Isotropy constraints on powerful sources of ultrahigh-energy cosmic rays at 10¹⁹ eV

Anisotropy in the arrival direction distribution of ultrahigh-energy cosmic rays (UHECRs) produced by powerful sources is numerically evaluated. We show that nondetection of significant anisotropy at $\approx {10}^{19}$ eV at present and in future experiments imposes general upper limits on UHECR proton luminosity of steady sources as a function of source redshifts. The upper limits constrain the existence of typical steady ${10}^{19}$ eV UHECR sources in the local universe and limit their local density to $\gtrsim {10}^{-3}$ Mpc ${}^{-3},$ assuming average intergalactic magnetic fields less than ${10}^{-9}$ G. This isotropy, being stronger than that measured at the highest energies, may indicate the transient generation of UHECRs. Our calculations are applied for extreme high-frequency-peaked BL Lacertae objects 1ES 0229+200, 1ES 1101–232, and 1ES 0347–121, to test the UHECR-induced cascade model, in which beamed UHECR protons generate TeV radiation in transit from sources. While the magnetic-field structure surrounding the sources affects the required absolute cosmic-ray luminosity of the blazars, the magnetic-field structure surrounding the Milky Way directly affects the observed anisotropy. If these magnetic fields are weak enough, significant UHECR anisotropy from these blazars is detectable by the Pierre Auger Observatory unless the maximum energy of UHECR protons is below 10¹⁹ eV. Furthermore, if these are the sources of UHECRs above 10¹⁹ eV, a local magnetic structure surrounding the Milky Way is needed to explain the observed isotropy at $\sim {10}^{19}$ eV, which may be incompatible with large magnetic structures around all galaxies for the UHECR-induced cascade model to work with reasonable jet powers.