Interpretation of AMS-02 beryllium isotope fluxes using data-driven production cross sections

The beryllium isotopic fluxes are measured up to $12\mathrm{GeV}/n$ energies by the AMS-02 Collaboration with unprecedented precision. As secondary cosmic rays (CRs), the Be isotopes include both stable and unstable species, which are crucial for constraining the propagation parameters of the Galactic CRs. However, when constraining the Galactic propagation parameters it shows inconsistency by using ${}^{10}\mathrm{Be}/{}^9\mathrm{Be}$ and by using Be/B data. We attribute this mainly to the uncertainties of the ${}^9\mathrm{Be}$ production cross section, while the ${}^7\mathrm{Be}$ and ${}^{10}\mathrm{Be}$ have much better cross section measurements. Therefore, we employ ${}^{10}\mathrm{Be}$ and ${}^7\mathrm{Be}$, instead of ${}^9\mathrm{Be}$, to constrain the propagation parameters. We parametrize the cross sections that utilize all the available experimental data. The propagation parameters are well-constrained, with the diffusion halo thickness at $5.67\pm 0.76\mathrm{kpc}$, representing a moderate value compared to previous analogous works. Combining the well-constrained CR propagation model and the recent measurements of ${}^9\mathrm{Be}$ flux, we conversely constrain the major production cross section of ${}^9\mathrm{Be}$ and find that it ought to be remarkably lower than previously thought. With the revised ${}^9\mathrm{Be}$ production cross section the predicted $\mathrm{Be}/\mathrm{B}$ ratio by the propagation model is now consistent with the measurement of AMS-02. It should be noted that with the unprecedented precision of the CR data measured by AMS-02 the CR data are potentially used to check the nucleon production cross sections, as shown in the present work.

Figure 1

Channels: $\mathrm{C}+\mathrm{p}⟶{}^{10}\mathrm{B}$. The blue line is the cross section ${\sigma }_0$ obtained by the data-driven parametrization. The blue band is the $1\sigma$ confidence interval allowed by the cross section measurements, the definition of which is referred to Eq. (4).

Figure 2

Comparison between cross section uncertainties (${\omega }_1$ in Table 2) and best-fit renormalization factors ($\mu$ in Table 3).

Figure 3

Top panel: The B spectrum calculated with the best-fit parameters (green solid line) compared with the AMS-02 experimental data [53]. The red solid line represents the result without using the [Ba05] data and renormalizing the cross section. Bottom panel: The ${}^7\mathrm{Be}$ spectrum calculated with the best-fit parameters compared with the AMS-02 experimental data [25].

Figure 4

Top panel: Cross section measurements of the channel $\mathrm{O}+\mathrm{p}⟶{}^{10}\mathrm{Be}$, compared with three possible parametrizations based on different adoption of data. Bottom panel: The calculated ${}^{10}\mathrm{Be}$ fluxes based on three possible parametrizations.

Figure 5

The prediction of $\mathrm{Be}/\mathrm{B}$ ratios based on three possible parametrizations defined in the Fig. 4 and the $2\sigma$ confidence interval (yellow band) of the bestfit parametrization, compared with the AMS-02 observation [5].

Figure 6

Cross section of $\mathrm{O}+\mathrm{p}⟶{}^9\mathrm{Be}$ constrained by the AMS-02 ${}^9\mathrm{Be}$ data (green band), compared with the available cross section measurements by different experiments. The reference parametrizations are taken from the GALPROP code.

Figure 7

Spectra calculated with or without [Yi69] data. Top panel: The ${}^9\mathrm{Be}$ and ${}^{10}\mathrm{Be}$ spectra compared with AMS-02 measurements [25]. Middle panel: The ${}^{10}\mathrm{Be}/{}^9\mathrm{Be}$ ratio compared with measurements [25, 71, 77, 78]. Bottom panel: The $\mathrm{Be}/\mathrm{B}$ ratio compared with AMS-02 measurements [5].

Figure 8

Channels: $\mathrm{C}+\mathrm{p}⟶\mathrm{B}$ or Be isotopes. The parametrizations [GAL12] shown in the figures were taken from the GALPROP code.

Figure 9

Channels: $\mathrm{O}+\mathrm{p}⟶\mathrm{B}$ or Be isotopes. The parametrizations [GAL12] shown in the figures were taken from the GALPROP code.