Flux calculations in an inhomogeneous Universe: weighting a flux-limited galaxy sample

Many astrophysical problems arising within the context of ultra-high energy cosmic rays, very-high energy gamma rays or neutrinos, require calculation of the flux produced by sources tracing the distribution of galaxies in the Universe. We discuss a simple weighting scheme, an application of the method introduced by Lynden-Bell in 1971, that allows the calculation of the flux sky map directly from a flux-limited galaxy catalog without cutting a volume-limited subsample. Using this scheme, the galaxy distribution can be modeled up to large scales while representing the distribution in the nearby Universe with maximum accuracy. We consider fluctuations in the flux map arising from the finiteness of the galaxy sample. We show how these fluctuations are reduced by the weighting scheme and discuss how the remaining fluctuations limit the applicability of the method.