. Lopez Gehler and M. Pato, Dark matter constraints from box-shaped gamma-ray features, JCAP 07 (2012) 043 [arXiv:1205.0007] [INSPIRE].

    Article  ADS  Google Scholar 

  61. S. Li et al., Study of the boxlike dark matter signals from dwarf spheroidal galaxies with Fermi-LAT data, Phys. Rev. D 97 (2018) 083007 [INSPIRE].

  62. Z.-Q. Shen, Z.-Q. Xia and Y.-Z. Fan, Search for Line-like and Box-shaped Spectral Features from Nearby Galaxy Clusters with 11.4 Years of Fermi Large Area Telescope Data, Astrophys. J. 920 (2021) 1 [arXiv:2108.00363] [INSPIRE].

  63. DAMPE collaboration, Search for gamma-ray spectral lines with the DArk Matter Particle Explorer, Sci. Bull. 67 (2022) 679 [arXiv:2112.08860] [INSPIRE].

  64. DAMPE collaboration, An algorithm to resolve γ-rays from charged cosmic rays with DAMPE, Res. Astron. Astrophys. 18 (2018) 027 [arXiv:1712.02939] [INSPIRE].

  65. K.-K. Duan et al., DmpIRFs and DmpST: DAMPE instrument response functions and science tools for gamma-ray data analysis, Res. Astron. Astrophys. 19 (2019) 132 [arXiv:1904.13098] [INSPIRE].

    Article  ADS  Google Scholar 

  66. S. Xu et al., A Milliarcsecond-accurate Position for Sagittarius A*, Astrophys. J. 940 (2022) 15 [arXiv:2210.03390].

  67. T.-C. Liu, J.-G. Cheng, Y.-F. Liang and E.-W. Liang, Search for gamma-ray line signals around the black hole at the galactic center with DAMPE observation, Sci. China Phys. Mech. Astron. 65 (2022) 269512 [arXiv:2203.08078] [INSPIRE].

    Article  ADS  Google Scholar 

  68. J.R. Mattox et al., The Likelihood Analysis of EGRET Data, Astrophys. J. 461 (1996) 396 [INSPIRE].

  69. H. Chernoff, On the Distribution of the Likelihood Ratio, Ann. Math. Stat. 25 (1954) 573 [INSPIRE].

  70. B.T. Chiang, S.L. Shapiro and J. Shelton, Faint dark matter annihilation signals and the Milky Way’s supermassive black hole, Phys. Rev. D 102 (2020) 023030 [arXiv:1912.09446] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  71. G. Alvarez and H.-B. Yu, Density spikes near black holes in self-interacting dark matter halos and indirect detection constraints, Phys. Rev. D 104 (2021) 043013 [arXiv:2012.15050] [INSPIRE].

    Article  ADS  Google Scholar 

  72. S. Balaji, D. Sachdeva, F. Sala and J. Silk, Dark matter spikes around Sgr A* in γ-rays, JCAP 08 (2023) 063 [arXiv:2303.12107] [INSPIRE].

    Article  ADS  Google Scholar 

  73. Y. Cheng, S.-F. Ge, J. Sheng and T.T. Yanagida, Dark Matter Annihilation via Breit-Wigner Enhancement with Heavier Mediator, arXiv:2309.12043 [INSPIRE].

  74. P. Sandick, K. Sinha and T. Yamamoto, Black Holes, Dark Matter Spikes, and Constraints on Simplified Models with t-Channel Mediators, Phys. Rev. D 98 (2018) 035004 [arXiv:1701.00067] [INSPIRE].

    Article  ADS  Google Scholar 

  75. K. Christy, J. Kumar and P. Sandick, Constraining p-wave dark matter annihilation with gamma-ray observations of M87, Phys. Rev. D 108 (2023) 103042 [arXiv:2305.05155] [INSPIRE].

    Article  ADS  Google Scholar 

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Acknowledgments

We thank an anonymous referee for useful comments on gravitational potential. YST, MWY, ZQG and ZQX are supported by the National Key Research and Development Program of China (No. 2022YFF0503304), and the Project for Young Scientists in Basic Research of the Chinese Academy of Sciences (No. YSBR-092). CTL and XYL are supported by the Special funds for postdoctoral overseas recruitment, Ministry of Education of China (No. 164080H0262403). This research has made use of data obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA’s Goddard Space Flight Center. This research has made use of the data resources from DArk Matter Particle Explorer (DAMPE) satellite mission supported by Strategic Priority Program on Space Science, and China data service provided by National Space Science Data Center of China.

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Authors and Affiliations

  1. Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, 210023, China

    Meiwen Yang, Zhi-Qi Guo, Xiao-Yi Luo & Chih-Ting Lu

  2. Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, 210023, China

    Meiwen Yang, Zhi-Qi Guo, Zhao-Qiang Shen, Zi-Qing Xia, Yue-Lin Sming Tsai & Yi-Zhong Fan

  3. School of Astronomy and Space Science, University of Science and Technology of China, Hefei, 230026, China

    Yue-Lin Sming Tsai & Yi-Zhong Fan

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Yang, M., Guo, ZQ., Luo, XY. et al. Searching accretion-enhanced dark matter annihilation signals in the Galactic Centre. J. High Energ. Phys. 2024, 94 (2024). https://doi.org/10.1007/JHEP10(2024)094

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  • Received: 20 July 2024

  • Accepted: 14 September 2024

  • Published: 10 October 2024

  • DOI: https://doi.org/10.1007/JHEP10(2024)094

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Keywords

  • Axions and ALPs
  • Particle Nature of Dark Matter
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