Observation of the Identical Rigidity Dependence of He, C, and O Cosmic Rays at High Rigidities by the Alpha Magnetic Spectrometer on the International Space Station

We report the observation of new properties of primary cosmic rays He, C, and O measured in the rigidity (momentum/charge) range 2 GV to 3 TV with 90 × 10 6 helium, 8 . 4 × 10 6 carbon, and 7 . 0 × 10 6 oxygen nuclei collected by the Alpha Magnetic Spectrometer (AMS) during the first five years of operation. Above 60 GV, these three spectra have identical rigidity dependence. They all deviate from a single power law above 200 GV and harden in an identical way.

We report the observation of new properties of primary cosmic rays He, C, and O measured in the rigidity (momentum/charge) range 2 GV to 3 TV with 90 × 10 6 helium, 8.4 × 10 6 carbon, and 7.0 × 10 6 oxygen nuclei collected by the Alpha Magnetic Spectrometer (AMS) during the first five years of operation. Above 60 GV, these three spectra have identical rigidity dependence. They all deviate from a single power law above 200 GV and harden in an identical way. DOI: 10.1103/PhysRevLett.119.251101 Helium, carbon, and oxygen are among the most abundant nuclei in cosmic rays. They are called primary cosmic rays and are thought to be mainly produced and accelerated in astrophysical sources. Precise knowledge of their spectra in the GV-TV rigidity region provides important insights to the origin, acceleration, and subsequent propagation processes of cosmic rays in the Galaxy [1].
Previously, the precision measurement of the helium flux with the AMS has been reported [2] based on 50 × 10 6 helium events collected over the first 2.5 years of operations.
In this Letter we report the precise measurements of the helium, carbon, and oxygen fluxes in cosmic rays in the rigidity range from 1.9 GV to 3 TV for helium and carbon, and 2.2 GV to 3 TV for oxygen based on data collected by AMS during the first five years (May 19, 2011to May 26, 2016 of operation aboard the International Space Station (ISS). The total error is ∼3% at 100 GV for both Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. the carbon and oxygen fluxes and ∼1.5% at 100 GV for the helium flux.
Detector.-The layout and description of the Alpha Magnetic Spectrometer (AMS) detector are presented in Ref. [13]. The key elements used in this measurement are the permanent magnet [14], the silicon tracker [15], and the four planes of time of flight (TOF) scintillation counters [16]. Further information on the performance of the TOF is included in the Detector section of the Supplemental Material (SM) [17]. The AMS also contains a transition radiation detector (TRD), a ring imaging Čerenkov detector (RICH), an electromagnetic calorimeter (ECAL), and an array of 16 anticoincidence counters.
The tracker has nine layers, the first (L1) at the top of the detector, the second (L2) above the magnet, six (L3 to L8) within the bore of the magnet, and the last (L9) above the ECAL. L2 to L8 constitute the inner tracker.
Each layer of the tracker provides an independent measurement of the charge Z with a resolution of ΔZ=Z ¼ 9% for helium, 5% for carbon, and 4% for oxygen. Overall, the inner tracker has a resolution of ΔZ=Z ¼ 3.5% for helium, 2% for carbon, and 1.5% for oxygen.
The spatial resolution in each tracker layer is 6.5 μm in the bending direction for helium, 5.1 μm for carbon, and 6.3 μm for oxygen [18]. Together, the tracker and the magnet measure the rigidity R of charged cosmic rays, with a maximum detectable rigidity (MDR) of 3.2 TV for helium, 3.7 TV for carbon, and 3.4 TV for oxygen over the 3 m lever arm from L1 to L9.
Helium, carbon, and oxygen nuclei traversing AMS were triggered as described in Ref. [2]. The trigger efficiencies have been measured to be >94% for helium and >97% for carbon and oxygen over the entire rigidity range.
Monte Carlo (MC) simulated events were produced using a dedicated program developed by the collaboration based on the GEANT-4.10.1 package [19]. The program simulates electromagnetic and hadronic interactions of particles in the material of the AMS and generates detector responses. The Glauber-Gribov model [19] tuned to reproduce the AMS helium data, see Fig. SM 1(a) and SM 1(b) in Ref. [2], was used for the description of the nuclei inelastic cross sections.
Event selection.-In the first five years, the AMS has collected 8.5 × 10 10 cosmic ray events. The collection time used in this analysis includes only those seconds during which the detector was in normal operating conditions and, in addition, the AMS was pointing within 40°of the local zenith and the ISS was outside of the South Atlantic Anomaly. Because of the geomagnetic field, this collection time increases with rigidity, becoming constant at 1.23 × 10 8 s above 30 GV.
Helium events were selected as described in Ref. [2]. After selection the event sample contains 90 × 10 6 helium events with a purity >99.9%.
Carbon and oxygen events are required to be downward going and to have a reconstructed track in the inner tracker which passes through L1. In the highest rigidity region, R ≥ 1.13 TV, the track is also required to pass through L9. Track fitting quality criteria such as a χ 2 =d:o:f: < 10 in the bending coordinate are applied, similar to Refs. [2,20,21].
The measured rigidity is required to be greater than a factor of 1.2 times the maximum geomagnetic cutoff within the AMS field of view. The cutoff was calculated by backtracing [22] particles from the top of the AMS out to 50 Earth's radii using the most recent IGRF model [23].
Charge measurements on L1, the inner tracker, the upper TOF, the lower TOF, and, for R > 1.13 TV, L9 are required to be compatible with charge Z ¼ 6 for carbon and Z ¼ 8 for oxygen, as shown in Fig. 1 of the SM [17] for the inner tracker. This selection yields purities of 99% for carbon and >99.8% for oxygen. The residual backgrounds for carbon and oxygen are discussed in the Event Selection section of the SM [17] and in Ref. [24]. After background subtraction we obtain 8.4 × 10 6 carbon and 7.0 × 10 6 oxygen nuclei. The overall uncertainty due to background  [17] multiplied byR 2.7 with their total errors as functions of rigidity. Earlier measurements of helium, see Fig. 4 in Ref. [28], and carbon [12] fluxes in rigidity are also shown. (d) The dependence of the helium, carbon, and oxygen spectral indices on rigidity. In (d), for clarity, the horizontal positions of the helium and oxygen data points are displaced with respect to carbon. As seen, above 60 GV (indicated by the unshaded region) the spectral indices are identical. subtraction is <0.5% for carbon and negligible for oxygen over the entire rigidity range.
Data analysis.-The isotropic flux Φ i in the ith rigidity bin ðR i ; R i þ ΔR i Þ is given by where N i is the number of events corrected for bin-to-bin migration, A i is the effective acceptance, ϵ i is the trigger efficiency, and T i is the collection time. In this Letter, the helium and carbon fluxes were measured in 68 bins from 1.9 GV to 3.0 TV, and the oxygen flux was measured in 67 bins from 2.2 GV to 3.0 TV with bin widths chosen according to the rigidity resolution. The bin widths are identical for all nuclei.
The bin-to-bin migration of events was corrected using the unfolding procedure described in Ref. [20] independently for the helium, carbon, and oxygen samples. These corrections, ðN i − ℵ i Þ=ℵ i where ℵ i is the number of observed events in bin i, are þ14% at 3 GV, þ6% at 5 GV, −4% at 150 GV, and −6% at 3 TV for carbon and very similar for oxygen. For helium, these corrections are very close to those published in Ref. [2].
Extensive studies were made of the systematic errors. These errors include the uncertainties in the background estimations discussed above, the trigger efficiency, the geomagnetic cutoff factor, the acceptance calculation, the rigidity resolution function, and the absolute rigidity scale.
The systematic error on the fluxes associated with the trigger efficiency measurement is <0.7% for these nuclei over the entire rigidity range.
The geomagnetic cutoff factor was varied from 1.0 to 1.4, resulting in a negligible systematic uncertainty (<0.1%) in the rigidity range below 30 GV.
The effective acceptances A i were calculated using MC simulation and corrected for small differences between the data and simulated events related to (a) event reconstruction and selection, namely in the efficiencies of velocity determination, track finding, charge determination, and tracker quality cuts and (b) the details of inelastic interactions of nuclei in the AMS materials. The total corrections to the acceptance were found to be <2.5% up to 500 GV and <3.5% at 3 TV for helium and carbon, and <3.5% up to 500 GV and <5.0% at 3 TV for oxygen. The systematic errors on the fluxes associated with the reconstruction and selection are <1% over the entire rigidity range for all nuclei.
The material traversed by nuclei between L1 and L9 is composed primarily of carbon and aluminum. The helium flux systematic errors due to uncertainties in the inelastic cross sections for He þ C and He þ Al were discussed in detail in Ref. [2]. The systematic error on the carbon and oxygen fluxes due to uncertainties of inelastic cross sections was evaluated in a similar way as discussed in detail in the Data Analysis section of the SM [17] using data from Ref. [25] and found to be <2.2% for C and <2.7% for O up to 100 GV and 3% for C and 3.5% for O at 3 TV.
The rigidity resolution functions Δð1=RÞ for helium, carbon, and oxygen have a pronounced Gaussian core characterized by widths σ and non-Gaussian tails more than 2.5σ away from the center [2]. The resolution functions have been verified with the procedures described in detail in Ref. [21]. As an example, Fig. 4 of the SM [17] shows that the measured tracker bending coordinate accuracies of 6.5 μm for helium, 5.1 μm for carbon, and 6.3 μm for oxygen are in a good agreement with the simulation. This yields MDRs of 3.2 TV for helium, 3.7 TV for carbon, and 3.4 TV for oxygen with 5% uncertainty. This also provides the uncertainties of 10% on the amplitudes of the non-Gaussian tails. The systematic error on the fluxes due to the rigidity resolution functions was obtained by repeating the unfolding procedure while varying the widths of the Gaussian cores of the resolution functions by 5% and by independently varying the amplitudes of the non-Gaussian tails by 10%. The resulting systematic error on the fluxes is less than 1% below 300 GVand 4% at 3 TV for these nuclei.
There are two contributions to the systematic uncertainty on the rigidity scale [20]. The first is due to residual tracker misalignment. This error was estimated by comparing the E=p ratio for electrons and positrons, where E is the energy measured with the ECAL and p is the momentum measured with the tracker. It was found to be 1=30 TV −1 [26]. The second systematic error on the rigidity scale arises from the magnetic field map measurement and its temperature corrections. The error on the helium, carbon, and oxygen fluxes due to uncertainty on the rigidity scale is <1% up to 300 GV and 6.5% at 3 TV.
Much effort has been spent in understanding the systematic errors [2,20,21]. For this Letter, additional verification was performed. Figure 5 of the SM [17] shows the ratio of two measurements for the (a) carbon and (b) oxygen fluxes from 2.2 GV to 1.13 TV performed using events passing through L1 to L8, with MDR 1.5 TV for carbon and 1.3 TV for oxygen, and using events passing through L1 to L9. The good agreement between the measurements verifies the systematic errors on unfolding, due to the difference in the resolution functions, and the systematic errors on acceptance, due to the difference in geometric factor and the amount of material traversed.
Most importantly, several independent analyses were performed on the same data sample by different study groups. The results of those analyses are consistent with this Letter.
Results.-The measured helium, carbon, and oxygen fluxes including statistical and systematic errors are reported in Tables I, II, and III of the SM [17] as functions of the rigidity at the top of the AMS detector. Figure 1 shows the (a) helium, (b) carbon, and (c) oxygen fluxes as functions of rigidity with their total errors, the quadratic sum of statistical and systematic errors. In this and the subsequent figures, the points are placed along the abscissa atR calculated for a flux ∝ R −2.7 [27]. Earlier measurements of the helium [28] and carbon [12] fluxes in rigidity are also shown. The AMS measurement of the helium flux is distinctly different from the results of Ref. [28] which shows a sharp spectrum shape change. The AMS measurement of the carbon flux is also distinctly different from the results of Ref. [12], which are 20-25% lower above 20 GV.
To examine the rigidity dependence of the fluxes, the variation of the flux spectral indices with rigidity was obtained in a model independent way. The flux spectral indices were calculated from over nonoverlapping rigidity intervals above 8.48 GV, with a variable width to have sufficient sensitivity to determine γ. The results are presented in Fig. 1(d). As seen, the magnitude and the rigidity dependence of the helium, carbon, and oxygen spectral indices are very similar. In particular, all spectral indices are identical within the measurement errors above 60 GV and all spectral indices harden with rigidity above ∼200 GV. Figure 2 shows the AMS (a) helium, (b) carbon, and (c) oxygen fluxes as a function of kinetic energy per nucleon E K together with the results of previous experiments. At high energies, the AMS measurement of the helium flux is distinctly different from the previous experiments. The AMS measurements of the carbon and oxygen fluxes at high energies are also very different from previous measurements, being about 20-40% higher above 10 GeV=n.
To examine the difference between the rigidity dependence of the helium, carbon, and oxygen fluxes in detail, first, the ratio of the helium flux to the oxygen flux, or He=O ratio, was computed using the data in Tables I and III of the SM [17], and it was reported in Table IV of the SM [17], with its statistical and systematic errors. Figure 3(a) shows the He=O ratio with total errors, the quadratic sum of statistical and systematic errors, together with the cosmic ray propagation model GALPROP [31] prediction based on data available before the AMS. As seen in Fig. 3(a), above 60 GV the He=O ratio measured by the AMS is well fit by a constant value of 27.9 AE 0.6 with a χ 2 =d:o:f: ¼ 16=27. This is in disagreement with the GALPROP model which predicts a He=O ratio decreasing with rigidity. Figure 6 of the SM [17] shows the AMS He=O ratio as a function of kinetic energy per nucleon E K together with the results of a previous experiment [6].
Similarly, the ratio of the carbon flux to the oxygen flux, or the C=O ratio, was computed using the data in Tables II and III of the SM [17] and reported in Table V of SM [17], with its statistical and systematic errors. Figure 3(b) shows the C=O ratio with total errors together with the GALPROP model prediction based on data available before the AMS. As seen in Fig. 3(b), above 60 GV, the C=O ratio measured by the AMS is well fit by a constant value of 0.91 AE 0.02 with a χ 2 =d:o:f: ¼ 25=27. This is again in disagreement with the GALPROP model which predicts a C=O ratio decreasing with rigidity. Figure 7 of the SM [17] shows the AMS C=O ratio as a function of kinetic energy per nucleon E K together with the results of previous experiments [4,5,[7][8][9][10][11]. As seen, the C=O ratio measured by the AMS is within 10% of unity.
It is important to note that, whereas protons, helium, carbon, and oxygen are all considered primary cosmic rays, the independence of the measured C=O and He=O flux ratios with rigidity is completely different from the proton to helium flux ratio rigidity dependence, see Fig. 2(b) of Ref. [2]. None of these unexpected results, including the p/He flux ratio rigidity dependence [24,32], can be explained by the current understanding of cosmic rays.
In conclusion, we have presented precise, high statistics measurements of the helium, carbon, and oxygen fluxes from 2 GV to 3 TV, with detailed studies of the systematic K together with previous measurements [4][5][6][7][8][9][10][11][12]28,29]. For the AMS where Z, M, and A are the 4 He, 12 C, or 16 O charge, mass, and atomic mass numbers, respectively. Data from other experiments were extracted using Ref. [30]. errors. These measurements show that the fluxes deviate from a single power law. Their spectral indices all progressively harden above 200 GV. Surprisingly, above 60 GV, the three fluxes have identical rigidity dependence, as illustrated in Fig. 4. Above 60 GV, the helium to oxygen flux ratio is constant at 27.9 AE 0.6 and the carbon to oxygen flux ratio is constant at 0.91 AE 0.02.