Cosmic-Ray Boron Flux Measured from $8.4\mathrm{GeV}/n$ to $3.8\mathrm{TeV}/n$ with the Calorimetric Electron Telescope on the International Space Station

We present the measurement of the energy dependence of the boron flux in cosmic rays and its ratio to the carbon flux in an energy interval from $8.4\mathrm{GeV}/n$ to $3.8\mathrm{TeV}/n$ based on the data collected by the Calorimetric Electron Telescope (CALET) during $\sim 6.4\mathrm{yr}$ of operation on the International Space Station. An update of the energy spectrum of carbon is also presented with an increase in statistics over our previous measurement. The observed boron flux shows a spectral hardening at the same transition energy $E_0\sim 200\mathrm{GeV}/n$ of the C spectrum, though B and C fluxes have different energy dependences. The spectral index of the B spectrum is found to be $\gamma =-3.047\pm 0.024$ in the interval $25<E<200\mathrm{GeV}/n$. The B spectrum hardens by $\mathrm{\Delta }{\gamma }_B=0.25\pm 0.12$, while the best fit value for the spectral variation of C is $\mathrm{\Delta }{\gamma }_C=0.19\pm 0.03$. The $\mathrm{B}/\mathrm{C}$ flux ratio is compatible with a hardening of $0.09\pm 0.05$, though a single power-law energy dependence cannot be ruled out given the current statistical uncertainties. A break in the $\mathrm{B}/\mathrm{C}$ ratio energy dependence would support the recent AMS-02 observations that secondary cosmic rays exhibit a stronger hardening than primary ones. We also perform a fit to the $\mathrm{B}/\mathrm{C}$ ratio with a leaky-box model of the cosmic-ray propagation in the Galaxy in order to probe a possible residual value ${\lambda }_0$ of the mean escape path length $\lambda$ at high energy. We find that our $\mathrm{B}/\mathrm{C}$ data are compatible with a nonzero value of ${\lambda }_0$, which can be interpreted as the column density of matter that cosmic rays cross within the acceleration region.

Figure 1

CALET (a) boron and (b) carbon flux (multiplied by $E^{2.7}$) and (c) ratio of boron to carbon, as a function of kinetic energy per nucleon $E$. Error bars of CALET data (red) represent the statistical uncertainty only, while the yellow band indicates the quadratic sum of statistical and systematic errors. Also plotted are other direct measurements [1, 2, 3, 4, 5, 7, 8, 34, 35]. An enlarged version of the figure is available in Fig. S8 in Supplemental Material [31].

Figure 2

CALET B (red dots) and C (black dots) energy spectra are fitted with DPL functions (magenta line for C and blue line for (B) in the energy range $[25,3800]\mathrm{GeV}/n$. The B spectrum is multiplied by a factor 5 to overlap the low-energy region of the C spectrum. The dashed lines represent the extrapolation of a SPL function fitted to data in the energy range $[25,200]\mathrm{GeV}/n$. $\mathrm{\Delta }\gamma$ is the change of the spectral index above the transition energy $E_0^C$ (from the fit to C data), represented by the vertical green dashed line. The green band shows the error interval of $E_0^C$.

Figure 3

The CALET $\mathrm{B}/\mathrm{C}$ ratio fitted to different functions. The error bars are the sum in quadrature of statistical and systematic uncertainties. The data are fitted to a DPL (solid blue line) and a SPL (dashed blue line) function in the energy interval $[25,3800]\mathrm{GeV}/n$. The red and green lines represent the fitted functions from a leaky-box model [Eq. (4)] with the ${\lambda }_0$ parameter left free to vary and fixed to zero, respectively.