Figure 1: Geometry of the diffusive volume. | |
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Figure 2: Geometry of the diffusive volume in the limit . | |
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Figure 3: Geometry of the diffusive volume in the limit . | |
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Figure 4: Cosmic ray probability density as a function of (distance of the source in the disk), for several values of L and for a disk of radius R=20 kpc. Big stars are for unbounded model, dotted line is for a spherical boundary at radius R, small stars are for top and bottom boundaries, and solid lines are for cylindrical boundaries. | |
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Figure 5: Deviation from the pure density profile, , due to the various effects studied here: escape from the boundaries, spallations and Galactic wind. In this latter case, the choice has been made to show the similar behavior at large . The case of a radioactive species has also been shown. It should be noticed, however, that in most interesting cases, the scale length is much smaller than the others, so that in this case the propagation is dominated by radioactive decay and spallations and Galactic wind can be safely discarded. | |
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Figure 6: Integrated probability that a particle detected at the origin was emitted inside the ring of radius , in the three situations considered. The solid dark line is obtained when only the leakage through the boundaries is considered, in which case the radii scale as with . The dotted, respectively dashed, line is obtained when only the spallations, respectively only the convective wind, are considered. The solid grey line indicates the probability that the primary progenitor of a secondary detected in the solar neighborhood was emitted from within a given distance. | |
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Figure 7: Grammage crossed as a function of the origin, for some of the models discussed in the text and for a typical value of K=0.03 kpc2 Myr-1. | |
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Figure 8: 99%-surfaces for R =20 kpc and three cases, L =2 kpc, L = 5 kpc and L=10 kpc. | |
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Figure 9: Left panel: as a function of the diffusion spectral index for different rigidities ; from top to bottom, GV, GV and GV. The parameter , as well as , is not very sensitive to the halo size L. Right panel: as a function of for GV (upper curves) and GV (lower curves) for four species: p ( mb), ( mb), B-CNO ( mb) and Fe ( mb). For the latter species we plotted the same three L values as in left panel. The behavior for other species is similar so that we only plotted the case L=6 kpc. | |
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Figure 10: (50-90-99)%-surfaces (protons and Fe nuclei are considered), in a typical diffusion model with L=6 kpc and . | |
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Figure 11: 99%-surfaces for several species. The left panel corresponds to primary species (protons, CNO and Fe) while the right panel corresponds to the progenitors of secondary species (B and sub-Fe), for L=6 kpc and . | |
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Figure 12: 99%-surfaces for several , in the case L=6 kpc. The left panel corresponds to protons while the right panel corresponds to Fe nuclei. | |
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Figure 13: 99%-surfaces for several L, in the case . The left panel corresponds to protons while the right panel corresponds Fe nuclei. | |
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Figure 14: Fraction (in %) of the Galactic sources contributing to the fraction f of the cosmic ray flux at the solar position, for protons and Fe nuclei, for the particular diffusion model L=6 kpc, . | |
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Figure 15: Realistic values of and for two extreme halo sizes L and diffusion slope . As all results in this section, propagation parameters fit B/C and are taken from MTD02. | |
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Figure 16: Radial distribution of the proton flux for the models discussed in this study, compared to the source radial distribution of Case & Bhattacharya (1998) given Eq. (19). For each of the values L=2 kpc and L=10 kpc, the three values , 0.6 and 0.85 are presented, the flatter distribution corresponding to the lower . Also shown is the gamma-ray emissivity per gas atom ( COS-B Bloemen 1989), which is proportional to the proton flux, as given by COS-B (open circles, Bloemen 1989) and EGRET (triangles, Strong & Mattox 1996), along with the proton flux obtained with the Strong & Moskalenko (1998) distribution (see Sect. 6). | |
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