Diffusive propagation of cosmic rays from supernova remnants in the Galaxy. I: spectrum and chemical composition

TL;DR

This study models how the random distribution of supernova remnants influences the cosmic ray spectrum and composition at Earth, highlighting the effects of diffusion, spallation, and Galactic structure on observed cosmic ray properties.

Contribution

It introduces a stochastic model of cosmic ray propagation considering supernova remnant distribution and diffusion, explaining spectral features and composition variations observed at Earth.

Findings

Stochastic effects cause deviations from simple spectral models.

Spallation accounts for spectral differences among nuclei.

Model matches observed proton and helium spectra above 1 TeV.

Abstract

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)\sim 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 $N(E)\propto E^{-\alpha}$ 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 slight differences in spectral slopes between different nuclei, providing a possible explanation for the recent CREAM observations. For $\delta=1/3$ we find that the slope of the proton and helium spectra are $\sim 2.67$ and $\sim 2.6$ respectively at energies above 1 TeV (to be compared with the measured values of $2.66\pm 0.02$ and $2.58\pm 0.02$). For $\delta=0.6$ the hardening of the He spectra is not observed. 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.