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 _ { 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 .