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Anisotropy in the arrival direction distribution of ultrahigh-energy cosmicrays (UHECRs) produced by powerful sources is numerically evaluated. We showthat, taking account of the Galactic magnetic field, nondetection ofsignificant anisotropy at $\approx 10^{19}$ eV at present and in futureexperiments imposes general upper limits on UHECR proton luminosity of steadysources as a function of source redshifts. The upper limits constrain theexistence of typical steady sources in the local universe and limit the localdensity of $10^{19}$ eV UHECR sources to be $\gtrsim 10^{-3}$ Mpc$^{-3},$assuming average intergalactic magnetic fields less than $10^{-9}$ G. Thisisotropy, which is stronger than measured at the highest energies, may indicatethe transient generation of UHECRs. Our anisotropy calculations are applied forextreme high-frequency-peaked BL Lac objects 1ES 0229+200, 1ES 1101-232, and1ES 0347-121, to test the UHECR-induced cascade model, in which beamed UHECRprotons generate TeV radiation in transit from sources. While themagnetic-field structure surrounding the sources affects the required absolutecosmic-ray luminosity of the blazars, the magnetic-field structure surroundingthe Milky Way directly affects the observed anisotropy. If both of the magneticfields are weak enough, significant UHECR anisotropy from these blazars shouldbe detectable by the Pierre Auger Observatory unless the maximum energy ofUHECR protons is well below $10^{19}$ eV. Furthermore, if these are the sourcesof UHECRs above $10^{19}$ eV, a local magnetic structure surrounding the MilkyWay is needed to explain the observed isotropy at $\sim 10^{19}$ eV, which maybe incompatible with large magnetic structures around all galaxies for theUHECR-induced cascade model to work with reasonable jet powers.

Isotropy constraints on powerful sources of ultrahigh-energy cosmic rays at $10^{19}$ eV