Precision Measurement of the Helium Flux in Primary Cosmic Rays of Rigidities 1.9 GV to 3 TV with the Alpha Magnetic Spectrometer on the International Space Station

Knowledge of the precise rigidity dependence of the helium flux is important in understanding the origin, acceleration, and propagation of cosmic rays. A precise measurement of the helium flux in primary cosmic rays with rigidity (momentum/charge) from 1.9 GV to 3 TV based on 50 million events is presented and compared to the proton flux. The detailed variation with rigidity of the helium flux spectral index is presented for the first time. The spectral index progressively hardens at rigidities larger than 100 GV. The rigidity dependence of the helium flux spectral index is similar to that of the proton spectral index though the magnitudes are different. Remarkably, the spectral index of the proton to helium flux ratio increases with rigidity up to 45 GV and then becomes constant; the flux ratio above 45 GV is well described by a single power law.

Figure 1

(a) The AMS helium flux [22] multiplied by ${\tilde{R}}^{2.7}$ with its total error as a function of rigidity. (b) The flux as a function of kinetic energy per nucleon $E_K$ multiplied by $E_K^{2.7}$ compared with measurements since the year 2000 [3, 4, 5, 6]. For the AMS results $E_K\equiv (\sqrt{4{\tilde{R}}^2+M^2}-M)/4$ where $M$ is the ${}^4\mathrm{He}$ mass as the AMS flux was treated as containing only ${}^4\mathrm{He}$. (c) Fit of Eq. (3) to the AMS helium flux. For illustration, the dashed curve uses the same fit values but with $R_0$ set to infinity.

Figure 2

(a) The dependence of the helium and proton [8] spectral indices on rigidity. (b) The $p/\mathrm{He}$ ratio as a function of rigidity compared with recent measurements [4, 6]. The solid blue curve indicates the fit of a single power law, Eq. (2), to the AMS data. As seen, above 45 GV the ratio is well described by a single power law. (c) The rigidity dependence of the $p/\mathrm{He}$ spectral index ${\gamma }_{p/\mathrm{He}}$ as measured by AMS. As seen, ${\gamma }_{p/\mathrm{He}}$ increases up to about 45 GV. Above 45 GV it becomes constant at ${\gamma }_{p/\mathrm{He}}=-0.077\pm 0.002(\text{fit})\pm 0.007(\text{sys})$ as indicated by the solid blue line. The dashed blue lines are the total error (the sum in quadrature of the fit and systematic errors).