Implications of ultra-high-energy cosmic rays for transient sources

The origin of ultra-high-energy cosmic rays (UHECRs) is one of the biggest mysteries in astroparticle physics. We study the possibility that UHECRs come from transient sources, propagating in the Galactic and intergalactic space. Based on the recent observational results, we estimate upper and lower bounds on the rate of transient UHECR sources and required isotropic cosmic-ray energy input per burst as 0:1 Gpc¡3 yr¡1 < Â0 < 103:5 Gpc¡3 yr¡1 and 1049:5 ergs < Eiso HECR < 1054 ergs, through constraining the apparent burst duration, i.e., dispersion in arrival times of UHECRs. Then, we discuss implications of proposed transient candidates such as gamma-ray bursts and active galactic nuclei. Especially, we demonstrate expected spectra of cumulative high-energy neutrinos and ultra-high-energy gamma rays from individual nearby transient sources.