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

Abstract: This work presents a scenario of ultra-high energy cosmic ray source distribution where a nearby source is solely responsible for the anisotropies in arrival directions of cosmic rays while the rest of the sources contribute only isotropically. An analytical approach focused on large-scale anisotropies, which are influenced by deflections in a Kolmogorov-type turbulent magnetic field, is employed to provide more general results. When the recent Pierre Auger Observatory angular power spectrum above 8 EeV is used the restricted model gives, under the assumption of the small angle approximation, a solution where 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 single source $\eta=0.03\pm 0.01$. Furthermore, the solution can be translated into constraints on the source distance, luminosity, and extra-galactic magnetic field strength. For Centaurus A and the Virgo cluster the required relation between the coherence length and the RMS magnetic field strength is obtained: a coherence length of $~\sim 100\,\mathrm{kpc}$ would imply the RMS field strength around $1\,\mathrm{nG}$ for iron dominated and above $10\,\mathrm{nG}$ for proton dominated composition. We also performed trajectory simulations with our publicly available code CRPropa to show that our analytical model can serve as a good approximation as long as the deflections in cosmic magnetic fields can be described as a random walk. The simulations showed that generally structured fields tend to suppress large-scale anisotropies, especially the dipole, compared to anisotropies at smaller scales described by higher multipoles.