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Published November 1, 2025 | Version Published
Journal Article Open

Distinct Solar Energetic Particle Shock Intensity–Diffusion Coefficient Relationships in the Inner Heliosphere

Creators

  • 1. ROR icon Princeton University
  • 2. ROR icon Harvard-Smithsonian Center for Astrophysics
  • 3. Department of Planetary Sciences, Lunar and Planetary Lab, Tucson, AZ 85721, USA
  • 4. ROR icon Johns Hopkins University Applied Physics Laboratory
  • 5. ROR icon Goddard Space Flight Center
  • 6. ROR icon California Institute of Technology
  • 7. ROR icon University of Delaware
  • 8. ROR icon Mahidol University
  • 9. ROR icon University of New Hampshire
  • 10. ROR icon Southwest Research Institute
  • 11. ROR icon The University of Texas at San Antonio
  • 12. ROR icon University of California, Berkeley
  • 13. ROR icon Smithsonian Astrophysical Observatory

Abstract

It has been inferred from theory that the spatial diffusion coefficient (κ) upstream of shocks is anticorrelated with the intensity of solar energetic particles (SEPs) at the shock (jshock) motivated by quasi-linear theory (QLT). This is because a lower κ along the magnetic field (κ∥) implies that particles are trapped for longer, providing more acceleration and resulting in a higher jshock. However, the simplest version of DSA predicts that jshock is determined by the source of the injected population at the shock and plasma density jump with no relation to κ for low-energy SEPs. Here, we identify the relationship between κ and jshock, whose form is unknown, using Parker Solar Probe observations of eight shocks within 1 au. We estimate a characteristic κfit along the shock normal by fitting the upstream SEP intensity profiles with a 1D steady-state transport model for acceleration and escape assuming pitch-angle isotropy in the plasma frame. Also, we estimate κ∥ based on the magnetic power spectral density using QLT for comparison with κfit. Our results show that both quantities are anticorrelated with jshock. Instead of a uniform relationship between κ and jshock, we find distinct relationships appearing as potential power laws manifested across SEP events with no obvious radial dependence from 0.07 to 0.74 au. These relationships may be grouped by similar shock parameters (in terms of speed, strength, and orientation). Our findings raise questions about SEP transport and its radial dependence within 1 au and provide important observational constraints for models of shock-accelerated particles.

Copyright and License

© 2025. The Author(s). Published by the American Astronomical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Acknowledgement

We thank the IS⊙IS team and everyone that made the PSP mission possible. The IS⊙IS data and visualization tools are available to the community at https://spacephysics.princeton.edu/missions-instruments/PSP. PSP was designed and built and is operated by the Johns Hopkins Applied Physics Laboratory as part of NASA’s Living with a Star (LWS) program (contract NNN06AA01C). F.F. was partially supported by NASA award 80NSSC21K1766. D.R. was partially supported by Thailand’s National Science and Technology Development Agency (NSTDA) and the National Research Council of Thailand (NRCT) under the High-Potential Research Team Grant Program (N42A650868). M.A.D. is supported by NASA award 80NSSC25K7687. This work was partially supported by a subcontract at University of Delaware (SUB0000165) under the LWS program (NNN06AA01C).

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Additional details

Related works

Is supplemented by
Dataset: https://spacephysics.princeton.edu/missions-instruments/PSP (URL)

Funding

National Aeronautics and Space Administration
NNN06AA01C
National Aeronautics and Space Administration
80NSSC21K1766
National Science and Technology Development Agency
National Research Council of Thailand
N42A650868
National Aeronautics and Space Administration
80NSSC25K7687
University of Delaware
SUB0000165

Dates

Accepted
2025-10-07
Available
2025-10-27
Published

Caltech Custom Metadata

Caltech groups
Space Radiation Laboratory, Division of Physics, Mathematics and Astronomy (PMA)
Publication Status
Published