Observation of New Properties of Secondary Cosmic Rays Lithium, Beryllium, and Boron by the Alpha Magnetic Spectrometer on the International Space Station

We report on the observation of new properties of secondary cosmic rays Li, Be, and B measured in the rigidity (momentum per unit charge) range 1.9 GV to 3.3 TV with a total of 5 . 4 × 10 6 nuclei collected by AMS during the first five years of operation aboard the International Space Station. The Li and B fluxes have an identical rigidity dependence above 7 GVand all three fluxes have an identical rigidity dependence above 30 GV with the Li = Be flux ratio of 2 . 0 (cid:1) 0 . 1 . The three fluxes deviate from a single power law above 200 GV in an identical way. This behavior of secondary cosmic rays has also been observed in the AMS measurement of primary cosmic rays He, C, and O but the rigidity dependences of primary cosmic rays and of secondary cosmic rays are distinctly different. In particular, above 200 GV, the secondary cosmic rays harden more than the primary cosmic rays.

We report on the observation of new properties of secondary cosmic rays Li, Be, and B measured in the rigidity (momentum per unit charge) range 1.9 GV to 3.3 TV with a total of 5.4 × 10 6 nuclei collected by AMS during the first five years of operation aboard the International Space Station. The Li and B fluxes have an identical rigidity dependence above 7 GV and all three fluxes have an identical rigidity dependence above 30 GV with the Li=Be flux ratio of 2.0 AE 0.1. The three fluxes deviate from a single power law above 200 GV in an identical way. This behavior of secondary cosmic rays has also been observed in the AMS measurement of primary cosmic rays He, C, and O but the rigidity dependences of primary cosmic rays and of secondary cosmic rays are distinctly different. In particular, above 200 GV, the secondary cosmic rays harden more than the primary cosmic rays. DOI: 10.1103/PhysRevLett.120.021101 Lithium, beryllium, and boron nuclei in cosmic rays are thought to be produced by the collisions of nuclei with the interstellar medium [1]. They are called secondary cosmic rays. Over the last 50 years, only a few experiments have measured the lithium [2][3][4] and beryllium [2][3][4][5][6] fluxes in cosmic rays above a few GV. Typically, these measurements have errors larger than 50% at 100 GV. For the boron flux, measurements [2][3][4][5][6][7][8][9][10][11] have errors larger than 15% at 100 GV.
Precise measurements of primary cosmic rays, protons, helium, carbon, and oxygen, by AMS [12][13][14] have shown a hardening of all their spectra above 200 GV. In addition, above 60 GV, the spectra of He, C, and O were found to have an identical rigidity dependence. The detailed knowledge of lithium, beryllium, and boron fluxes rigidity dependences is important to study the origin of the hardening in cosmic ray fluxes. There are many theoretical models describing the behavior of cosmic rays. For example, if the hardening in cosmic rays is related to the injected spectra at their source, then similar hardening is expected both for secondary and primary cosmic rays [15]. However, if the hardening is related to propagation properties in the Galaxy then a stronger hardening is expected for the secondary with respect to the primary cosmic rays [16]. The theoretical models have their limitations, as none of them predicted the observed spectral behavior of the primary cosmic rays He, C, and O. Furthermore, none of the theoretical models predict the observed spectral behavior of the secondary cosmic rays Li, Be, and B reported in this Letter.
In this Letter we report the precise measurement of the lithium, beryllium, and boron fluxes in cosmic rays in the rigidity range from 1.9 GV to 3.3 TV. This measurement is based on 1.9 × 10 6 lithium, 0.9 × 10 6 beryllium, and 2.6 × 10 6 boron nuclei collected by AMS during the first 5 y (May 19, 2011 to May 26, 2016) of operation aboard the International Space Station (ISS). The total error on each of the fluxes is 3%-4% in the 100-108 GV bin.
Detector.-The layout and description of the AMS detector are presented in Ref. [17]. The key elements used in this measurement are the permanent magnet [18], the silicon tracker [19], and the four planes of time of flight (TOF) scintillation counters [20]. Further information on the layout and the performance of the silicon tracker and the TOF is included in Ref. [21], see also Ref. [22]. 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.
Li, Be, and B nuclei traversing AMS were triggered as described in detail in Ref. [13]. The trigger efficiencies for 3 ≤ Z ≤ 5 events were measured to be > 98% 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 [23]. The program simulates electromagnetic and hadronic interactions of particles in the material of AMS and generates detector responses. The Glauber-Gribov model [23] tuned to reproduce the AMS helium data, see  [13], was used for the description of the nuclei inelastic cross sections. The Monte Carlo event samples have sufficient statistics such that they do not contribute to the errors.
Event selection.-In the first five years 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, AMS was pointing within 40°of the local zenith and the ISS was outside of the South Atlantic Anomaly. Because of the influence of the geomagnetic field, this collection time for galactic cosmic rays increases with rigidity becoming constant at 1.23 × 10 8 seconds above 30 GV.
Events are required to be downward going, to have a reconstructed track in the inner tracker, and to pass through L1. In the highest rigidity region, R ≥ 1.3 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. [12][13][14]24].
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 particles from the top of AMS out to 50 Earth's radii [25] using the most recent IGRF [26] geomagnetic model.
Charge measurements on tracker L1, the inner tracker, the upper TOF, and, for R ≥ 1.3 TV, tracker L9 are required to be compatible with charge Z ¼ 3, 4, and 5, as shown in Fig. 1 of the Supplemental Material [21] for the inner tracker. With this selection, the charge confusion from noninteracted nuclei is negligible over the whole rigidity range. The residual background comes from heavier nuclei which interact above tracker L2. The background resulting from interactions in the material between L1 and L2 (TRD and upper TOF) is evaluated by fitting the charge distribution of tracker L1 with charge distribution templates of Li, Be, B, and C. Then cuts are applied on the L1 charge as shown in Fig. 2 of the Supplemental Material [21]. The charge distribution templates are obtained using L2. These templates contain only noninteracting events by requiring that L1 and L3-L8 measure the same charge value. This background is < 0.5% for lithium and beryllium and < 3% for boron. The background from interactions on materials above L1 (thin support structures made by carbon fiber and aluminum honeycomb) has been estimated from simulation using MC samples generated according to AMS flux measurements [14,21,27]. The simulation of nuclear interactions has been validated using data, as shown in Fig. 3 of the Supplemental Material [21]. For Li, Be, and B these backgrounds are estimated to be 5%, 8%, and 5% at 2 GVand 2%, 13%, and 8% at 3.3 TV, respectively. The uncertainties on the fluxes due to these background corrections were evaluated to be < 1.5% in the whole 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-tobin migration, A i is the effective acceptance, ϵ i is the trigger efficiency, and T i is the collection time. In this Letter the fluxes were measured in 67 bins from 1.9 GV to 3.3 TV with bin widths chosen according to the rigidity resolution and available statistics. The bins are identical for all nuclei and, except for the highest rigidity bin, also PHYSICAL REVIEW LETTERS 120, 021101 (2018) 021101-3 identical with those used in our publication on the boron to carbon ratio [24]. The bin-to-bin migration of events was corrected using the unfolding procedure described in Ref. [12]. These corrections, ðN i − ℵ i Þ=ℵ i , where ℵ i is the number of observed events in bin i, are þ9% at 3 GV, þ3% at 5 GV, −5% at 150 GV, and −20% at 3.3 TV for lithium and very similar for beryllium and boron.
As discussed in Refs. [12][13][14]24], extensive studies were made of the systematic errors. These errors include the uncertainties in the two 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 is < 0.5% over the entire rigidity range. The geomagnetic cutoff factor was varied from 1.0 to 1.4 resulting in a negligible systematic uncertainty (less than 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 data and MC simulations 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 effective acceptances from the differences between data and MC simulation were found to be < 5% over the entire rigidity range. The systematic errors on the fluxes associated with the reconstruction and selection are < 2% over the entire rigidity range for all nuclei. The material traversed by nuclei between L1 and L9 is composed primarily of carbon and aluminum, as described in detail in Ref. [13]. To verify the MC predictions, event samples that traverse materials between L8 and L9 (lower TOF and RICH) without interacting are measured in data and compared with MC samples simulated with inelastic cross sections varied within AE10%. The resulting cross sections with the best agreement to data above 30 GV were chosen. Figure 4 of the Supplemental Material [21] shows the measured survival probabilities between L8 and L9 compared with simulation for lithium, beryllium, and boron. The survival probabilities are defined as the ratio of events which have the same charge value measured by L1-L9 to events which have the same charge value measured by L1-L8. Similarly, the survival probabilities between L1 and L2 have been calculated using data periods in which AMS was horizontal, i.e., ∼90°with respect to the zenith [13]. This independently verifies the inelastic cross sections. The systematic errors on the fluxes due to uncertainties of inelastic cross sections were evaluated to be < 2%-3% up to 100 GV. At higher rigidities, the small rigidity dependencies of the cross sections from the Glauber-Gribov model were treated as uncertainties and added in quadrature to the uncertainties from the measured interaction probabilities. The resulting systematic errors on the fluxes were evaluated to be < 3%-4% at 3.3 TV.
The rigidity resolution functions Δð1=RÞ for Li, Be, and B have a pronounced Gaussian core characterized by width σ and non-Gaussian tails more than 2.5σ away from the center [13]. The resolution functions have been verified with the procedures described in detail in Ref. [24]. First, the differences of the coordinates measured in L3 or L5 to those obtained from the track fit using the measurements from L1, L2, L4, L6, L7, and L8 were compared between data and simulation. This procedure directly measures the tracker bending coordinate accuracy of 5.3-5.8 μm for Li, Be, and B, as shown in Fig. 5 of the Supplemental Material [21]. The comparisons for the tails of the distributions are shown in Fig. 6 of the Supplemental Material [21]. Second, the distributions of the scattering angle, defined as the angular difference between the inner tracker track and the L1 to L2 trajectory, were compared between data and simulation for Li, Be, and B and found to be in good agreement similar to Fig. SM 6 of Ref. [24]. This comparison verifies the multiple, nucleus-nucleus elastic, and quasielastic scatterings. The procedures provide the MDR of 3.5 TV for Li, 3.6 TV for Be, and 3.7 TV for B with 5% uncertainty and provide the uncertainties of 20% on the amplitudes of the non-Gaussian tails.
The systematic errors on the fluxes due to the rigidity resolution functions were obtained by repeating the unfolding procedure while varying the width of the Gaussian core of the resolution functions by 5% and by independently varying the amplitudes of the non-Gaussian tails by 20%. The resulting systematic errors on the fluxes are < 1.5% below 200 GVand increase to 8%-10% at 3.3 TV.
There are two contributions to the systematic uncertainty on the rigidity scale, discussed in detail in Ref. [12]. 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 [28]. 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 below 1% up to 200 GV and increases to 5%-7% at 3.3 TV.
Much effort has been spent to validate the systematic errors [12][13][14]24]. As an example, Fig. 7 of the Supplemental Material [21] shows the ratio of the measurements of the Li, Be, and B fluxes from 1.9 GV to 1.3 TV performed using events passing through L1 to L8 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, as well as the systematic errors on acceptance, due to the difference in geometric factor and the amount of material traversed. PHYSICAL REVIEW LETTERS 120, 021101 (2018) 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 lithium, beryllium, and boron fluxes including statistical and systematic errors are reported in Tables I, II, and III of the Supplemental Material [21] as a function of the rigidity at the top of the AMS detector. Figure 1 shows the lithium, beryllium, and boron fluxes as a function of rigidity 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 [29]. As seen, the Li and B fluxes have an identical rigidity dependence above ∼7 GV and all three secondary fluxes have an identical rigidity dependence above ∼30 GV. The different rigidity dependence of the Be flux is most likely due to the significant presence of the radioactive 10 Be isotope [27], which has a half life of 1.4 MY. Figure 8 of the Supplemental Material [21] shows the lithium, beryllium, and boron fluxes as a function of kinetic energy per nucleon E K together with earlier measurements [2][3][4][5][6][7][8][9][10][11]. Data from other experiments have been extracted using Ref. [30]. For the AMS measurement E K ¼ ð − MÞ=A where Z, M, and A are the Li, Be, and B charge, mass and atomic mass number, respectively. The atomic mass numbers, averaged by isotopic composition obtained from AMS low energy measurements [27], are 6.5 AE 0.1 for Li, 8.0 AE 0.2 for Be, and 10.7 AE 0.1 for B. The systematic errors on the fluxes due to these uncertainties were added in quadrature to the total errors.
To examine the rigidity dependence of the fluxes, detailed variations of the flux spectral indices with rigidity were obtained in a model-independent way. The flux spectral indices γ were calculated from over rigidity intervals bounded by 7.09, 12.0, 16.6, 22.8, 41.9, 60.3, 192, and 3300 GV. The results are presented in Fig. 2 together with the spectral indices of helium, carbon, and oxygen [14]. As seen, the magnitude and the rigidity dependence of the lithium, beryllium, and boron spectral indices are nearly identical, but distinctly different from the rigidity dependence of helium, carbon, and oxygen. In addition, above ∼200 GV, Li, Be, and B all harden more than He, C, and O. To examine the difference between the rigidity dependence of primary and secondary cosmic rays in detail, the ratios of the lithium, beryllium, and boron fluxes to the carbon and oxygen fluxes were computed using the data in Tables I, II, and III of the Supplemental Material [21] and Tables II and III of Ref. [14], and are reported in Tables IV-IX [14]. For clarity, the Li, B, He, and O data points are displaced horizontally. The shaded regions are to guide the eye. As seen, the magnitude and the rigidity dependence of the Li, Be, and B spectral indices are nearly identical, but distinctly different from the rigidity dependence of the He, C, and O spectral indices. Above ∼200 GV the Li, Be, and B fluxes all harden more than the He, C, and O fluxes. See also Fig. 3.
where Φ S =Φ P are the ratios of the secondary to primary fluxes over rigidity intervals [60.  and ½192-3300 GV and shown in Fig 3. Above ∼200 GV these spectral indices exhibit an average hardening of 0.13 AE 0.03. Figures 9 and  10 of the Supplemental Material [21] show all secondary to primary flux ratios together with the results of Eq. (3). This additionally verifies that at high rigidities the secondary cosmic rays harden more than the primary cosmic rays. This additional hardening of secondary cosmic rays is consistent with expectations when the hardening of cosmic ray fluxes is due to the propagation properties in the Galaxy [16].
To examine the rigidity dependence of the secondary cosmic rays in detail, the lithium to boron Li=B and beryllium to boron Be=B flux ratios were computed using the data in Tables I, II, and III of the Supplemental Material [21] and reported in Tables X and XI of the Supplemental Material [21] with their statistical and systematic errors.  [21]. The Li and B fluxes have an identical rigidity dependence above ∼7 GV and all three secondary fluxes have an identical rigidity dependence above ∼30 GV. In Figs. 13, 14, and 15 of the Supplemental Material [21], we compare our flux ratios converted to E K using the procedure described in Ref. [24] with earlier measurements [2][3][4][5][6][7][8][9][10][11][31][32][33].
In conclusion, we have presented precise, high statistics measurements of the lithium, beryllium, and boron fluxes from 1.9 GV to 3.3 TV with detailed studies of the systematic errors. The Li and B fluxes have identical rigidity dependence above 7 GV and all three fluxes have identical rigidity dependence above 30 GV with the Li=Be flux ratio of 2.0 AE 0.1. The three fluxes deviate from a single power law above 200 GV in an identical way. As seen in Fig. 4, this behavior of secondary cosmic rays has also been observed in primary cosmic rays He, C, and O [14] but the rigidity dependences of primary cosmic rays and of secondary cosmic rays are distinctly different. In particular, above 200 GV, the spectral indices of secondary cosmic rays harden by an average of 0.13 AE 0.03 more than the primaries. These are new properties of cosmic rays.
We thank former NASA Administrator Daniel S. Goldin for his dedication to the legacy of the ISS as a scientific  [21] with the AMS primary cosmic ray fluxes [14] multiplied byR 2.7 with their total error as a function of rigidity above 30 GV. For display purposes only, the C, O, Li, Be, and B fluxes were rescaled as indicated. For clarity, the He, O, Li, and B data points above 400 GV are displaced horizontally. As seen, the three secondary fluxes have an identical rigidity dependence above 30 GV, as do the three primary fluxes above 60 GV. The rigidity dependences of primary cosmic rays fluxes and of secondary cosmic rays fluxes are distinctly different.