- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Survival of ultraheavy nuclei in astrophysical sources: Applications to protomagnetar outflows

Nick Ekanger1,2,3,*, Mukul Bhattacharya4,5,6, Kohta Murase6,7,8,9, and Shunsaku Horiuchi3,10,11

  • *Contact author: ekangernj@astr.tohoku.ac.jp
PDF

Phys. Rev. D 114, 063031 – Published 14 September, 2026

DOI: https://doi.org/10.1103/p1n3-hc7k

Abstract

Outflows of rapidly rotating protomagnetars have been considered as attractive sites for the synthesis of nuclei heavier than iron, but the question remains whether these nuclei are able to survive against photodisintegration as they make their way out of their formation environments. In this work, we present new analytic fitting formulas for the photodisintegration cross sections applicable to heavy nuclei beyond iron. We confirm that the results from the TALYS simulations are consistent with the theory of the giant dipole resonance, and apply the obtained new formulas to investigate whether ultraheavy nuclei entrained in protomagnetar outflows can be disintegrated by thermal and nonthermal photons before leaving the stellar envelope. We explore two outflow models: a spherical wind model and a jetted outflow model. For nuclei accelerated to the bulk speed of these outflows, their survival depends on the model and engine properties. For spherical winds, nuclei may survive for the first ∼100  s postcore collapse, but as the wind Lorentz factor increases, the photodisintegration optical depth sharply rises, and nuclei may no longer survive. For the jetted outflows arising from progenitors surrounded with stellar envelopes, nuclei can only survive before the jet breakout time in cases where the central engine has high spin-down energy, that is, with a high magnetic field strength and shorter spin period. In progenitors with more extended envelopes, the jet breakout time is much longer, allowing for nonthermal photons to readily photodisintegrate nuclei in high spin-down energy cases. These results also outline some of the necessary, but not yet sufficient, conditions to source ultrahigh-energy cosmic-ray nuclei.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (85)

  1. J. Blümer, R. Engel, and J. R. Hörandel, Cosmic rays from the knee to the highest energies, Prog. Part. Nucl. Phys. 63, 293 (2009).
  2. K. Kotera and A. V. Olinto, The astrophysics of ultrahigh-energy cosmic rays, Annu. Rev. Astron. Astrophys. 49, 119 (2011).
  3. R. Alves Batista, J. Biteau, M. Bustamante, K. Dolag, R. Engel, K. Fang, K.-H. Kampert, D. Kostunin, M. Mostafa, K. Murase et al., Open questions in cosmic-ray research at ultrahigh energies, Front. Astron. Space Sci. 6, 23 (2019).
  4. L. A. Anchordoqui, Ultra-high-energy cosmic rays, Phys. Rep. 801, 1 (2019).
  5. A. Aab et al. (Pierre Auger Collaboration), The Pierre Auger Cosmic Ray Observatory, Nucl. Instrum. Methods Phys. Res., Sect. A 798, 172 (2015).
  6. T. Abu-Zayyad, R. Aida, M. Allen, R. Anderson, R. Azuma, E. Barcikowski, J. W. Belz, D. R. Bergman, S. A. Blake, R. Cady et al., The cosmic-ray energy spectrum observed with the surface detector of the telescope array experiment, Astrophys. J. 768, L1 (2013).
  7. K. Greisen, End to the cosmic ray spectrum?, Phys. Rev. Lett. 16, 748 (1966).
  8. G. T. Zatsepin and V. A. Kuz’min, Upper limit of the spectrum of cosmic rays, Sov. J. Exp. Theor. Phys. Lett. 4, 78 (1966).
  9. J. Abraham et al. (Pierre Auger Collaboration), Observation of the suppression of the flux of cosmic rays above 4×1019  eV, Phys. Rev. Lett. 101, 061101 (2008).
  10. R. U. Abbasi et al. (High Resolution Fly’s Eye Collaboration), First observation of the Greisen-Zatsepin-Kuzmin suppression, Phys. Rev. Lett. 100, 101101 (2008).
  11. A. A. Halim et al. (Pierre Auger Collaboration), Constraining the sources of ultra-high-energy cosmic rays across and above the ankle with the spectrum and composition data measured at the Pierre Auger Observatory, J. Cosmol. Astropart. Phys. 05 (2023) 024.
  12. L. A. Anchordoqui, M. T. Dova, T. P. McCauley, S. Reucroft, and J. D. Swain, Possible explanation for the tail of the cosmic ray spectrum, Phys. Lett. B 482, 343 (2000).
  13. B. T. Zhang, K. Murase, N. Ekanger, M. Bhattacharya, and S. Horiuchi, Ultraheavy ultrahigh-energy cosmic rays, Phys. Rev. Lett. 136, 181002 (2026).
  14. Y. Jiang, B. T. Zhang, and K. Murase, Energetics of ultrahigh-energy cosmic-ray nuclei, Phys. Rev. D 104, 043017 (2021).
  15. M. Kuznetsov and P. Tinyakov, Uhecr mass composition at highest energies from anisotropy of their arrival directions, J. Cosmol. Astropart. Phys. 04 (2021) 065.
  16. C. A. Norman, D. B. Melrose, and A. Achterberg, The origin of cosmic rays above 10 18.5 eV, Astrophys. J. 454, 60 (1995).
  17. C. D. Dermer, S. Razzaque, J. D. Finke, and A. Atoyan, Ultra-high-energy cosmic rays from black hole jets of radio galaxies, New J. Phys. 11, 065016 (2009).
  18. A. Pe’er, K. Murase, and P. Meszaros, Radio quiet AGNs as possible sources of ultra-high energy cosmic rays, Phys. Rev. D 80, 123018 (2009).
  19. H. Takami and S. Horiuchi, The production of ultra high energy cosmic rays during the early epochs of radio-loud AGN, Astropart. Phys. 34, 749 (2011).
  20. K. Murase, C. D. Dermer, H. Takami, and G. Migliori, Blazars as ultra-high-energy cosmic-ray sources: Implications for TeV gamma-ray observations, Astrophys. J. 749, 63 (2012).
  21. E. Waxman, Cosmological gamma-ray bursts and the highest energy cosmic rays, Phys. Rev. Lett. 75, 386 (1995).
  22. M. Milgrom and V. Usov, Ascertaining the core collapse supernova mechanism: The state of the art and the road ahead, Astrophys. J. Lett. 449, L37 (1995).
  23. K. Murase, K. Ioka, S. Nagataki, and T. Nakamura, High energy neutrinos and cosmic-rays from low-luminosity gamma-ray bursts?, Astrophys. J. Lett. 651, L5 (2006).
  24. K. Murase, K. Ioka, S. Nagataki, and T. Nakamura, High-energy cosmic-ray nuclei from high- and low-luminosity gamma-ray bursts and implications for multi-messenger astronomy, Phys. Rev. D 78, 023005 (2008).
  25. R.-Y. Liu and X.-Y. Wang, Energy spectrum and chemical composition of ultrahigh energy cosmic rays from semi-relativistic hypernovae, Astrophys. J. 746, 40 (2012).
  26. J. Arons, Magnetars in the metagalaxy: An origin for ultra–high-energy cosmic rays in the nearby universe, Astrophys. J. 589, 871 (2003).
  27. K. Murase, P. Meszaros, and B. Zhang, Probing the birth of fast rotating magnetars through high-energy neutrinos, Phys. Rev. D 79, 103001 (2009).
  28. K. Fang, K. Kotera, and A. V. Olinto, Newly-born pulsars as sources of ultrahigh energy cosmic rays, Astrophys. J. 750, 118 (2012).
  29. K. Fang, K. Kotera, K. Murase, and A. V. Olinto, Testing the newborn pulsar origin of ultrahigh energy cosmic rays with EeV neutrinos, Phys. Rev. D 90, 103005 (2014); 92, 129901(E) (2015).
  30. H. Takami, K. Kyutoku, and K. Ioka, High-energy radiation from remnants of neutron star binary mergers, Phys. Rev. D 89, 063006 (2014).
  31. X. Rodrigues, D. Biehl, D. Boncioli, and A. M. Taylor, Binary neutron star merger remnants as sources of cosmic rays below the “Ankle”, Astropart. Phys. 106, 10 (2019).
  32. K. Murase and M. Fukugita, Energetics of high-energy cosmic radiations, Phys. Rev. D 99, 063012 (2019).
  33. G. R. Farrar, Binary neutron star mergers as the source of the highest energy cosmic rays, Phys. Rev. Lett. 134, 081003 (2025).
  34. D. Caprioli, ”Espresso” acceleration of ultra-high-energy cosmic rays, Astrophys. J. Lett. 811, L38 (2015).
  35. S. S. Kimura, K. Murase, and B. T. Zhang, Ultrahigh-energy cosmic-ray nuclei from black hole jets: Recycling galactic cosmic rays through shear acceleration, Phys. Rev. D 97, 023026 (2018).
  36. R. Mbarek and D. Caprioli, Bottom-up acceleration of ultra-high-energy cosmic rays in the jets of active galactic nuclei, Astrophys. J. 886, 8 (2019).
  37. R. Mbarek, D. Caprioli, and K. Murase, High-energy neutrino emission from Espresso-reaccelerated ions in jets of active galactic nuclei, Astrophys. J. 942, 37 (2023).
  38. B. T. Zhang, K. Murase, S. S. Kimura, S. Horiuchi, and P. Mészáros, Low-luminosity gamma-ray bursts as the sources of ultrahigh-energy cosmic ray nuclei, Phys. Rev. D 97, 083010 (2018).
  39. D. Boncioli, D. Biehl, and W. Winter, On the common origin of cosmic rays across the ankle and diffuse neutrinos at the highest energies from low-luminosity gamma-ray bursts, Astrophys. J. 872, 110 (2019).
  40. B. T. Zhang and K. Murase, Ultrahigh-energy cosmic-ray nuclei and neutrinos from engine-driven supernovae, Phys. Rev. D 100, 103004 (2019).
  41. B. T. Zhang, K. Murase, F. Oikonomou, and Z. Li, High-energy cosmic ray nuclei from tidal disruption events: Origin, survival, and implications, Phys. Rev. D 96, 063007 (2017); 96, 069902(A) (2017).
  42. B. D. Metzger, D. Giannios, and S. Horiuchi, Heavy nuclei synthesized in gamma-ray burst outflows as the source of ultrahigh energy cosmic rays, Mon. Not. R. Astron. Soc. 415, 2495 (2011).
  43. S. Horiuchi, K. Murase, K. Ioka, and P. Mészáros, The survival of nuclei in jets associated with core-collapse supernovae and gamma-ray bursts, Astrophys. J. 753, 69 (2012).
  44. M. Bhattacharya, S. Horiuchi, and K. Murase, On the synthesis of heavy nuclei in protomagnetar outflows and implications for ultra-high energy cosmic rays, Mon. Not. R. Astron. Soc. 514, 6011 (2022).
  45. N. Ekanger, M. Bhattacharya, and S. Horiuchi, Systematic exploration of heavy element nucleosynthesis in protomagnetar outflows, Mon. Not. R. Astron. Soc. 513, 405 (2022).
  46. N. Ekanger, M. Bhattacharya, and S. Horiuchi, Nucleosynthesis in outflows of compact objects and detection prospects of associated kilonovae, Mon. Not. R. Astron. Soc. 525, 2040 (2023).
  47. T. A. Thompson, P. Chang, and E. Quataert, Magnetar spin-down, hyperenergetic supernovae, and gamma-ray bursts, Astrophys. J. 611, 380 (2004).
  48. X.-Y. Wang, S. Razzaque, and P. Meszaros, On the origin and survival of UHE cosmic-ray nuclei in GRBs and hypernovae, Astrophys. J. 677, 432 (2008).
  49. J. L. Puget, F. W. Stecker, and J. H. Bredekamp, Photonuclear interactions of ultrahigh energy cosmic rays and their astrophysical consequences., Astrophys. J. 205, 638 (1976).
  50. F. W. Stecker and M. H. Salamon, Photodisintegration of ultrahigh-energy cosmic rays: A new determination, Astrophys. J. 512, 521 (1999).
  51. E. Khan, S. Goriely, D. Allard, E. Parizot, T. Suomijarvi, A. J. Koning, S. Hilaire, and M. C. Duijvestijn, Photodisintegration of ultra-high-energy cosmic rays revisited, Astropart. Phys. 23, 191 (2005).
  52. M. Bhattacharya, J. A. Carpio, K. Murase, and S. Horiuchi, High-energy neutrino emission from magnetised jets of rapidly rotating protomagnetars, Mon. Not. R. Astron. Soc. 521, 2391 (2023).
  53. A. M. Soderberg et al., Relativistic ejecta from X-ray flash XRF 060218 and the rate of cosmic explosions, Nature (London) 442, 1014 (2006).
  54. R. Margutti, A. M. Soderberg, M. H. Wieringa, P. G. Edwards, R. A. Chevalier, B. J. Morsony, R. Barniol Duran, L. Sironi, B. A. Zauderer, D. Milisavljevic, A. Kamble, and E. Pian, The signature of the central engine in the weakest relativistic explosions: GRB 100316D, Astrophys. J. 778, 18 (2013).
  55. R. Margutti, D. Milisavljevic, A. M. Soderberg, C. Guidorzi, B. J. Morsony, N. Sanders, S. Chakraborti, A. Ray, A. Kamble, M. Drout, J. Parrent, A. Zauderer, and L. Chomiuk, Relativistic supernovae have shorter-lived central engines or more extended progenitors: The case of SN 2012ap, Astrophys. J. 797, 107 (2014).
  56. K. Murase, B. Dasgupta, and T. A. Thompson, Quasithermal neutrinos from rotating protoneutron stars born during core collapse of massive stars, Phys. Rev. D 89, 043012 (2014).
  57. J. A. Carpio, N. Ekanger, M. Bhattacharya, K. Murase, and S. Horiuchi, Quasithermal GeV neutrinos from neutron-loaded magnetized outflows in core-collapse supernovae: Spectra and light curves, Phys. Rev. D 110, 083012 (2024).
  58. K. Murase and J. F. Beacom, Neutrino background flux from sources of ultrahigh-energy cosmic-ray nuclei, Phys. Rev. D 81, 123001 (2010).
  59. K. Murase and J. F. Beacom, Very-high-energy gamma-ray signal from nuclear photodisintegration as a probe of extragalactic sources of ultrahigh-energy nuclei, Phys. Rev. D 82, 043008 (2010).
  60. B. T. Zhang and K. Murase, Nuclear and electromagnetic cascades induced by ultra-high-energy cosmic rays in radio galaxies: Implications for centaurus A, Mon. Not. R. Astron. Soc. 524, 76 (2023).
  61. A. J. Koning and D. Rochman, Modern nuclear data evaluation with the TALYS code system, Nucl. Data Sheets 113, 2841 (2012).
  62. A. J. Koning, D. Rochman, J. C. Sublet, N. Dzysiuk, M. Fleming, and S. van der Marck, TENDL: Complete nuclear data library for innovative nuclear science and technology, Nucl. Data Sheets 155, 1 (2019).
  63. S. Karakula and W. Tkaczyk, The formation of the cosmic ray energy spectrum by a photon field, Astropart. Phys. 1, 229 (1993).
  64. R. B. Firestone, The origin of the giant dipole resonance, arXiv:2009.03356.
  65. M. Goldhaber and E. Teller, On nuclear dipole vibrations, Phys. Rev. 74, 1046 (1948).
  66. S. Agostinelli et al. (GEANT4 Collaboration), GEANT4–a simulation toolkit, Nucl. Instrum. Methods Phys. Res., Sect. A 506, 250 (2003).
  67. J. P. Rachen, Interaction Processes and Statistical Properties of the Propagation of Cosmic Rays in Photon Backgrounds, Ph.D. thesis, Max-Planck-Institute for Radioastronomy, Bonn, 1996.
  68. D. Allard, E. Parizot, E. Khan, S. Goriely, and A. V. Olinto, UHE nuclei propagation and the interpretation of the ankle in the cosmic-ray spectrum, Astron. Astrophys. 443, L29 (2005).
  69. P. Goldreich and W. H. Julian, Pulsar electrodynamics, Astrophys. J. 157, 869 (1969).
  70. N. Bucciantini, J. Arons, and E. Amato, Modelling spectral evolution of pulsar wind nebulae inside supernova remnants, Mon. Not. R. Astron. Soc. 410, 381 (2011).
  71. A. N. Timokhin and A. K. Harding, On the polar cap cascade pair multiplicity of young pulsars, Astrophys. J. 810, 144 (2015).
  72. K. Murase, K. Kashiyama, K. Kiuchi, and I. Bartos, Gamma-ray and hard X-ray emission from pulsar-aided supernovae as a probe of particle acceleration in embryonic pulsar wind nebulae, Astrophys. J. 805, 82 (2015).
  73. K. Kashiyama, K. Murase, I. Bartos, K. Kiuchi, and R. Margutti, Multi-messenger tests for fast-spinning newborn pulsars embedded in stripped-envelope supernovae, Astrophys. J. 818, 94 (2016).
  74. B. D. Metzger, D. Giannios, T. A. Thompson, N. Bucciantini, and E. Quataert, The protomagnetar model for gamma-ray bursts, Mon. Not. R. Astron. Soc. 413, 2031 (2011).
  75. J. A. Pons, S. Reddy, M. Prakash, J. M. Lattimer, and J. A. Miralles, Evolution of proto–neutron stars, Astrophys. J. 513, 780 (1999).
  76. G. Drenkhahn, Acceleration of GRB outflows by Poynting flux dissipation, Astron. Astrophys. 387, 714 (2002).
  77. O. Bromberg, J. Granot, and T. Piran, On the composition of GRBs’ Collapsar jets, Mon. Not. R. Astron. Soc. 450, 1077 (2015).
  78. K. Murase, M. Mukhopadhyay, A. Kheirandish, S. S. Kimura, and K. Fang, Neutrinos from the brightest gamma-ray burst?, Astrophys. J. Lett. 941, L10 (2022).
  79. D. Giannios and H. C. Spruit, Spectral and timing properties of a dissipative GRB photosphere, Astron. Astrophys. 469, 1 (2007).
  80. M. V. Kossov, Approximation of photonuclear interaction cross-sections, Eur. Phys. J. A 14, 377 (2002).
  81. N. Globus, D. Allard, R. Mochkovitch, and E. Parizot, UHECR acceleration at GRB internal shocks, Mon. Not. R. Astron. Soc. 451, 751 (2015).
  82. D. Boncioli, A. Fedynitch, and W. Winter, Nuclear physics meets the sources of the ultra-high energy cosmic rays, Sci. Rep. 7, 4882 (2017).
  83. L. Morejon, A. Fedynitch, D. Boncioli, D. Biehl, and W. Winter, Improved photomeson model for interactions of cosmic ray nuclei, J. Cosmol. Astropart. Phys. 11 (2019) 007.
  84. H.-J. Lü and B. Zhang, A test of the millisecond magnetar central engine model of gamma-ray bursts with swift data, Astrophys. J. 785, 74 (2014).
  85. J. C. David, Spallation reactions: A successful interplay between modeling and applications, Eur. Phys. J. A 51, 68 (2015).

Outline

Information

Phys. Rev. D 114, 063031– Published 14 September, 2026
  • Received 10 March 2026
  • Accepted 5 August 2026
Article part of CHORUS
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation