Cosmic rays from transrelativistic supernovae

We derive constraints that must be satisfied by the sources of ∼10 ¹⁵ to ∼10¹⁸eV cosmic rays, under the assumption that the sources are Galactic. We show that while these constraints are not satisfied by ordinary supernovae (SNe), which are believed to be the sources of ≲10¹⁵ eV cosmic rays, they may be satisfied by the recently discovered class of transrelativistic supernovae (TRSNe), which were observed in association with gamma-ray bursts. We define TRSNe as SNe that deposit a large fraction, f_R > 10^-2, of their kinetic energy in mildly relativistic, γβ > 1, ejecta. The high-velocity ejecta enable particle acceleration to ∼10¹⁸ eV, and the large value of f _R (compared to f_R ∼ 10^-7 for ordinary SNe) ensures that if TRSNe produce the observed ∼10₁₈ eV cosmic-ray flux, they do not overproduce the flux at lower energies. This, combined with the estimated rate and energy production of TRSNe, imply that Galactic TRSNe may be the sources of cosmic rays with energies up to ∼10¹⁸ eV.