Relativistic electron acceleration at the bow shock of Jupiter and beyond

Collisionless shocks are ubiquitous in space plasmas throughout the Universe and are widely believed to be primary sites of cosmic ray acceleration^1,2. 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 transient^4,5. 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 shocks^9,10.