RELATIVE COMPOSITION AND ENERGY SPECTRA OF LIGHT NUCLEI IN COSMIC RAYS: RESULTS FROM AMS-01

In order to reject events with large nuclear scattering or poorly reconstructed trajectories, a set of quality cuts was applied to the selected candidates as follows.

• 1.  
  Tracks fitted with large χ² were discarded according to a rigidity-dependent requirement on Q = χ²/f(R), where R is the measured rigidity.
• 2.  
  The particle rigidity was measured as R₁ (R₂) using the first (last) three hits along the reconstructed track. Tracks with poor agreement between R, R₁, and R₂ were removed according to cuts on A₁ = (R₁ − R)/R and A₂ = (R₂ − R)/R.
• 3.  
  Consistency between β and R measurements was required. This cut acted on the tails of the reconstructed mass distributions of the detected particles.
• 4.  
  Silicon planes with no hit associated with the track were inspected in the region around the track extrapolation. The absence of additional hits was required within a distance d of 2 mm from the track extrapolation.

As an indicator of mismeasured particles, a fraction of ∼4% of events with negative measured rigidity (R < 0) was found in the reconstructed data before applying the selection cuts. These events were used as a control sample to define the selection. The total selection efficiency was found to be substantially charge independent over the whole energy range considered. In Figure 2, the distributions of some quantities that were used for the selection are shown for boron and carbon in comparison with the Monte Carlo (MC) simulation. The agreement between data and MC simulation in general is good; in the tails of the distributions, especially A₂, the MC simulation is less accurate in describing the measured behavior (some few percent of the sample). However, these features have similar magnitudes for the considered species and on average cancel out in the ratio, as shown in the lower panels of the figure. Similar conclusions can be drawn for the ratios Li/C and Be/C.

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Each elemental species is identified by its charge Z. The dynamical response of the TOF scintillators allowed particle discrimination up to Z = 2. The analysis of particle charge for Z>2 events was performed by the study of the energy losses recorded in the silicon layers. The ionization energy generated by a charged particle in a silicon microstrip detector was collected as a cluster of adjacent strips. Tracker clusters were recognized online and then reprocessed with the reconstruction software. A multistep procedure of normalization of the cluster signals was performed (Tomassetti 2009). The method accounted for saturation effects, electronics response, particle inclination, and velocity dependence of the energy loss. The charge identification algorithm, applied to the corrected signals, was based on the maximum likelihood method which determines the most likely value of Z corresponding to the maximum value of the log-likelihood function:

$$\begin{equation} L(Z) = \log _{10}\lbrace \prod _{k=1}^{k=6}P_{Z}^{k}(x_{k},\beta)\rbrace. \end{equation} \tag{ 1 }$$

The k-index refers to the six silicon layers, x_k are the corrected cluster signals as observed in the kth layer. The normalized P^k_Z(x_k, β) functions are the probabilities of a given charge Z with velocity β to produce a signal x_k in the kth layer. These probability density functions were estimated with a high-purity reference sample of flight data, and describe the energy-loss distributions x_k around a mean value μ_Z,β ∝ (Z²/β²)log(γ) as expected by the Bethe–Bloch formula. This β–Z dependence is shown in Figure 3 for Z = 3–8 (dashed lines) superimposed on the mean energy deposition from the measured tracker signals. Due to inefficiencies in charge collection, some energy losses may produce charge responses which do not carry reliable information on the particle charge. For this reason, not all the six clusters were used to determine Z. For each reconstructed track, the most reliable set of three clusters Ω = {k₁, k₂, k₃} was selected by also using Ω as a parameter of log likelihood function:

$$\begin{equation} L(Z,\Omega) = \log _{10}\big\lbrace P_{Z}^{k_1}\cdot P_{Z}^{k_2}\cdot P_{Z}^{k_3} \big\rbrace, \end{equation} \tag{ 2 }$$

where the free parameters to be determined are Z, ranging from 3 (lithium) to 8 (oxygen), and Ω, running over all the three-fold combinations {k₁, k₂, k₃} of the tracker signals. Though the final estimation of Z was provided by three tracker clusters, all the selected clusters were processed in Equation (2). An identification inefficiency of a few percent was achieved with this algorithm. On the basis of the final charge spectrum shown in Figure 4, the determination of B and C was done with a charge resolution better than 0.14 charge units.

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The charge assignment procedure was studied in terms of efficiency and contamination. Each nucleus of charge 3 ⩽ Z ⩽ 8 produces a charge estimation $\hat{Z}$ which can be related to its true impinging charge Z by using a set of coefficients $F_{Z}^{\hat{Z}}$.

The 6 × 6 matrix ||F|| is diagonally dominated, and each off-diagonal element $F_{Z}^{\hat{Z}}$ represents the probability of a nuclear species Z to be misidentified as $\hat{Z}$ due to interactions in the detector material and fluctuations of the energy loss:

$$\begin{equation} F_{Z}^{\hat{Z}}=P(\hat{Z}|Z). \end{equation} \tag{ 3 }$$

Two different contributions produce a charge migration $Z\rightarrow \hat{Z}$.

• 1.  
  After interacting in the upper TOF material, an incoming nucleus Z may fragment and physically turn into $\hat{Z}$. These events were typically rejected by the anticoincidence veto. However, a fraction of them produces a clean track in the tracker, passing trigger and selection. Since $\hat{Z} < Z$, the corresponding matrix is triangular.
• 2.  
  Fluctuations of the measured energy loss produce a nonzero $Z\rightarrow \hat{Z}$ migration probability. This charge spillover is typically symmetric and in most cases comes from adjacent charges, i.e., $\hat{Z}=Z\pm 1$.

Both the effects were studied with MC simulations. The second contribution was also estimated with the data. Possible charge migrations from/to the Z < 3 and Z>8 species were also considered, in particular to achieve a suitable separation of the Z>2 candidates from the background of the more abundant helium flux. Helium–lithium separation was performed with the combination of both TOF and tracker energy depositions and studied with the help of data from the calibration beam test during which the detector was probed with pure helium beams at 0.75, 1.8, 3.6, and 8 GeV nucleon⁻¹ of kinetic energy (Aguilar et al. 2002). Contamination from He to the selected Z>2 sample was estimated to be less than 10⁻⁴ of the helium sample. The effects of charge misassignment in the measured secondary-to-primary ratios turned out to be smaller than the statistical uncertainties; this effect is included in the systematic errors (Section 4.3).

By the term exposure time ΔT^Z(E), we mean the effective data taking duration with AMS-01 capable of receiving a new trigger from a galactic particle of charge Z in the energy interval ΔE. The detection is influenced by the trigger livetime fraction α and the geomagnetic field modulation. Though no atmospheric or trapped particles are expected in our Z>2 fluxes, the position-dependent geomagnetic cutoff introduces different distortions of the measured energy spectrum for different nuclear species. Hence, only particles with rigidity greater than R^Th = 1.25 · R_C were accepted, where R_C is the rigidity cutoff obtained from the Störmer estimation in the corrected geomagnetic coordinates for 1998 (Smart & Shea 2005). The entire orbit was divided into 45,000 time intervals of $\delta t \sim 10\,\rm s$. For each time bin δt_k, the mean values of R^Th_k and α_k (trigger livetime fraction) were computed. The exposure time ΔT^Z(E) was then calculated for each particle Z, rigidity R, and energy E ∈ ΔE as

$$\begin{equation} \Delta T^{Z}(E)= \sum _{k} \alpha _{k} \cdot H^{Z}_{k}\big(R,R_{k}^{{\rm Th}}\big) \cdot \delta t_{k}, \end{equation} \tag{ 5 }$$

where $R= \left(\frac{A}{Z} \right) \sqrt{E^{2}+ 2M_{p}E}$, H = 1 for R>R^Th, and H = 0 for R < R^Th, i.e., the sum is restricted to only the time intervals above cutoff. The result describes the effective exposure of AMS-01 to CRs in that energy bin coming from outside the magnetosphere. Note that ΔT^Z(E) as a function of the kinetic energy per nucleon is different for different A/Z isotopes; since A/Z is slightly different for the elements under consideration, their corresponding exposure times do not completely cancel in the flux ratios.

The detector acceptance A^Z(E) of Equation (4) is the convolution of geometrical factors with the energy-dependent efficiency , including trigger, reconstruction, and selection efficiencies. The acceptances of each species A^Z were determined with the MC simulation (Sullivan 1971). 2 × 10⁸ trajectories were generated in the energy range 0.2–50 GeV nucleon⁻¹, according to an isotropic distribution and a power-law momentum distribution ∝p⁻¹. The recorded MC simulation events were sent through the same analysis chain as for the measured data. Background fluxes were also simulated, up to Z = 8.

Though systematic uncertainties arising from many steps of the analysis are suppressed in the ratios, differences in the trigger efficiencies of the two species are present, as expected, from the charge dependence of delta ray production and fragmentation effects in the detector material. The spillover from adjacent charges also produces net effects on the measurements.

The MC simulation determination of the acceptance gave a statistical uncertainty of ∼1%–4%, increasing with energy. A^Z(E) decreases with increasing energy and charge, due to the trigger conditions against interacting particles. In the events collected from the flight, the dedicated unbiased data set⁴⁴ did not give enough statistics for an energy-dependent validation of the Z>2 trigger efficiency with the measured data; hence, this estimation must rely on simulation results. Since CR interactions with the detector material can play an important role in the observed behavior of the trigger response, a GEANT3-based MC simulation does not guarantee a model-independent description of the experimental setup. Therefore, this study was performed with three different models. A Virtual MC application (Hrivnacova et al. 2003) was developed for AMS-01. The simulation natively supports the particle transport codes GEANT3 and GEANT4 (Agostinelli et al. 2003). An additional interface with FLUKA (Fassò et al. 2005) was developed (Oliva 2007; Tomassetti 2009). Since the quantities that enter into our measurements are the ratios η_T between the corresponding acceptances A^Li/A^C, A^Be/A^C, and A^B/A^C, the systematic errors on the trigger efficiency were estimated observing the scatter between the three different models. Results of this approach are summarized in Figure 6. From the figure the charge-dependent behavior of the trigger response is clear; the energy dependence of the trigger efficiency is more pronounced for higher charges. Good agreement was found between GEANT4 and FLUKA; nevertheless, for each ratio, the full envelope of the three model curves was considered as the uncertainty band of the trigger efficiency.

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Another source of uncertainty comes from the isotopic composition of the measured nuclei. In order to compute bin-to-bin ratios, all the elemental fluxes were determined in a common grid of kinetic energy per nucleon E. The rigidity to energy conversion required the A/Z ratio of each charged species. To first approximation A/Z ≈ 2 for the light Z>2 nuclei under study; however, according to existing measurements and model calculations, more realistic isotopic mixtures can be considered for the Li–Be–B group (Hams et al. 2004; Ahlen et al. 2000; Webber et al. 2002; Buffington et al. 1978). Hence, we assumed isotopic fractions ⁶Li/(⁶Li +⁷Li) =0.5 ± 0.15, ⁷Be/(⁷Be +⁹Be) =0.65 ± 0.15, and ¹⁰B/(¹⁰B +¹¹B) =0.35 ± 0.15, accounting for these uncertainties in the estimation of the systematic error. In the left panels of Figure 7, we cross-checked our measured ratios with independent measurements obtained with the TOF system, which provided a direct measurement of the velocity and hence kinetic energy per nucleon. Results from the tracker measurement and the TOF measurement are consistent. The right panels of Figure 7 show the reconstructed mass distributions for the Li–Be–B events above cutoff with β < 0.95. Though the AMS-01 mass resolution did not allow an event-to-event isotopic separation, the data are in good agreement with the MC simulation which contains the assumed mixtures.

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A detailed summary of the uncertainties on the measured ratios Li/C, Be/C, and B/C is presented in terms of relative errors in Figure 8. The sources of uncertainties taken into account are the statistics of collected events, MC simulation statistics, contamination due to charge misidentification (Section 3.3), uncertainty on isotopic composition, and trigger efficiency uncertainty.

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A composition fit technique for determining the isotopic ratio ⁷Li/⁶Li in four rigidity intervals between 2.5 and 6.3 GV was performed (Zhou 2009). The best fits were obtained by leaving the amplitudes for both isotopes free in all four rigidity intervals as shown in Figure 9. The fits gave unique minima for the ⁷Li/⁶Li ratios in each rigidity region, providing an average ratio of 1.07 ± 0.16 in the region 2.5–6.3 GV. The results are shown in Figure 10 with the previous experimental data (De Nolfo et al. 2003; Webber et al. 2002; Hams et al. 2004; Ahlen et al. 2000; Webber & Kish 1979; Buffington et al. 1978); the latter are converted into units of rigidity, allowing a direct comparison with our data. Point values are listed in Table 1. Our measurement agrees with the previous data and extends them to higher energies. In summary, our new measurements of ⁷Li/⁶Li extends to 6.3 GV of rigidity (∼2 GeV nucleon⁻¹ of kinetic energy) with a constant ratio of about equal abundance of both isotopes.

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Results for the Li/C, Be/C, and B/C ratios are presented in Figure 11 with the existing experimental data (Webber et al. 1972; Orth et al. 1978; Lezniak & Webber 1978; Engelmann et al. 1990; Ahn et al. 2008; De Nolfo et al. 2003).

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The energy range 0.35–45 GeV nucleon⁻¹ is limited by selection inefficiencies below ∼0.35 GeV nucleon⁻¹ and the lack of statistics above 45 GeV nucleon⁻¹. The error bars in the figure represent the sum in quadrature of statistical errors with the systematic uncertainties. These results are summarized in Table 2.

Our B/C ratio measurement agrees well with the results from the first flight of CREAM in 2004 (Ahn et al. 2008) and with the data collected by HEAO-3-C2 (Engelmann et al. 1990) from 1979 October and 1980 June. The Be/C ratio is consistent, within errors, with the HEAO data, but not with balloon data Orth et al. (1978). Our Li/C data have unprecedented accuracy in a poorly explored energy region. In comparison with balloon data from Orth et al. (1978), our data indicate a quite different trend in the high-energy part of the Li/C ratio.

In these ratios, the main progenitors of boron nuclei are primary CRs (CNO). In contrast, the abundances of Li and Be also depend on secondary progenitors Be and B through tertiary contributions such as B→Be, Be→Li, and B→Li.

However, the observed shapes of the measured ratios Li/C and Be/C suggest their suitability in constraining the propagation parameters: their decreasing behavior with increasing energy is a direct consequence of the magnetic diffusion experienced by their progenitors, while the characteristic peak around ∼1 GeV nucleon⁻¹ is a strong indicator of low-energy phenomena like stochastic reacceleration or convective transport with the galactic wind.

For the sake of completeness, in Figure 12 and Table 3 we report the secondary-to-secondary ratios Li/Be, Li/B, and Be/B. Though their values can be derived from the secondary-to-primary ratios of Table 2, a dedicated analysis of uncertainty was done for these channels. These quantities are less sensitive to the propagation parameters because all the secondaries have the same origin and undergo similar astrophysical processes. These ratios are also found to be less influenced by solar modulation. Hence, these relative abundances maximize the effects of the nuclear aspects of the CR propagation: decays, fragmentations, and catastrophic losses. As pointed out in Webber & Soutoul (1998), the Be/B ratio is sensitive to the radioactive decay of the beryllium (numerator) which enriches the boron flux (denominator); thus, a precise measurement of the Be/B ratio provides constraints on the galactic halo size as well as the ¹⁰Be/⁹Be ratio. The observed increasing behavior of the Be/B ratio is due to the relativistic lifetime dilation of the unstable Be. However, the migration ¹⁰Be→¹⁰B involves only a small fraction of the elemental flux, and the present data are still affected by sizeable errors.

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To describe our results, we made use of GALPROP v50.1p,⁴⁵ a numerical code that incorporates all the astrophysical inputs of the CR galactic transport (Strong & Moskalenko 1998). We described the propagation in the framework of the diffusive-reacceleration model, which has been very successful in the description of the CR nuclei fluxes (Moskalenko et al. 2002). GALPROP solves the diffusion transport equation for a given source distribution and boundary conditions for all the galactic CRs. In this model, the magnetic diffusion is described in terms of a rigidity-dependent diffusion coefficient D = βD₀(R/R₀)^δ. The magnitude of the diffusion, related to the level of hydromagnetic turbulence, is controlled by the parameter D₀ which fixes the normalization of D(R) at the reference rigidity R₀. The spectral index δ is linked to the density of the magnetic irregularities at small scales. Reacceleration is an energy gain of charged particles due to scattering on hydromagnetic waves moving at Alfvén speed V_a in the ISM. This process is described as a diffusion in the momentum space and controlled by the parameter V_a. The source spectra q(R) are assumed to have a pure power-law dependence in rigidity, i.e., q(R) ∝ R^−α. The boundary conditions are expressed by imposing free escape at the galactic halo boundaries, in particular by the halo height H. Energy losses and catastrophic losses over the ISM are included. The code makes use of an up-to-date nuclear reaction network, including decay rates and fragmentation cross sections for all the relevant channels. Semi-empirical models for cross section calculations are tuned with the measured data, where available (Moskalenko & Mashnik 2003). Equilibrium solutions are provided for the local interstellar spectra (LIS) of all the galactic CRs. In our description, we used a 2D cylindrically symmetric model of the galaxy. For the heliospheric propagated fluxes, we adopted the force field description of the solar wind (Gleeson & Axford 1968). We used ϕ = 450 MV as the modulation parameter, consistent with 1998 June (Wiedenbeck et al. 2007). The parameter values of our GALPROP settings are listed in Table 4.

In Figures 11 and 12, our data are compared with the model calculation in the heliosphere (solid lines). The LIS ratios (dashed lines) are shown for reference. Our results for the B/C ratio, the Li/C ratio, and the ⁷Li/⁶Li isotopic fraction of Figure 10 are described quite well within the uncertainties. It is difficult, however, to accommodate the Li and B description with the Be/C ratio by means of only astrophysical parameters. Beryllium appears to be overproduced in the model by a factor of ∼10%–15 %. This discrepancy is also apparent in the previous measurements. The ratios Be/B and Li/Be in Figure 12 also indicate this feature, whereas the Li/B ratio is well described by our GALPROP tune.

It is worth noting that the production of Li and Be involves very complex reaction chains due to the multichannel character of the CR fragmentation. Moreover, cross sections for the tertiary processes LiBeB + ISM→LiBe are less well known than for the interactions CNO + ISM→LiBeB. Spallation contributions like ¹¹B→⁹Be are measured at only a few energy points. Other channels such as ¹⁰B→⁹Be, ^14,15N→⁹Be or ^10,11B→⁷Be are not measured at all and rely on extrapolated parameterizations (Moskalenko & Mashnik 2003). Spallation processes involving interstellar helium are even less well understood. The lack of cross section measurements limits the model predictions to uncertainties of ∼10%–20 % in the Li/C and Be/C ratios (De Nolfo et al. 2006). Understanding fragmentation is a key factor in establishing final conclusions concerning CR propagation.