In this paper we investigate the effect of stochasticity in the spatial and temporal distribution of supernova remnants on the spectrum and chemical composition of cosmic rays observed at Earth. The calculations are carried out for different choices of the diffusion coefficient D(E) experienced by cosmic rays during propagation in the Galaxy. In particular, at high energies we assume that D(E) alpha E-delta, with delta = 1/3 and delta = 0.6 being the reference scenarios. The large scale distribution of supernova remnants in the Galaxy is modeled following the distribution of pulsars, with and without accounting for the spiral structure of the Galaxy. We find that the stochastic fluctuations induced by the spatial and temporal distribution of supernovae, together with the effect of spallation of nuclei, lead to mild but sensible violations of the simple, leaky-box-inspired rule that the spectrum observed at Earth is N(E) alpha E-alpha with alpha = gamma + delta, where gamma is the slope of the cosmic ray injection spectrum at the sources. Spallation of nuclei, even with the small rates appropriate for He, may account for small differences in spectral slopes between different nuclei, possibly providing an explanation for the recent CREAM observations. For delta = 1/3 we find that the slope of the proton and helium spectra are similar to 2.67 and similar to 2.6 respectively (with fluctuations depending on the realization of source distribution) at energies around similar to 1TeV (to be compared with the measured values of 2.66 +/- 0.02 and 2.58 +/- 0.02). For delta = 0.6 the hardening of the He spectra is not observed. The stochastic effects discussed above cannot be found in ordinary propagation calculations, such as GALPROP, where these effects and the point like nature of the sources are not taken into account. We also comment on the effect of time dependence of the escape of cosmic rays from supernova remnants, and of a possible clustering of the sources in superbubbles. In a second paper we will discuss the implications of these different scenarios for the anisotropy of cosmic rays.
|Titolo:||Diffusive propagation of cosmic rays from supernova remnants in the Galaxy. I: spectrum and chemical composition|
|Data di pubblicazione:||2012|
|Appare nelle tipologie:||1.1 Articolo in rivista|