Cosmic Rays below Z=30 in a diffusion model: new constraints on propagation parameters

TL;DR

This paper constrains cosmic-ray propagation parameters within a diffusion framework by fitting B/C and related nuclear ratios using semi-analytical, two-dimensional solutions that include convection, reacceleration, energy losses, and spallation. The authors demonstrate strong parameter correlations among the diffusion coefficient index $\delta$, normalization $K_0$, halo height $L$, convection $V_c$, and Alfvén speed $V_a$, and they rule out models without convection or without reacceleration. They find that only a form with $K(E)=K_0\,\beta\,\mathcal{R}^{\delta}$ provides good fits, with $\delta$ in the range $[0.45,0.85]$ and a favored region around $\delta\approx 0.6$–$0.7$; a Kolmogorov spectrum $\delta=1/3$ is excluded. The work bridges diffusion theory with observational data, demonstrating that improved measurements (e.g., Be isotopes, antiprotons) can substantially sharpen constraints on propagation and impact dark-matter-related antiproton studies.

Abstract

Cosmic ray nuclei fluxes are expected to be measured with high precision in the near future. For instance, high quality data on the antiproton component could give important clues about the nature of the astronomical dark matter. A very good understanding of the different aspects of cosmic ray propagation is therefore necessary. In this paper, we use cosmic ray nuclei data to give constraints on the diffusion parameters. Propagation is studied with semi-analytical solutions of a diffusion model, and we give new analytical solutions for radioactively produced species. Our model includes convection and reacceleration as well as the standard energy losses. We perform a $χ^2$ analysis over B/C data for a large number of configurations obtained by varying the relevant parameters of the diffusion model. A very good agreement with B/C data arises for a number of configurations, all of which are compatible with sub-Fe/Fe data. Different source spectra $Q(E)$ and diffusion coefficients $K(E)$ have been tried, but for both parameters only one form gives a good fit. Another important result is that models without convection or without reacceleration are excluded. We find that the various parameters, i.e. the diffusion coefficient normalisation $K_0$ and spectral index $δ$, the halo thickness $L$, the Alfvén velocity $V_a$, and the convection velocity $V_c$ are strongly correlated. We obtain limits on the spectral index $δ$ of thediffusion coefficient, and in particular we exclude a Kolmogorov spectrum ($δ= 1/3$).

Figures (8)

• Figure 1: The $\chi^2$ (adjustment to B/C data, see text) has been computed in all the parameter space for $\delta=0.6$ (defined by $K=K_0{\cal R}^\delta$). A best $\chi^2$ is obtained for each $L$ and $K_0/L$. Left figure displays the $\chi^2$ values in the $K_0/L$ -- $L$ plane. It is truncated for $\chi^2>50$. Right figure shows the iso--$\chi^2$ lines of the previous surface.
• Figure 2: As in Fig. \ref{['fig2']}, a best $\chi^2$ is obtained for each $V_c$ and $V_a/\sqrt{K_0}$. Left and right figures are similar to those in Fig. \ref{['fig2']}.
• Figure 3: This curve displays the computed ratio of ($^{10}$B+$^{11}$B)/($^{12}$C+$^{13}$C+$^{14}$C) for a configuration giving a reduced $\chi^2_r \approx 1.3$. The experimental points are from heao-3 (solid circles), isee (triangles), imp-8 (empty circle), voyager (square) and balloons (crosses).
• Figure 4: This curve displays the computed ratio of (Sc+Ti+V)/Fe for the same configuration as in Fig. \ref{['fig1']}. The experimental points are from heao-3 (solid circles), isee (triangles), voyager (square) and balloons (crosses).
• Figure 5: Theses curves display the computed flux of Oxygen for the same configuration as in figure \ref{['fig1']}. The solid line corresponds to $\delta + \alpha_{Oxygen}=2.68$, the dotted line to $\delta + \alpha_{Oxygen}=2.80$ (see text for details). The experimental points are from heao-3.