Properties of Iron Primary Cosmic Rays: Results from the Alpha Magnetic Spectrometer

We report the observation of new properties of primary iron (Fe) cosmic rays in the rigidity range 2.65 GV to 3.0 TV with 0 . 62 × 10 6 iron nuclei collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. Above 80.5 GV the rigidity dependence of the cosmic ray Fe flux is identical to the rigidity dependence of the primary cosmic ray He, C, and O fluxes, with the Fe = O flux ratio being constant at 0 . 155 (cid:1) 0 . 006 . This shows that unexpectedly Fe and He, C, and O belong to the same class of primary cosmic rays which is different from the primary cosmic rays Ne, Mg, and Si class.

We report the observation of new properties of primary iron (Fe) cosmic rays in the rigidity range 2.65 GV to 3.0 TV with 0.62 × 10 6 iron nuclei collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. Above 80.5 GV the rigidity dependence of the cosmic ray Fe flux is identical to the rigidity dependence of the primary cosmic ray He, C, and O fluxes, with the Fe=O flux ratio being constant at 0.155 AE 0.006. This shows that unexpectedly Fe and He, C, and O belong to the same class of primary cosmic rays which is different from the primary cosmic rays Ne, Mg, and Si class. Primary iron cosmic rays are the most abundant heavy nuclei beyond silicon. They are thought to be mostly produced and accelerated in astrophysical sources. Iron interaction cross sections with the interstellar medium (p, He) are significantly larger than those of lighter nuclei (He, C, O, Ne, Mg, and Si). Therefore, iron nuclei interact much more with the interstellar medium during propagation. Precise knowledge of the iron spectrum in the GV-TV rigidity region provides important information on the origin, acceleration, and propagation processes of cosmic rays in the Galaxy [1]. Previously, the precision measurements of the primary cosmic ray He, C, and O fluxes and Ne, Mg, and Si fluxes with the Alpha Magnetic Spectrometer experiment (AMS) have been reported [2,3]. These measurements revealed an identical rigidity dependence of the He, C, and O fluxes above 60 GV and their deviation from a single power law (hardening) above ∼200 GV. The AMS results also revealed unexpected differences in the rigidity dependence of the Ne, Mg, 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. and Si fluxes compared to the He, C, and O fluxes. To date, iron nuclei (Z ¼ 26) are the highest charge cosmic rays measured by AMS. The rigidity dependence of the iron flux compared with that of lower-charge primary cosmic rays provides new insights into the origin and propagation of cosmic rays [4,5].
In this Letter we report the precise measurement of the Fe flux in the rigidity range from 2.65 GV to 3.0 TV based on 0.62 × 10 6 iron nuclei collected by AMS during the first 8.5 years (May 19, 2011 to October 30, 2019) of operation aboard the International Space Station (ISS). The total flux error is 4.8% at 100 GV.
Detector.-The layout and description of the AMS detector are presented in Ref. [18]. The key elements used in this measurement are the permanent magnet [19], the nine layers silicon tracker [20], L1-L9, and the four planes of time of flight TOF scintillation counters [21]. AMS also contains a transition radiation detector, a ring imaging Čerenkov detector, an electromagnetic calorimeter, and an array of 16 anticoincidence counters. Further details on the detector, trigger, and Monte Carlo (MC) simulation are contained in Refs. [22][23][24] and in the Supplemental Material [25].
Event selection.-In the first 8.5 yr AMS has collected 1.50 × 10 11 cosmic ray events. Iron 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. Charge measurements on L1, the inner tracker, the upper TOF, and, for R > 1.2 TV, the lower TOF, and L9 are required to be compatible with charge Z ¼ 26, namely, 23.2<Z L1 <27.6, 24.7 < Z UTOF < 27.6; 25.5 < Z InnerTracker < 26.5, Z LTOF >24.7, 24.6 < Z L9 < 28.8. Details of the event selection are contained in Refs. [23,[26][27][28][29] and in the Supplemental Material [25].
The event selection yields purities of > 97% over the entire rigidity range. The impurities have two sources. The main source is a residual background from Mn nuclei due to the finite AMS charge resolution. It has been estimated as a function of rigidity by selecting events with tight charge cuts on L1 and upper and lower TOF and found to be less than 3% over the entire rigidity range, see Fig. S2 of the Supplemental Material [25]. The second source is the residual background from the interactions of heavy nuclei such as Co and Ni in the AMS materials above L2. It is negligible, < 0.3%, over the entire rigidity range, as shown in Fig. S3 of the Supplemental Material [25].
After background subtraction we obtain 0.62 × 10 6 iron nuclei. The uncertainty due to background subtraction is < 0.7% independent of rigidity. It was estimated by varying the purity of the Fe sample from 95% to 99% and also by taking into account the statistical and systematic uncertainties in the template fit, see Fig. S3 of the Supplemental Material [25].
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 flux was measured in 49 bins from 2.65 GV to 3.0 TV, with bin widths chosen according to the rigidity resolution and available statistics.
The bin-to-bin migration of events was corrected using the unfolding procedure described in Ref. [26]. These corrections, ðN i − ℵ i Þ=ℵ i where ℵ i is the number of observed events in bin i, are þ33% at 3 GV decreasing smoothly to þ11% at 10 GV, þ2% at 80 GV, þ1% at 150 GV, and −2% at 3 TV.
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% 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 total corrections to the effective acceptance from the differences between data and MC simulation were found to be <5% over the entire rigidity range. The systematic error on the flux associated with the reconstruction and selection is <1% over the entire rigidity range.
The material traversed by nuclei from the top of AMS to L9 is composed primarily of carbon and aluminum. The survival probabilities of Fe nuclei due to interactions in the materials were measured using cosmic ray data collected by AMS as described in Ref. [30]. The simulation of nuclear interactions has been validated with data using all AMS measured nuclear charge changing cross sections (Fe → He...Mn þ X). Figure S4a of the Supplemental PHYSICAL REVIEW LETTERS 126, 041104 (2021) Material [25] shows three examples Fe → Cr þ X, Fe → Si þ X, and Fe → O þ X; Fig. S4b shows the comparison between the simulated and measured Fe survival probabilities between L1 and L2 in TRD and upper TOF; Fig. S5 shows the nuclei inelastic cross section of He, B, C, N, O, Ne, Mg, Si, S, and Fe on a C target measured by AMS at 15 GV rigidity as a function of nuclei charge radius [31]. The systematic error due to uncertainties in the evaluation of the inelastic cross section is < 4% up to 100 GV. Above 100 GV, the small rigidity dependence of the cross section from the Glauber-Gribov model [24] was treated as an uncertainty and added in quadrature to the uncertainties from the measured interaction probabilities [30]. Therefore, the corresponding systematic errors on the Fe flux is < 4% up to 100 GV and rises smoothly to 4.5% at 3 TV.
The rigidity resolution function for Fe has a pronounced Gaussian core characterized by width σ and non-Gaussian tails more than 2.5σ away from the center [23]. Figure S6 of Supplemental Material [25] shows the complete AMS rigidity resolution function as smearing matrices for the L1-L8 and L1-L9 configurations. The resolution function has been verified with the procedures described in detail in Ref. [27]. The systematic error on the flux due to the rigidity resolution function was obtained by repeating the unfolding procedure while varying the width of the Gaussian core of the resolution function by 5% and by independently varying the amplitude of the non-Gaussian tails by 10% [23]. The resulting systematic error on the flux is less than 1% below 300 GV and smoothly increases to 2.5% at 3 TV.
There are two contributions to the systematic uncertainty on the rigidity scale [26]. 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 [32]. The second systematic error on the rigidity scale arises from the magnetic field map measurement and its temperature corrections [26]. The error on the Fe flux due to uncertainty on the rigidity scale is < 1% up to 300 GV and increases smoothly to 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 consistent with this Letter.
Results.-The measured Fe flux including statistical and systematic errors is reported in Table SI of Supplemental Material [25] as a function of the rigidity at the top of the AMS detector. Figure 1(a) shows the Fe flux as a function of rigidityR with the total errors, the sum in quadrature of statistical and systematic errors. In the figure the points are placed along the abscissa atR calculated for a flux ∝ R −2.7 [33]. For comparison, Fig. 1(a) also shows our latest results on the oxygen flux from Refs. [2,34]. To examine the rigidity dependence of the Fe flux, the variation of the flux spectral indices with rigidity was obtained in a model independent way from γ ¼ d½logðΦÞ=d½logðRÞ ð2Þ over nonoverlapping rigidity intervals bounded by 7.09, 12.0, 16.6, 28.8, 45.1, 80.5, 175.0, and 3000.0 GV. The results are presented in Fig. 1(b) together with the spectral index of the oxygen flux from Ref. [34]. As seen from Fig. 1, above 80.5 GV the iron flux and spectral index follow the oxygen flux and spectral index, with the iron flux behavior being consistent with the observed hardening of the oxygen flux. Figure 2 shows the AMS iron flux as a function of kinetic energy per nucleon E K together with earlier measurements [6,7,[9][10][11][12][13][14][15][16]. Data from other experiments have been extracted using Ref. [35].
To compare the rigidity dependence of the Fe flux with that of He, C, and O primary cosmic ray fluxes, which have identical rigidity dependence above 60 GV [2,34], the ratio of the iron flux to the oxygen flux [34], Fe=O, was computed and is reported in Table SII of the Supplemental Material [25]. To compare the AMS result with previous measurements, the Fe=O ratio was converted from rigidity to kinetic energy per nucleon using the procedure described in Ref. [27]. Figure S7 of the Supplemental Material [25] shows the AMS Fe=O flux ratio as a function of kinetic energy per nucleon together with earlier measurements [6,7,11,13,15,16]. As seen, the AMS result provides an accurate functional energy dependence of the Fe=O flux ratio. Figure 3(a) shows the AMS Fe=O ratio as a function of rigidity with total errors together with a constant value fit above 80.5 GV. The fit yields Fe=O ¼ 0.155 AE 0.006 with χ 2 =d:o:f: ¼ 8=11. This, together with Fig. 1, shows that Fe belongs to the same class of primary cosmic rays as He, C, and O. Figure 3(b) shows the comparison of the Fe=O flux ratio with the cosmic ray propagation model GALPROP [36] prediction based on data available before AMS and with the latest GALPROP and HELMOD model [37] prediction based on published AMS data without including data in this Letter. As seen from Fig. 3(b), neither of these two models describes our data.
Cosmic ray nuclei fragment during their propagation in the Galaxy. Because of their different inelastic cross sections with the interstellar media, the fraction of nuclei which fragments at a given rigidity is different for iron and oxygen [38,39]. This, together with the propagation time (or Galactic leakage rate) rigidity dependence may significantly affect the measured Fe=O flux ratio [37]. Historically, there are several simple models describing the propagation of primary cosmic ray nuclei through the interstellar medium such as the "slab" and the "leakybox" models. In the slab model cosmic rays of a given rigidity traverse an equal amount of matter. In the leakybox model the amount of matter traversed by cosmic rays of a given rigidity is distributed exponentially [40]. per nucleon E K multiplied by E 2.7 K together with earlier measurements [6,7,[9][10][11][12][13][14][15][16]. For the AMS measurement  To assess the overall Fe=O flux ratio rigidity dependence at the source, before propagation, we have fitted it over the entire rigidity range using the slab model, e −λ S ðσ A −σ A 0 Þ , describing the propagation of primary nuclei through the interstellar medium [40] together with a source term kðR=192 GVÞ Δ : where Φ A =Φ A 0 is the flux ratio of primary nuclei A and A 0 , k is a normalization factor, Δ is the flux ratio spectral index at the source, is a mean material grammage (g cm −2 ) with rigidity dependence from Refs. [4,34,41] and λ is the grammage at R ¼ 192 GV, is the mass averaged cross section of a nucleus A, f ¼ 0.28 AE 0.02 is the helium mass fraction in the interstellar medium [42], m p and m He are the proton and 4 He masses, and σ Aþp and σ AþHe are the corresponding nuclei inelastic cross sections with protons and helium in the interstellar medium, respectively, evaluated using measurements from Refs. [39,43]. The fit parameters are k, Δ, and λ. The fit yields k ¼ 0.203 AE 0.008, Δ ¼ −0.002 AE 0.017, and λ ¼ 1.04 AE 0.11 g cm −2 with χ 2 =d:o:f: ¼ 22=43. The Fe=O flux ratio fit result is shown in Fig. 3(c). As seen, the Δ parameter is consistent with zero, which implies that in this model the Fe=O flux ratio at the source is constant over the entire rigidity range, as illustrated by the green band in Fig. 3(c). As seen, the model of Eq. (3) provides a good description of the Fe=O flux ratio. For completeness, we have also studied Eq. (3) with primary flux ratios Fe=He, He=O, and Fe=Si. The results are reported in the Supplemental Material [25] and shown in Table SA and Fig. S8 of the Supplemental Material [25]. As seen, the model of Eq. (3) also provides a good description of the Fe=He, He=O, and Fe=Si flux ratios. As seen in Fig. S8 of Supplemental Material [25], in the model the Fe=O, Fe=He, and He=O flux ratios at the source are constant over the entire rigidity range, however, the Fe=Si flux ratio at the source is not constant (at the 3σ level). The results of this model are consistent with the observation that He, O, and Fe belong to one class of primary cosmic rays and Si belongs to a different class.
We have also fitted the AMS Fe=O and Fe=Si flux ratios using the leaky box model [40]. The details are discussed in the Supplemental Material [25] and shown in Fig. S9. As seen, the leaky box model fails to describe the AMS results.
Most importantly, independent of any model [36,37,44], the measured rigidity dependence of Fe above 80.5 GV follows the rigidity dependence of O, see Fig. 1(a) and Fig. 3(a). Therefore as shown in Fig. 4, unexpectedly Fe belongs to the He, C, and O class of primary cosmic rays [2,34], which is different from the rigidity dependence of Ne, Mg, and Si [3].
In conclusion, we have presented the precision measurement of the Fe flux as a function of rigidity from 2.65 GV to 3.0 TV, with detailed studies of the systematic errors. Above 80.5 GV the rigidity dependence of the cosmic ray Fe flux is identical to the rigidity dependence of the primary cosmic ray He, C, and O class, which is different from the rigidity dependence of primary cosmic rays Ne, Mg, and Si class. In particular, above 80.5 GV the Fe=O ratio is well described by a constant value of 0.155 AE 0.006. These are new and unexpected properties of primary iron cosmic rays.
We are grateful for important physics discussions with Pasquale Blasi, Fiorenza Donato, Jonathan Feng, and Igor Moskalenko. We thank former NASA Administrator Daniel S. Goldin for his dedication to the legacy of the ISS as a scientific laboratory and his decision for NASA to fly AMS as a DOE payload. We also acknowledge the continuous support of the NASA leadership, particularly William H. Gerstenmaier, and of the JSC and MSFC flight control teams that have allowed AMS to operate optimally on the ISS for over nine years. We are grateful for the