Galactic cosmic-ray model in the light of AMS-02 nuclei data

Cosmic ray (CR) physics has entered a precision-driven era. With the latest AMS-02 nuclei data (boron-to-carbon ratio, proton flux, helium flux, and antiproton-to-proton ratio), we perform a global fitting and constrain the primary source and propagation parameters of cosmic rays in the Milky Way by considering 3 schemes with different data sets (with and without $\overline{\mathrm{p}}/\mathrm{p}$ data) and different propagation models (diffusion-reacceleration and diffusion-reacceleration-convection models). We find that the data set with $\overline{\mathrm{p}}/\mathrm{p}$ data can remove the degeneracy between the propagation parameters effectively and it favors the model with a very small value of convection (or disfavors the model with convection). The separated injection spectrum parameters are used for proton and other nucleus species, which reveal the different breaks and slopes among them. Moreover, the helium abundance, antiproton production cross sections, and solar modulation are parametrized in our global fitting. Benefited from the self-consistence of the new data set, the fitting results show a little bias, and thus the disadvantages and limitations of the existed propagation models appear. Comparing to the best fit results for the local interstellar spectra ($\varphi =0$) with the VOYAGER-1 data, we find that the primary sources or propagation mechanisms should be different between proton and helium (or other heavier nucleus species). Thus, how to explain these results properly is an interesting and challenging question.

Figure 1

The global fitting results and the corresponding residuals to the AMS-02 B/C ratio, proton flux, helium flux, $\overline{\mathrm{p}}/\mathrm{p}$ ratio and $\overline{\mathrm{p}}$ flux data for Scheme I, II and III. The $2\sigma$ (deep red) and $3\sigma$ (light red) bound are also showed in the figures. Note that the $\overline{\mathrm{p}}$ flux data is not used in the global fitting and we show it for a cross validation. For Scheme I, we did not use the $\overline{\mathrm{p}}/\mathrm{p}$ ratio data either, and fix the value $c_{\overline{\mathrm{p}}}=1.34$ to show the results of $\overline{\mathrm{p}}/\mathrm{p}$ and $\overline{\mathrm{p}}$.

Figure 2

Fitting 1D probability and 2D credible regions of posterior PDFs for the combinations of all propagation parameters from Scheme I. The regions enclosing $\sigma$, $2\sigma$, and $3\sigma$ CL are shown in step by step lighter green. The red cross lines and marks in each plot indicates the best-fit value (largest likelihood).

Figure 3

Same as Fig. 2 but for Scheme II.

Figure 4

Same as Fig. 2 but for Scheme III.

Figure 5

Fitting 1D probability and 2D credible regions of posterior PDFs for the combinations of primary source parameters from Scheme I. The regions enclosing $\sigma$, $2\sigma$ and $3\sigma$ CL are shown in step by step lighter green. The red cross lines and marks in each plot indicates the best-fit value (largest likelihood).

Figure 6

Same as Fig. 5 but for Scheme II.

Figure 7

Same as Fig. 5 but for Scheme III.

Figure 8

Fitting 1D probability and 2D credible regions of posterior PDFs for the differences of primary source parameters (red for Scheme I, green for Scheme II, blue for Scheme III). The regions enclosing $\sigma$ and $2\sigma$ CL are indicated by the contours.

Figure 9

Fitting 1D probability and 2D credible regions of posterior PDFs for the combinations of nuisance parameters from Scheme I. The regions enclosing $\sigma$, $2\sigma$, and $3\sigma$ CL are shown in step by step lighter green. The red cross lines and marks in each plot indicates the best-fit value (largest likelihood).

Figure 10

Same as Fig. 9 but for Scheme II.

Figure 11

Same as Fig. 9 but for Scheme III.

Figure 12

The comparison between the best fitting results (with $\varphi =0$) and the VOYAGER-1 data for Scheme I, II, and III. The $2\sigma$ (deep red) and $3\sigma$ (light red) bound are also showed in the figures.

Figure 13

The comparison between the best fit results and the perturbation results which use different $D_0$ and $z_h$ values (labeled by the perturbations on $z_h$) with fixed $D_0/z_h$ at best fit parameters from Scheme II. The $\pm 1\mathrm{kpc}$ and $\pm 2\mathrm{kpc}$ perturbation results are presented by red and green dash lines. The $\sigma$ and $3\sigma$ of the fitting residuals are showed in deep blue and light blue in the lower panel of each sub-figures respectively.