{'fraction_non_alphanumeric': 0.04325158269936692, 'fraction_numerical': 0.032824386870245255, 'mean_word_length': 4.363195435092725, 'pattern_counts': {'":': 0, '<': 11, '<?xml version=': 0, '>': 4, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Properties of Neon, Magnesium, and Silicon Primary Cosmic Rays Results from the Alpha Magnetic Spectrometer

We report the observation of new properties of primary cosmic rays, neon (Ne), magnesium (Mg), and silicon (Si), measured in the rigidity range 2.15 GV to 3.0 TV with 1 . 8 × 10 6 Ne, 2 . 2 × 10 6 Mg, and 1 . 6 × 10 6 Si nuclei collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. The Ne and Mg spectra have identical rigidity dependence above 3.65 GV. The three spectra have identical rigidity dependence above 86.5 GV, deviate from a single power law above 200 GV, and harden in an identical way. Unexpectedly, above 86.5 GV the rigidity dependence of primary cosmic rays Ne, Mg, and Si spectra is different from the rigidity dependence of primary cosmic rays He, C, and O. This shows that the Ne, Mg, and Si and He, C, and O are two different classes of primary cosmic rays.


19
Sun Yat-Sen University (SYSU), Guangzhou 510275, China 20 Physics and Astronomy Department, University of Hawaii, Honolulu, Hawaii 96822, USA 21 National Aeronautics and Space Administration Johnson Space Center (JSC), Houston, Texas 77058, USA 22 Shandong Institute of Advanced Technology (SDIAT), Jinan, Shandong 250100, China 23 Shandong University (SDU), Jinan, Shandong 250100, China 24 Jülich Supercomputing Centre and JARA-FAME, Research Centre Jülich 52425 Jülich, Germany 25 Institut für Experimentelle Teilchenphysik, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany 26 Institut für Experimentelle und Angewandte Physik, Christian-Alberts-Universität zu Kiel We report the observation of new properties of primary cosmic rays, neon (Ne), magnesium (Mg), and silicon (Si), measured in the rigidity range 2.15 GV to 3.0 TV with 1.8 × 10 6 Ne, 2.2 × 10 6 Mg, and 1.6 × 10 6 Si nuclei collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. The Ne and Mg spectra have identical rigidity dependence above 3.65 GV. The three spectra have identical rigidity dependence above 86.5 GV, deviate from a single power law above 200 GV, and harden in an identical way. Unexpectedly, above 86.5 GV the rigidity dependence of primary cosmic rays Ne, Mg, and Si spectra is different from the rigidity dependence of primary cosmic rays He, C, and O. This shows that the Ne, Mg, and Si and He, C, and O are two different classes of primary cosmic rays. DOI: 10.1103/PhysRevLett.124.211102 Primary cosmic rays Ne, Mg, and Si are thought to be mainly produced and accelerated in astrophysical sources. Precise knowledge of their spectra in the gigavolt to teravolt rigidity region provides important information on the origin, acceleration, and propagation processes of cosmic rays in the Galaxy [1]. Previously, the precision measurement of the primary cosmic rays He, C, and O fluxes with the Alpha Magnetic Spectrometer experiment (AMS) has been reported [2], revealing an identical rigidity dependence of these three fluxes above 60 GV, including the unexpected deviation from a single power law (hardening) of their spectra above ∼200 GV. Differences in the rigidity dependence of Ne, Mg, and Si compared to He, C, and O provide new insights into the origin and propagation of cosmic rays [3,4].
Over the past 30 years there have been few measurements of Ne, Mg, and Si fluxes in kinetic energy per nucleon [5][6][7][8][9][10][11]. Typically these measurements have errors larger than 20% at 50 GeV=n. There are no measurements of Ne, Mg, and Si fluxes in rigidity.
In this Letter we report the precise measurements of the Ne, Mg, and Si fluxes in the rigidity range from 2.15 GV to 3.0 TV based on 1.8 × 10 6 Ne, 2.2 × 10 6 Mg, and 1.6 × 10 6 Si nuclei collected by AMS during the first 7 years (May 19, 2011 to May 26, 2018) of operation aboard the International Space Station (ISS). The total error is ∼5% at 100 GV for each flux.
Detector.-The layout and description of the AMS detector are presented in Ref. [12]. The key elements used in this measurement are the permanent magnet [13], the nine layers (L1 − L9) of silicon tracker [14], and the four planes of time of flight (TOF) scintillation counters [15]. AMS also contains a transition radiation detector, a ring imaging Čerenkov detector, an electromagnetic calorimeter (ECAL), and an array of 16 anticoincidence counters. Together, the tracker and the magnet measure the rigidity R of charged cosmic rays, with a maximum detectable rigidity of 3.2 TV for Z ¼ 10, 3.1 TV for Z ¼ 12, and 3.0 TV for Z ¼ 14 over the 3 m lever arm. Further information on the layout and the performance of the detector is included in Refs. [16,17].
Ne, Mg, and Si traversing AMS were triggered as described in Ref. [18]. The trigger efficiencies have been measured to be > 94% for the three nuclei over the entire rigidity range.
Monte Carlo (MC) simulated events were produced using a dedicated program developed by the collaboration based on the GEANT4-10.1 package [19]. The program simulates electromagnetic and hadronic interactions of particles in the material of AMS and generates detector responses.
Event selection.-In the first 7 years AMS has collected 120 × 10 9 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, 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, reaching 1.74 × 10 8 seconds above 30 GV.
Ne, Mg, and Si 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 ≥ 1.2 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. [18,20,21].
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 AMS out to 50 Earth's radii using the recent International Geomagnetic Reference Field model [23].
Charge measurements on L1, the inner tracker, the upper TOF, the lower TOF, and, for R > 1.2 TV, L9 are required to be compatible with charge Z ¼ 10 for Ne, Z ¼ 12 for Mg, and Z ¼ 14 for Si. As an example, Fig. S1 of Supplemental Material (SM) [16] shows the charge measurement for the inner tracker alone. The charge selection yields purities of > 98% for Ne and Mg and > 99.7% for Si. The impurities have two sources. The first source is a residual background from the interactions of heavy nuclei such as Na, Mg, Al, and Si in the material between L1 and L2 (the transition radiation detector and upper TOF). It has been evaluated by fitting the charge distribution from L1 with charge distribution templates of Na, Mg, Al, and Si as shown in Fig. S2 of SM [16] for Ne. The charge distribution templates are obtained from a selection of noninteracting samples at L2 by the use of the charge measurements with L1, upper TOF, and L3 − L8. This residual background is < 0.3% for the three nuclei over the entire rigidity range. The second source is a background from Na, Mg, Al, Si, P, S, and heavier nuclei interacting in materials above L1 (thin support structures made of carbon fiber and aluminum honeycomb). It has been estimated from simulation using MC samples generated according to AMS flux measurements [16,24] to be < 2% for Ne, < 1.5% for Mg, and negligible for Si over the entire rigidity range.
After background subtraction we obtain 1.8 × 10 6 neon, 2.2 × 10 6 magnesium, and 1.6 × 10 6 silicon nuclei. The overall uncertainty due to background subtraction is < 0.5% for the three nuclei 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 including geometric acceptance, event reconstruction and selection efficiencies, and inelastic interactions of nuclei in the AMS materials, as described below; ϵ i is the trigger efficiency; and T i is the collection time. In this Letter the fluxes were measured in 66 bins from 2.15 GV to 3.0 TV, with bin widths chosen according to the rigidity resolution. The bin widths are identical for the three nuclei and are identical with our previous publication on He, C, and O [2] with the exception of the first bin and the last four bins.
The bin-to-bin migration of events was corrected using the unfolding procedure described in Ref. [20]. These corrections, ðN i − ℵ i Þ=ℵ i , where ℵ i is the number of observed events in bin i, are þ18% at 3 GV, þ9% at 5 GV, −2% at 150 GV, and −5% at 3 TV for Ne and very similar for Mg and Si.
Extensive studies were made of the systematic errors. These errors include the uncertainties in the background evaluation 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 < 1% 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 vector determination, track finding, charge determination, and tracker quality cuts, and (b) the details of inelastic interactions of nuclei in the AMS materials. The systematic errors on the fluxes associated with the reconstruction and selection are < 1% over the entire rigidity range for the three nuclei.
The material traversed by nuclei from the top of AMS to L9 is composed primarily of carbon and aluminum. The survival probabilities for Ne, Mg, and Si nuclei due to interactions in the materials were measured using cosmic ray data collected by AMS as described in Ref. [25]. The systematic error due to uncertainties in evaluation of inelastic cross sections of all the materials traversed is < 3.5% up to 100 GV for the three fluxes. Above 100 GV, the small rigidity dependence of the cross sections from the Glauber-Gribov model [19] was treated as an uncertainty and added in quadrature to the uncertainties from the measured interaction probabilities [25]. The corresponding systematic errors on the three fluxes in the range of 100 GV to 3 TV were evaluated to be < 4%.
The rigidity resolution functions Δð1=RÞ for Ne, Mg, and Si have a pronounced Gaussian core characterized by widths σ and non-Gaussian tails more than 2.5σ away from the center [18]. The resolution functions have been verified with the procedures described in detail in Ref. [21]. As an example, Fig. S3 of SM [16] shows that the measured tracker bending coordinate accuracies are in a good agreement with the simulation. 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 GV and 2.5% 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 electromagnetic calorimeter 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 fluxes due to uncertainty on the rigidity scale is < 1% up to 300 GV and 6% at 3 TV.
Most importantly, several independent analyses were performed on the same data sample by different study groups. The results of those analyses are completely consistent with this Letter.
Results.-The measured Ne, Mg, and Si fluxes including statistical and systematic errors are reported in Tables SI-SIII of SM [16] as functions of the rigidity at the top of the AMS detector. To examine the difference in rigidity dependences of the Ne, Mg, and Si fluxes, the Ne=Mg and Si=Mg flux ratios were computed using the data in Tables SI-SIII of SM [16] and reported in Tables SIV and SV of SM [16] with their statistical and systematic errors. Figure 1(a) shows the Ne and Mg fluxes and Ne=Mg flux ratio, and Fig. 1(b) shows the Si and Mg fluxes and Si=Mg flux ratio, as functions of rigidityR with the total errors, the sum in quadrature 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]. To establish the rigidity intervals where the Ne, Mg, and Si fluxes have identical rigidity dependence, the fits of Ne=Mg and Si=Mg ratios have been performed to For the Ne=Mg ratio, the fit yields k Ne=Mg ¼ 0.84 AE 0.02, R Ne=Mg 0 ¼ 3.65 AE 0.5 GV, and Δ Ne=Mg ¼ 0.19 AE 0.08 with χ 2 =d:o:f: ¼ 42=64 over the entire rigidity range. From the fit results we found that the Ne and Mg fluxes have an identical rigidity dependence above 3.65 GV. Surprisingly, AMS has also observed an identical rigidity dependence above 7 GV between secondary cosmic ray Li and B fluxes [28].
From the fit results we conclude that all three fluxes have an identical rigidity dependence above 86.5 GV. This is a unique observation of the properties of Ne, Mg, and Si fluxes. Figure 2(a) shows the neon, Fig. 2(b) the magnesium, and Fig. 2(c) the silicon fluxes as a function of kinetic energy per nucleon E K together with earlier measurements [5][6][7][8][9][10][11]. Data from other experiments have been extracted using Ref. [29]. The results are presented in Fig. 3. As seen, the Ne and Mg spectral indices are identical in this rigidity range and the three flux spectral indices harden identically with rigidity above ∼200 GV.
To compare the rigidity dependence of the Ne, Mg, and Si fluxes with that of He, C, and O primary cosmic ray fluxes, which have identical rigidity dependence above 60 GV [2], the ratios of the neon, magnesium, and silicon fluxes to the oxygen flux were computed using the data in Tables SI-SIII of SM [16] and data in Ref. [30], and reported in Tables SVI-SVIII of SM [16], with statistical and systematic errors. To examine the rigidity dependence of Ne=O, Mg=O, and Si=O flux ratios, fits to the double power law, where C is a constant, to the ratios for rigidities above 20 GV have been performed and shown in Fig. S4 of − MÞ=A, where Z, M, and A are 20 10 Ne, 24 12 Mg, and 28 14 Si nuclei charge, mass, and atomic mass numbers, respectively. SM [16]. Figure 4 shows the rigidity dependence of the spectral indices Ne=O, Mg=O, and Si=O obtained from the fits. As seen, above 86.5 GV the spectral indices are δ Ne=O ¼ −0.046 AE 0.010, δ Mg=O ¼ −0.049 AE 0.011, and δ Si=O ¼ −0.040 AE 0.011, fully compatible with each other and incompatible with zero. Their average value is hδi ¼ −0.045 AE 0.008. The difference of hδi from zero by more than 5σ shows that the Ne, Mg, and Si is a different class of primary cosmic rays than He, C, and O. This is illustrated in Fig. 5, which shows the rigidity dependence of the Ne, Mg, and Si fluxes compared to rigidity dependence of the He, C, and O fluxes from Ref. [30] above 86.5 GV together with the fit results of He, C, and O fluxes and Ne, Mg, and Si fluxes with a function where C is the normalization constant and s quantifies the smoothness of the transition of the spectral index from γ for rigidities below the characteristic transition rigidity R 0 to γ þ Δγ for rigidities above R 0 [18]. The details of the fit procedures and parameters obtained are provided in the SM [16]. As seen, the rigidity dependences of Ne, Mg, and Si and He, C, and O are distinctly different.
The previous AMS results on primary cosmic rays He, C, and O [2] show, unexpectedly, that they have identical rigidity dependence above 60 GV and that they deviate from a single power law above 200 GV, whereas the secondary cosmic rays Li, Be, and B also have identical rigidity dependence above 30 GV and deviate from a single power law above 200 GV. The rigidity dependence of primary cosmic rays He, C, and O is distinctly different from secondary cosmic rays Li, Be, and B [28]. These results indicate there are two kinds of cosmic ray rigidity dependences. These observations have generated new developments in cosmic ray models [4,31]. The theoretical models have their limitations, as none of them predicted the observed spectral behavior of the cosmic rays. The results in this Letter on heavier primary cosmic rays Ne, Mg, and Si show that primary cosmic rays have at least two distinct classes of rigidity dependence. These unexpected results together with ongoing measurements of heavier elements in cosmic rays will enable us to determine how many classes of rigidity dependence exist in both primary and secondary cosmic rays and provide important input to the development of the theoretical models.  The green shaded area shows the fit result of He, C, and O fluxes from Ref. [30] with Eq. (5) together with fit errors [16]. The magenta shaded area shows the fit result of Ne, Mg, and Si fluxes from Ref. [16] with Eq. (5) when varying γ NeMgSi ¼ γ HeCO þ hδi, by AE0.008, from the value of hδi ¼ −0.045 AE 0.008.
In conclusion, we have presented precision measurements of the Ne, Mg, and Si fluxes rigidity dependence from 2.15 GV to 3.0 TV, with detailed studies of the systematic errors. The Ne and Mg spectra have identical rigidity dependence above 3.65 GV. The three spectra have identical rigidity dependence above 86.5 GV, deviate from a single power law above 200 GV, and harden in an identical way. Unexpectedly, above 86.5 GV the rigidity dependence of Ne, Mg, and Si spectra is different from the rigidity dependence of primary cosmic rays He, C, and O, which have identical rigidity dependence above 60 GV and harden above 200 GV. Above 86.5 GV, the Ne=O, Mg=O, and Si=O ratios can be described by a simple power law ∝ R δ with hδi ¼ −0.045 AE 0.008. This shows that the Ne, Mg, and Si and He, C, and O are two different classes of primary cosmic rays. These are new and unexpected properties of primary cosmic rays.