Properties of Heavy Secondary Fluorine Cosmic Rays: Results from the Alpha Magnetic Spectrometer

Precise knowledge of the charge and rigidity dependence of the secondary cosmic ray fluxes and the secondary-to-primary flux ratios is essential in the understanding of cosmic ray propagation. We report the properties of heavy secondary cosmic ray fluorine F in the rigidity R range 2.15 GV to 2.9 TV based on 0.29 million events collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. The fluorine spectrum deviates from a single power law above 200 GV. The heavier secondary-to-primary F/Si flux ratio rigidity dependence is distinctly different from the lighter B/O (or B/C) rigidity dependence. In particular, above 10 GV, the F = Si B = O ratio can be described by a power law R δ with δ ¼ 0 . 052 (cid:2) 0 . 007 . This shows that the propagation properties of heavy cosmic rays, from F to Si, are different from those of light cosmic rays, from He to O, and that the secondary cosmic rays have two classes.


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Sun Yat-Sen University (SYSU), Guangzhou, 510275, China Precise knowledge of the charge and rigidity dependence of the secondary cosmic ray fluxes and the secondary-to-primary flux ratios is essential in the understanding of cosmic ray propagation. We report the properties of heavy secondary cosmic ray fluorine F in the rigidity R range 2.15 GV to 2.9 TV based on 0.29 million events collected by the Alpha Magnetic Spectrometer experiment on the International Space Station. The fluorine spectrum deviates from a single power law above 200 GV. The heavier secondary-toprimary F/Si flux ratio rigidity dependence is distinctly different from the lighter B/O (or B/C) rigidity dependence. In particular, above 10 GV, the F=Si B=O ratio can be described by a power law R δ with δ ¼ 0.052 AE 0.007. This shows that the propagation properties of heavy cosmic rays, from F to Si, are different from those of light cosmic rays, from He to O, and that the secondary cosmic rays have two classes. Fluorine nuclei in cosmic rays are thought to be produced mostly by the collisions of heavy nuclei, such as Ne, Mg, and Si, with the interstellar medium. Together with the much more abundant Li, Be, and B cosmic rays, they are called secondary cosmic rays [1]. Fluorine is the only purely secondary cosmic ray between oxygen and silicon [2]. Fluorine is the heaviest pure secondary cosmic ray accurately measured by AMS.
Over the past 50 years, several experiments have measured the fluorine flux in cosmic rays in kinetic energy per nucleon [3][4][5][6][7][8] up to 100 GeV/n. The measurement errors exceed 100% at ∼50 GeV=n (∼100 GV in rigidity). There are no measurements of the F flux in rigidity. The secondary-to-primary flux ratios of light nuclei in cosmic rays, in particular, B/C or the more direct B/O, have been traditionally used to study the propagation of cosmic rays in the Galaxy [9]. In previous publications, AMS has shown that all light secondary-to-primary ratios, Li/C, Li/O, Be/C, Be/O, B/C, and B/O, deviate from a single power law (harden) above 200 GV [10,11]. This strongly favors that the hardening of all light cosmic rays is due to propagation effects [2,9,12]. Recently, AMS has also studied the properties of the heavy primary Ne, Mg, and Si fluxes [13] and found that they form a separate class of primary cosmic rays. Differences in the rigidity dependence of the F flux and light secondary cosmic ray Li, Be, and B fluxes, as well as differences in the rigidity dependence of light (B/O) and heavy (F/Si) secondary-to-primary flux ratios, provide new important insights on cosmic ray propagation.
In this Letter, we report the precise measurement of the F flux in the rigidity range from 2.15 GV to 2.9 TV based on 0.29 million fluorine 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 5.9% at 100 GV.
Detector.-The layout and description of the AMS detector are presented in Refs. [11,14] and shown in Fig. S1 of Supplemental Material [15]. The key elements used in this measurement are the permanent magnet [16], the nine layers, L1-L9, of silicon tracker [17][18][19], and the four planes of time of flight (TOF) scintillation counters [20]. Further information on the AMS layout, performance, trigger, and the simulations [21,22] is detailed in Supplemental Material [15].
Event selection.-In the first 8.5 years, AMS has collected 1.50 × 10 11 cosmic ray events. Fluorine events are required to be downward going and to have a reconstructed track in the inner tracker; see Fig. S2 in Supplemental Material [15] for a reconstructed fluorine event. Details of the event selection are contained in Refs. [23][24][25][26][27] and in Supplemental Material [15].
With this selection, the background from chargeadjacent noninteracting nuclei (O and Ne) due to the finite AMS charge resolution is negligible, < 0.5% over the whole rigidity range; see Fig. S3 in Supplemental Material [15]. The main background comes from heavier nuclei, such as Ne, Mg, and Si, which interact above tracker L2. It has two sources. First, the background resulting from interactions in the material between L1 and L2 (Transition Radiation Detector and upper TOF) is evaluated by fitting the charge distribution of tracker L1 with charge distribution templates of O, F, Ne, and Na. Then cuts are applied on the L1 charge as shown in Fig. S4 in Supplemental Material [15]. 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 varies from 4% to 15% depending on rigidity. Second, the background from interactions in materials above L1 (thin support structures made by carbon fiber and aluminum honeycomb) has been estimated from simulation using Monte Carlo samples generated according to AMS flux measurements. The simulation of nuclear interactions has been validated with data using nuclear charge changing cross sections (Ne; Mg; Si; … → F þ X) [22] measured by AMS, as shown in Fig. S5 in Supplemental Material [15]. This background is estimated to be 14% at 2 GV, 18% at 100 GV, and 15% at 2.9 TV.
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 flux was measured in 49 bins from 2.15 GV to 2.9 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. [23]. 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, decreasing smoothly to þ5% at 10 GV, −4% at 100 GV, −10% at 300 GV, and −20% at 2.9 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 Monte Carlo 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.
The material traversed by nuclei from the top of AMS to L9 is composed primarily of carbon and aluminum. PHYSICAL REVIEW LETTERS 126, 081102 (2021) 081102-3 The survival probabilities of F nuclei due to interactions in the materials were evaluated using cosmic ray data collected by AMS as described in Ref. [22]. The systematic error due to uncertainties in the evaluation of the inelastic cross section is < 3% up to 100 GV. Above 100 GV, the small rigidity dependence of the cross section from the Glauber-Gribov model [21] was treated as an uncertainty and added in quadrature to the uncertainties from the measured interaction probabilities [22]. The corresponding systematic error on the F flux is < 3% up to 100 GV and rises smoothly to 4% at 2.9 TV.
The rigidity resolution function for F has a pronounced Gaussian core characterized by width σ and non-Gaussian tails more than 2.5 σ away from the center [24]. 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% [24]. The resulting systematic error on the flux is less than 1% below 200 GV and smoothly increasing to 7% at 2.9 TV.
There are two contributions to the systematic uncertainty on the rigidity scale [23]. 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 [28]. The second systematic error on the rigidity scale arises from the magnetic field map measurement and its temperature corrections. The error on the F flux due to uncertainty on the rigidity scale is < 1% up to 200 GV and increases smoothly to 6.5% at 2.9 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 F flux including statistical and systematic errors is reported in Table SI in Supplemental Material [15] as a function of the rigidity at the top of the AMS detector. Figure 1(a) shows the F flux as a function of rigidityR with the total errors, the sum in quadrature of statistical and systematic errors. In this and subsequent figures, the data points are placed along the abscissa atR calculated for a flux ∝ R −2.7 [29]. For comparison, Fig. 1(a) also shows the AMS results on the boron flux [11]. As seen, at high rigidities, the rigidity dependences of the F and B fluxes are identical; at low rigidities, they are different. To examine the rigidity dependence of the F flux, the variation of the flux spectral index γ with rigidity was obtained in a model-independent way from over nonoverlapping rigidity intervals bounded by 7.09, 12.0, 16.6, 28.8, 45.1, 175.0, and 2900.0 GV. The results are presented in Fig. 1(b) together with the B spectral index [11].
As seen from Fig. 1(b), in the rigidity interval 175-2900 GV, the F spectral index is similar to the B spectral index. In particular, both fluxes harden above ∼200 GV.
To directly compare the rigidity dependence of the F flux with that of the light secondary cosmic ray B flux [11], the ratio of the F flux to the B flux, F/B, was computed and is reported in Table SII in Supplemental Material [15]. To establish the rigidity interval where the F and B fluxes may have identical rigidity dependence, the F/B flux ratio above 7 GV has been fit with  Figure 2 shows the AMS fluorine flux as a function of kinetic energy per nucleon E K together with earlier measurements [3][4][5][6][7]. Data from other experiments have been extracted using Ref. [30].
To compare the rigidity dependence of the F flux with that of the Ne, Mg, and Si primary cosmic ray fluxes, which have an identical rigidity dependence above 80.5 GV [13], the ratio of the F flux to the characteristic heavy primary Si flux, F/Si, was computed and is reported in Table SIII in Supplemental Material [15]. Figure S7 in Supplemental Material [15] shows the AMS F/Si flux ratio as a function of kinetic energy per nucleon together with earlier measurements [3][4][5][6][7]. Figure 3(a) shows the AMS F/Si flux ratio as a function of rigidity together with the AMS B/O flux ratio [11].
The variation with rigidity of the spectral index Δ of the F/Si flux ratio was obtained by fitting it with CðR=175 GVÞ Δ 1 ; R ≤ 175 GV; K together with earlier measurements [3][4][5][6][7]. For the AMS measurement, where Z, M, and A are the 19 9 F nuclear charge, mass, and atomic mass numbers, respectively.  [31] and the GALPROP-HELMOD model [2], respectively. (b) The AMS ½ðF=SiÞ=ðB=OÞ ratio as a function of rigidity with total errors. The solid blue curve shows the fit results of Eq. (5). As seen, the rigidity dependence of the F/Si and B/O flux ratios are distinctly different. Above 10 GV, the ½ðF=SiÞ=ðB=OÞ ratio can be described by a single power law ∝ R δ with δ ¼ 0.052 AE 0.007 (a 7σ difference from zero). of Eq. (4); see Supplemental Material [15] for details. Figure 3(a) also shows the AMS F/Si fit results with Eq. (4) together with the predictions of the cosmic ray propagation model GALPROP [31] and of the latest GALPROP-HELMOD model [2]  To compare the rigidity dependence of the F/Si flux ratio with the lighter secondary-to-primary B/O flux ratio in detail, the ½ðF=SiÞ=ðB=OÞ ratio was computed and shown in Fig. 3(b). Over the entire rigidity range, ½ðF=SiÞ=ðB=OÞ can be fitted with The fit yields k ¼ 0.39 AE 0.01, R 0 ¼ 9.8 AE 0.9 GV, δ l ¼ −0.055 AE 0.013, and δ ¼ 0.052 AE 0.007 with χ 2 =d:o:f: ¼ 24=45. As seen, the rigidity dependences of the F/Si and B/O flux ratios are distinctly different. Most importantly, the latest AMS result shows that above 10 GV the ½ðF=SiÞ=ðB=OÞ ratio can be described by a single power law ∝ R δ with δ ¼ 0.052 AE 0.007 (a 7σ difference from zero). This shows, unexpectedly, that the heavier secondary-to-primary F/Si flux ratio rigidity dependence is distinctly different from the lighter B/O (or B/C) rigidity dependence, indicating that the propagation properties of heavy cosmic rays, from F to Si, are different from those of light cosmic rays, from He to O. As shown in Fig. S8 in Supplemental Material [15], the ½ðF=SiÞ=ðB=OÞ ratio does not change with time below 20 GV; i.e., solar modulation on the ½ðF=SiÞ=ðB=OÞ ratio does not affect the fit results with Eq. (5).
From the results of Eq. (5) and of the Si/O flux ratio rigidity dependence above 86.5 GV [13], we expect F=B ¼ ½ðF=SiÞ=ðB=OÞ × ðSi=OÞ ∝ R 0.012AE0.013 or that F/B is compatible with a constant at high rigidities, > 86.5 GV. This is indeed what is observed, as shown in Fig. 1(c). Figure 4 shows the rigidity dependence of the F flux together with the rigidity dependence of the two primary classes He, C, and O and Ne, Mg, and Si and the rigidity dependence of the light secondary Li, Be, and B cosmic ray fluxes above 30 GV [11]. As seen, the rigidity dependence of the F flux is different from the rigidity dependence of Li, Be, and B. This shows that the secondary cosmic rays also have two classes but that the rigidity dependence of the two secondary classes is distinctly different from the rigidity dependence of the two primary classes.
In conclusion, we have presented the precision measurement of the F flux as a function of rigidity from 2.15 GV to 2.9 TV, with detailed studies of the systematic errors. The fluorine spectrum deviates from a single power law above 200 GV. The heavier secondary-to-primary F/Si flux ratio rigidity dependence is distinctly different from the lighter B/O (or B/C) rigidity dependence. In particular, above 10 GV, the ½ðF=SiÞ=ðB=OÞ ratio can be described by a power law R δ with δ ¼ 0.052 AE 0.007, revealing that the propagation properties of heavy cosmic rays, from F to Si, are different from those of light cosmic rays, from He to O. This shows that the secondary cosmic rays also have two classes but that the rigidity dependence of the two secondary classes is distinctly different from the rigidity dependence of the two primary classes. These are new and unexpected properties of 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 Johnson Space Center (JSC) and Marshall Space Flight Center (MSFC) flight control teams that have allowed AMS to operate optimally on the ISS for over nine years. We are grateful for the support of Jim Siegrist, Glen Crawford, and their staff of the DOE including resources from the National Energy Research Scientific Computing Center under Contract No. DE-AC02-05CH11231. We gratefully acknowledge the strong support from CERN including Fabiola Gianotti, and the CERN IT department including Bernd Panzer-Steindel, and from the European Space Agency including Johann-Dietrich Wörner and Simonetta Di Pippo. We also acknowledge the continuous support from MIT and its School of Science, Michael Sipser, and the Laboratory for Nuclear Science, Boleslaw Wyslouch. Research supported by Chinese Academy of Sciences, Institute of High Energy