2012A&A...544A..92B

Measurements of cosmic ray fluxes with the PAMELA and CREAM experiments show unexpected spectral features between 200GeV and 100TeV. They might be caused by nearby and young cosmic ray sources. This can be studied in the myriad model, in which cosmic rays diffuse from point-like instantaneous sources that are located randomly throughout the Galaxy. To test this hypothesis, one must compute the flux generated by several local sources, but also the error bars associated to them. This turns out not to be straightforward, because the standard deviation is infinite when computed for the most general statistical ensemble. The goals of this paper are to provide a method to associate error bars to the flux measurements that have a clear statistical meaning, and to explore the relation between the myriad model and the more common source model based on a continuous distribution. To this end, we show that the quantiles of the flux distribution are well-defined, even though the standard deviation is infinite. They can be used to compute 68% confidence levels, for instance. We also used the known positions and ages of the local sources to reduce the statistical ensemble from which random sources are drawn in the myriad model. We present a method to evaluate meaningful error bars for the flux obtained in the myriad model. In this context, we also discuss the status of the spectral features observed in the proton flux by CREAM and PAMELA.