Implications of ultra-high-energy cosmic rays for transient sources in the auger era

We study ultra-high-energy cosmic rays (UHECRs) from transient sources, propagating in the Galactic and intergalactic space. Based on recent observational results, we also estimate upper and lower bounds on the rate of transient UHECR sources and the required isotropic cosmic-ray energy input per burst as 0.1 Gpc^-3 yr^-1 ≤ ρ₀ ≤ 10^3.5 Gpc^-3 yr^-1 and 10 erg ≤ ε^iso_hecr ≤ 10⁵⁴ erg by constraining the apparent burst duration, i.e., dispersion in arrival times of UHECRs. Based on these bounds, we discuss implications for proposed candidates such as gamma-ray bursts and active galactic nuclei.