All Figures

$\begin{figure} \par\includegraphics[width=4.5cm,clip]{3376f1.eps} \end{figure}$ Figure 1: Geometry of the diffusive volume.
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In the text

$\begin{figure} \par\includegraphics[width=3.6cm,clip]{3376f2.eps} \end{figure}$ Figure 2: Geometry of the diffusive volume in the limit $L\rightarrow \infty$ .
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In the text

$\begin{figure} \par\includegraphics[width=4.4cm,clip]{3376f3.eps} \end{figure}$ Figure 3: Geometry of the diffusive volume in the limit $R\rightarrow \infty$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{3376f4.eps} \end{figure}$ Figure 4: Cosmic ray probability density as a function of $r_{\rm s}$ (distance of the $\delta(\vec{r_{\rm s}})$ 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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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{3376f5.eps} \end{figure}$ Figure 5: Deviation from the pure $1/r_{\rm s}$ density profile, $N(r_{\rm s})/(1/4\pi K r_{\rm s})$ , due to the various effects studied here: escape from the $z=\pm L$ boundaries, spallations and Galactic wind. In this latter case, the choice $r_{\rm scale}=2r_{\rm w}$ has been made to show the similar behavior at large $r_{\rm s}$ . The case of a radioactive species has also been shown. It should be noticed, however, that in most interesting cases, the scale length $l_{\rm rad}$ 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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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{f6.eps} \end{figure}$ Figure 6: Integrated probability that a particle detected at the origin was emitted inside the ring of radius $r_{\rm s}$ , in the three situations considered. The solid dark line is obtained when only the leakage through the $z=\pm L$ boundaries is considered, in which case the radii scale as $r/r_{\rm scale}$ with $r_{\rm scale} = L$ . 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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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{f7.eps} \end{figure}$ 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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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{f8.eps}\end{figure}$ 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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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{f9.eps} \end{figure}$ Figure 9: Left panel: $\chi _{\rm w}(\delta ,{\cal R})$ as a function of the diffusion spectral index ${\delta }$ for different rigidities ${\cal R}$ ; from top to bottom, ${\cal R}=100$ GV, ${\cal R}=10$ GV and ${\cal R}=1$ GV. The parameter $\chi _{\rm w}$ , as well as $\chi _{\rm sp}$ , is not very sensitive to the halo size L. Right panel: $\chi _{\rm sp}(\delta ,{\cal R})$ as a function of ${\delta }$ for ${\cal R}=100$ GV (upper curves) and ${\cal R}=1$ GV (lower curves) for four species: p ( $\sigma \sim 40$ mb), $\bar{d}$ ( $\sigma \sim 100$ mb), B-CNO ( $\sigma \sim 250$ mb) and Fe ( $\sigma \sim 700$ 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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In the text

$\begin{figure} \par\includegraphics[width=4.3cm,clip]{f10a.eps}\includegraphics[width=4.3cm,clip]{f10b.eps} \end{figure}$ Figure 10: (50-90-99)%-surfaces (protons and Fe nuclei are considered), in a typical diffusion model with L=6 kpc and $\delta =0.6$ .
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In the text

$\begin{figure} \par\includegraphics[width=4.3cm,clip]{f11a.eps}\includegraphics[width=4.3cm,clip]{f11b.eps}\end{figure}$ 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 $\delta =0.6$ .
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In the text

$\begin{figure} \par\includegraphics[width=4.3cm,clip]{f12a.eps}\includegraphics[width=4.3cm,clip]{f12b.eps}\end{figure}$ Figure 12: 99%-surfaces for several ${\delta }$ , in the case L=6 kpc. The left panel corresponds to protons while the right panel corresponds to Fe nuclei.
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In the text

$\begin{figure} \par\includegraphics[width=4.3cm,clip]{f13a.eps}\includegraphics[width=4.3cm,clip]{f13b.eps}\end{figure}$ Figure 13: 99%-surfaces for several L, in the case $\delta =0.6$ . The left panel corresponds to protons while the right panel corresponds Fe nuclei.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{f14.eps} \end{figure}$ Figure 14: Fraction $f_{\rm s}$ (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, $\delta =0.6$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{f15.eps} \end{figure}$ Figure 15: Realistic values of $l_{\rm rad}/\sqrt{\tau_0/{\rm 1~Myr}}$ and $r_{\rm loss}$ for two extreme halo sizes L and diffusion slope ${\delta }$ . As all results in this section, propagation parameters fit B/C and are taken from MTD02.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{f16.eps} \end{figure}$ 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 $\delta =0.35$ , 0.6 and 0.85 are presented, the flatter distribution corresponding to the lower ${\delta }$ . 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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In the text

$\begin{figure} \par\includegraphics[width=4.5cm,clip]{3376f1.eps} \end{figure}$	Figure 1: Geometry of the diffusive volume.
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$\begin{figure} \par\includegraphics[width=3.6cm,clip]{3376f2.eps} \end{figure}$	Figure 2: Geometry of the diffusive volume in the limit $L\rightarrow \infty$ .
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$\begin{figure} \par\includegraphics[width=4.4cm,clip]{3376f3.eps} \end{figure}$	Figure 3: Geometry of the diffusive volume in the limit $R\rightarrow \infty$ .
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{3376f4.eps} \end{figure}$	Figure 4: Cosmic ray probability density as a function of $r_{\rm s}$ (distance of the $\delta(\vec{r_{\rm s}})$ 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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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{f7.eps} \end{figure}$	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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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{f8.eps}\end{figure}$	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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$\begin{figure} \par\includegraphics[width=4.3cm,clip]{f10a.eps}\includegraphics[width=4.3cm,clip]{f10b.eps} \end{figure}$	Figure 10: (50-90-99)%-surfaces (protons and Fe nuclei are considered), in a typical diffusion model with L=6 kpc and $\delta =0.6$ .
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$\begin{figure} \par\includegraphics[width=4.3cm,clip]{f11a.eps}\includegraphics[width=4.3cm,clip]{f11b.eps}\end{figure}$	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 $\delta =0.6$ .
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$\begin{figure} \par\includegraphics[width=4.3cm,clip]{f12a.eps}\includegraphics[width=4.3cm,clip]{f12b.eps}\end{figure}$	Figure 12: 99%-surfaces for several ${\delta }$ , in the case L=6 kpc. The left panel corresponds to protons while the right panel corresponds to Fe nuclei.
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$\begin{figure} \par\includegraphics[width=4.3cm,clip]{f13a.eps}\includegraphics[width=4.3cm,clip]{f13b.eps}\end{figure}$	Figure 13: 99%-surfaces for several L, in the case $\delta =0.6$ . The left panel corresponds to protons while the right panel corresponds Fe nuclei.
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{f14.eps} \end{figure}$	Figure 14: Fraction $f_{\rm s}$ (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, $\delta =0.6$ .
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{f15.eps} \end{figure}$	Figure 15: Realistic values of $l_{\rm rad}/\sqrt{\tau_0/{\rm 1~Myr}}$ and $r_{\rm loss}$ for two extreme halo sizes L and diffusion slope ${\delta }$ . As all results in this section, propagation parameters fit B/C and are taken from MTD02.
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