Spatial Origin of Galactic Cosmic Rays in Diffusion Models : I - Standard sources in the Galactic disk

The propagation of Galactic Cosmic Ray nuclei having energies between 100 MeV/nuc and several PeV/nuc is strongly believed to be of diffusive nature. The particles emitted by a source located at a given position in the disk do not pervade the whole Galaxy, but are rather confined to a smaller region whose spatial extension is related to the height of the diffusive halo, the Galactic wind and the spallation rate. Following the pioneering work of Jones (1978), we investigate the role of spallations and Galactic wind Vc, introducing two typical lengths rwind = 2K/Vc and rspal = K/hΓinel, where K is the diffusion coefficient, h the height of the Galactic disk and Γinel the spallation rate, related to the spallation cross sections. We find the regions of the disk from which a given fraction of cosmic rays detected in the Solar neighborhood were emitted (f -surfaces). After a general study, we apply the results to a realistic source distribution, with the propagation parameters obtained in our previous works by a systematic analysis of secondaryto-primary observed ratios (Maurin et al. 2002b). These f -surfaces correspond to rather small region of the Galactic disk, i.e. a few kpc, centered on our position, depending on the species as well as on the values of the propagation parameters. Another consequence is that for the models preferred by our previous analysis (i.e. large diffusion slope δ), only a fraction of a percent of the whole Galactic sources actually contribute to the Solar neighborhood Cosmic Ray flux. Moreover, a very small number of sources may be responsible for more than 15 % of the flux detected in the Solar neighborhood. This may point towards the necessity to go beyond the approximations of both homogeneity and stationarity.