This work presents a scenario of ultra-high energy cosmic ray sourcedistribution where a nearby source is solely responsible for the anisotropiesin arrival directions of cosmic rays while the rest of the sources contributeonly isotropically. An analytical approach focused on large-scale anisotropies,which are influenced by deflections in a Kolmogorov-type turbulent magneticfield, is employed to give more general results. When the recent Pierre AugerObservatory angular power spectrum above 8 EeV is used the model gives twosolutions: weaker RMS deflections $delta_mathrm{rms}^+ = (95pm 36)^circ$with the lower relative flux from the single source $eta^+=0.38pm 0.18$, orstronger RMS deflections $delta_mathrm{rms}^- = (113pm 24)^circ$ with thehigher relative flux $eta^-=0.49pm 0.23$. It is shown that the first solutionpredicts a lower dipole amplitude at higher energies compared to the secondsolution. Furthermore, these solutions can be translated into constraints onthe source distance, luminosity, and extragalactic magnetic field strength. ForCentaurus A and Virgo cluster the required relation between the coherencelength and the RMS magnetic field strength is obtained: a coherence length of$~sim 10,mathrm{kpc}$ would imply RMS field strengths above $1,mathrm{nG}$for iron dominated and above $10,mathrm{nG}$ for proton dominatedcomposition. A comparison of the model with advanced Monte Carlo techniques isperformed to show its applicability in a realistic, structured magnetic fieldand to analyze structured field effects on the anisotropies. The result of thecomparison shows a tendency of structured fields to suppress large scaleanisotropies, especially the dipole, compared to those anisotropies of smallerscales.
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