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Constraints on the local sources of ultra high-energy cosmic rays

Ultra high-energy cosmic rays (UHECRs) are believed to be protons accelerated in magnetized plasma outflows of extra-Galactic sources. The acceleration of protons to ∼ 1020 eV requires a source power L > 1047 erg s−1. The absence of steady sources of sufficient power within the GZK horizon of 100 Mpc, implies that UHECR sources are transient. We show that UHECR "flares" which produce a power-law spectrum of high energy protons and electrons with a slope d log N/d log E ≈ −2, should be accompanied by strong X-ray and γ-ray emission. X-ray and γ-ray surveys constrain flares which last less than a decade to satisfy at least one of the following conditions: (i) L > 1050 erg s−1; (ii) the power carried by accelerated electrons is lower by a factor > 102 than the power carried by magnetic fields or by > 103 than the power in accelerated protons; or (iii) the sources exist only at low redshifts, z << 1. The implausibility of requirements (ii) and (iii) argue in favor of transient sources with L > 1050 erg s−1.