Implications of Ultra-High-Energy Cosmic Rays for Transient Sources in   the Auger Era
  We study about ultra-high-energy cosmic rays (UHECRs) from transient sources, propagating in the Galactic and intergalactic space. Based on the recent observational results, we also 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 < rho_0 < 10^3.5 Gpc^-3 yr^-1 and 10^49.5 ergs < E_HECR^iso < 10^54 ergs, through 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. 
Kohta Murase, Hajime Takami