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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 provide more general results. When the recent PierreAuger Observatory angular power spectrum above 8 EeV is used the restrictedmodel gives, under the assumption of the small angle approximation, a solutionwhere the RMS deflection with respect to the line of sight is $\alpha_{\rm rms}= \left(50^{+11}_{-10}\right)^\circ$, while the relative flux from the singlesource $\eta=0.03\pm 0.01$. Furthermore, the solution can be translated intoconstraints on the source distance, luminosity, and extra-galactic magneticfield strength. For Centaurus A and the Virgo cluster the required relationbetween the coherence length and the RMS magnetic field strength is obtained: acoherence length of $~\sim 100\,\mathrm{kpc}$ would imply the RMS fieldstrength around $1\,\mathrm{nG}$ for iron dominated and above $10\,\mathrm{nG}$for proton dominated composition. We also performed trajectory simulations withour publicly available code CRPropa to show that our analytical model can serveas a good approximation as long as the deflections in cosmic magnetic fieldscan be described as a random walk. The simulations showed that generallystructured fields tend to suppress large-scale anisotropies, especially thedipole, compared to anisotropies at smaller scales described by highermultipoles.

Anisotropies of Ultra-high Energy Cosmic Rays Dominated by a Single Source in the Presence of Deflections