Grammage of cosmic rays around Galactic supernova remnants

The residence time of cosmic rays (CRs) in the Galaxy is usually inferred from the measurement of the ratio of secondary-to-primary nuclei, for instance the boron (B)/carbon (C) ratio, which provides an estimate of the amount of matter traversed by CRs during their propagation, the so-called CR grammage. However, after being released by their parent sources, for instance, supernova remnants, CRs must cross the disc of the Galaxy, before entering the much lower density halo, in which they are believed to spend most of their time before eventually escaping the Galaxy. In the near-source region, the CR propagation is shown to be dominated by the nonlinear self-generation of waves. Here we show that due to this effect, the time that CRs with energies up to similar to 10 TeV spend within a distance L-c similar to 100 pc from the sources is much larger than naive estimates would suggest. Depending on the level of ionization of the medium surrounding the source, the grammage accumulated in the source vicinity may be a non-negligible fraction of the total grammage traversed throughout the whole Galaxy. Moreover, there is an irreducible grammage that CRs traverse while trapped downstream of the shock that accelerated them, though this contribution is rather uncertain. We conclude that some caution should be used in inferring parameters of Galactic CR propagation from measurements of the B/C ratio.