Relativistic electron acceleration at the bow shock of Jupiter and beyond

Article Relativistic electron acceleration at the bow shock of Jupiter and beyond https://doi.org/10.1038/s41586-026-10473-z Received: 28 October 2025 Savvas Raptis1 ✉, Drew L. Turner1, Damiano Caprioli2, Jamey R. Szalay3, George Clark1 & Colby C. Haggerty4 Accepted: 31 March 2026 Published online: 3 June 2026 Open access Check for updates Collisionless shocks are ubiquitous in space plasmas throughout the Universe and are widely believed to be primary sites of cosmic ray acceleration1,2. The prevailing mechanism, diffusive shock acceleration, requires particles to repeatedly cross the shock front, gaining energy with each crossing. The maximum achievable energy is fundamentally constrained by the Hillas criterion, which relates the physical scale of the accelerator to the maximum particle energy3. However, the scarcity of direct observational constraints for acceleration sites limits our ability to predict maximum particle energies across most astrophysical systems. Here, using data from the Juno spacecraft of NASA, we show the direct evidence of relativistic electron acceleration (≥1 MeV) upstream of the bow shock of Jupiter, powered by a large-scale foreshock transient4,5. Leveraging these and complementary Solar System observations, we propose a universal scaling law for the Hillas limit that empirically connects the observable size of a transient to maximum particle energy. Applying this scaling to various environments, from planetary bow shocks6 to protostellar jets7 and supernova remnants8, yields a simple model of maximum obtainable particle energies ranging from MeV scales up to about tens of GeV, and about tens of TeV, respectively, providing an observationally grounded method for constraining maximum cosmic ray energies at astrophysical shocks9,10. Collisionless shocks are ubiquitous structures in the Universe, widely believed to be the primary sites at which particles are accelerated to relativistic energies, contributing to the cosmic ray population1–3,11. The dominant mechanism, diffusive shock acceleration (DSA), describes how particles gain energy by repeatedly crossing a shock front. However, a long-standing challenge, known as the ‘injection problem’, is that DSA is only efficient for particles that are energetic enough to outrun the shock, a process that depends on the shock inclination and strength, which is not fully understood in all regimes12–14. A promising solution lies in the dynamic environment of the foreshock (‘precursor’ in the astrophysics community)15,16, which forms upstream of shocks under an oblique or quasi-parallel geometry, where the angle between the shock normal and the ambient magnetic field, θBn ≲ 45°. Within this region, large-scale structures known as foreshock transients can efficiently accelerate low-energy suprathermal particles to relativistic speeds. Recent observations at the bow shock of Earth have demonstrated that these transients can accelerate electrons to about 1 MeV through a powerful synergy of reinforced shock acceleration, pitch angle scattering and geometric trapping4,5,17–19. The resulting particle spectra have been shown to be well described by a E−1.5 power law attributed to non-relativistic particles undergoing DSA at strong shocks, underscoring the effectiveness of this mechanism and positioning quasi-parallel shocks as exceptional particle accelerators2,8,13,20,21. Crucially, these transients (named within the heliophysics community as hot flow anomalies (HFAs), foreshock bubbles and spontaneous HFAs 1 (SHFAs), among others) are fundamental properties of collisionless shocks, forming in diverse plasma environments while scaling with the properties of the host system and its precursor and foreshock22,23. The universality of these transient processes is confirmed by observations throughout our Solar System, with foreshock transients identified at Mercury24, Venus25, Mars25–27, Earth4,5,17–19, Jupiter28 and Saturn29. Studies have shown that the physical scale of these transients correlates directly with the size of the primary planetary bow shock28. Applying a principle equivalent to the Hillas limit3, which connects the size of an accelerator to the maximum particle energy, this scaling suggests a potential link between the global size of a shock system and the maximum particle energy it can produce5, a hypothesis further supported by kinetic simulations that have consistently reproduced these structures across various parameters22,30,31. In this work, we present direct evidence of relativistic (>1 MeV) electrons upstream of the bow shock of Jupiter, conclusively linking their acceleration to a foreshock transient. We demonstrate that the observed energies are consistent with predictions from a scaling law that connects the system size (S) to the acceleration region (L) in foreshock transients and subsequently to an upper energy limit (Emax). By validating this scaling with multi-planetary data, we extend our analysis to astrophysical objects, including protostellar jets and supernova remnants. This framework bridges the observational gap between heliophysics and astrophysics through the planetary examples within the Solar System, offering an empirically grounded model for estimating The Johns Hopkins University Applied Physics Laboratory, Laurel, MD, USA. 2Department of Astronomy and Astrophysics and E. Fermi Institute, The University of Chicago, Chicago, IL, USA. Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA. 4Institute for Astronomy, University of Hawai‘i, Honolulu, HI, USA. ✉e-mail: 3 Nature | Vol 654 | 4 June 2026 | 47 Article Foreshock transient a Solar wind Bow shock E/q (keV Q–1) 106 100 105 10 –1 Ion differential energy intensity (cm–2 sr–1 s–1) 107 101 104 b nH (cm–3) 4 2 0 c 103 Electron differential number intensity (cm–2 sr–1 s–1 keV–1) E (keV) 103 102 102 101 d 108 E (keV) 107 100 106 105 104 10–1 Electron differential number intensity (cm–2 sr–1 s–1 keV–1) 109 101 103 B (nT) e 10 |B| 5 Bx By Bz 0 –5 10:00 12:00 14:00 16:00 18:00 20:00 1 October 2023 Fig. 1 | In situ observations of the foreshock transient and bow shock crossing at Jupiter. Overview of Juno plasma and magnetic field observations on 1 October 2023 between 08:00 and 20:00 UTC. a, Ion energy spectrogram from the JADE instrument. b, Proton number density (nH) derived from JADE (cm−3). c, High-energy electron spectrogram from the JEDI instrument. d, Low-energy electron spectrogram from JADE. e, Magnetic field components and magnitude from the MAG instrument. The interval containing foreshock transients (approximately 11:00–13:00 UTC) is delimited by vertical black dashed lines. The most energetic transient event is highlighted by the purpleshaded region (approximately 12:30–12:50 UTC); this interval corresponds to a strong signal intensity exceeding ambient levels across all energy channels in the high-energy electron spectrum (c). For compar (...truncated)