On energy spectra of UHE cosmic rays accelerated in supergalactic accretion flows

Some ultra-high energy (UHE) cosmic ray (CR) events may be correlated with the Local Supercluster plane. We consider acceleration of such particles at the large-scale accretion flows of matter towards such plane and/or accretion flows onto galaxy clusters. The formed shocks and the general compression flow are expected to allow for CR diffusive acceleration of UHE particles. For a simplified flow geometry we consider a stationary acceleration of such CRs and we discuss influence of model parameters on a particle spectral index. We show that the general convergent flow pattern leads naturally to very flat proton spectra with the phase-space spectral indices $\sigma \approx 3.0$, as compared to the `canonical' shock value of 4.0.