Deciphering the Local Interstellar Spectra of Secondary Nuclei with the Galprop/Helmod Framework and a Hint for Primary Lithium in Cosmic Rays

The state-of-the-art propagation code GALPROP is widely employed for modeling of CRs and associated emissions from the Milky Way, and now has about 23 years of development behind it (Moskalenko & Strong 1998; Strong & Moskalenko 1998). The GALPROP code uses information from astronomy, particle, and nuclear physics to predict CRs, γ-rays, synchrotron emission and its polarization in a self-consistent manner—it provides the modeling framework unifying many results of individual measurements in physics and astronomy spanning in energy coverage, types of instrumentation, and the nature of detected species. The GALPROP code range of physical validity covers sub-keV—PeV energies for particles and from 10⁻⁶ eV—PeV for photons. Over the years the project has been widely recognized as a standard modeling tool for Galactic CR propagation and associated diffuse emissions (radio, X-rays, γ-rays). The GALPROP code is public and is extensively used by many experimental groups, and by thousands of individual researchers worldwide for interpretation of their data and for making predictions.

The key concept underlying the GALPROP code is that various kinds of data, e.g., direct CR measurements, $\bar{p}$, e^±, γ-rays, synchrotron radiation, and so forth, are all related to the same Galaxy and hence have to be modeled self-consistently (Moskalenko et al. 1998). The goal for the GALPROP-based models is to be as realistic as possible and to make use of available astronomical information, nuclear and particle data, with a minimum of simplifying assumptions (Strong et al. 2007).

The GALPROP code (Strong & Moskalenko 1998) solves a system of about 90 transport equations (time-dependent partial differential equations in 3D or 4D: spatial variables plus energy) with a given source distribution and boundary conditions for all CR species (¹H–⁶⁴Ni, $\bar{p}$, e^±). This includes convection, distributed reacceleration, energy losses, nuclear fragmentation, radioactive decay, and production of secondary particles and isotopes. The numerical solution is based on a Crank–Nicholson implicit second-order scheme (Press et al. 1992). The spatial boundary conditions assume free particle escape. For a given halo size the diffusion coefficient, as a function of momentum and propagation parameters, is determined from secondary-to-primary nuclei ratios, typically B/C, [Sc+Ti+V]/Fe, and/or $\bar{p}/p$. If reacceleration is included, the momentum-space diffusion coefficient D_pp is related to the spatial coefficient D_xx (=β D₀R^δ) (Seo & Ptuskin 1994), where δ = 1/3 for a Kolmogorov spectrum of interstellar turbulence or δ = 1/2 for an Iroshnikov–Kraichnan cascade, R is the magnetic rigidity.

The injection spectra of CR species are parameterized by the rigidity-dependent function:

$$\begin{eqnarray}&&q(R)\propto {\left(R/{R}_{0}\right)}^{-{\gamma }_{0}}\prod _{i=0}^{2}{\left[1+{\left(R/{R}_{i}\right)}^{\displaystyle \frac{{\gamma }_{i}-{\gamma }_{i+1}}{{s}_{i}}}\right]}^{{s}_{i}},\end{eqnarray} \tag{ 1 }$$

where γ_i=0,1,2,3 are the spectral indices, R_i=0,1,2 are the break rigidities, and s_i are the smoothing parameters (s_i is negative/positive for $| {\gamma }_{i}| \lessgtr | {\gamma }_{i+1}|$).

The GALPROP code computes a complete network of primary, secondary, and tertiary CR production starting from input source abundances. GALPROP includes K-capture, electron pickup, and stripping processes (Pratt et al. 1973; Wilson 1978; Crawford 1979), and knock-on electrons (Abraham et al. 1966; Berrington & Dermer 2003). Cross sections are based on the extensive LANL database, nuclear codes, and parameterizations (Mashnik et al. 2004; see also a compilation in Génolini et al. 2018). The most important isotopic production cross sections are calculated using our fits to major production channels (Moskalenko & Mashnik 2003; Moskalenko et al. 2003; Génolini et al. 2018). Other cross sections are computed using phenomenological codes (Silberberg et al. 1998; Webber et al. 2003) renormalized to the data where they exist. The nuclear reaction network is built using the Nuclear Data Sheets.

GALPROP calculates production of secondary particles in pp-, pA-, Ap-, AA-interactions. Calculations of $\bar{p}$ production and propagation are detailed in Moskalenko et al. (2002, 2003), and Kachelriess et al. (2015, 2019). Production of neutral mesons (π⁰, K⁰, ${\bar{K}}^{0}$, etc.), and secondary e^± is calculated using the formalism by Dermer (1986a, 1986b), as described in Moskalenko & Strong (1998), or recent parameterizations by Kamae et al. (2006), Kachelrieß & Ostapchenko (2012), and Kachelriess et al. (2014, 2019). γ-ray production and synchrotron emission are calculated using the propagated CR distributions, including primary e⁻, secondary e^±, and for γ-rays—including secondary p from inelastic processes (Strong et al. 2004, 2010; Porter et al. 2008; Orlando & Strong 2013).

More details on GALPROP, including the description of all involved processes and reactions, can be found in dedicated publications (Moskalenko & Jourdain 1997; Moskalenko & Strong 1998, 2000; Strong & Moskalenko 1998; Strong et al. 2000, 2004, 2007, 2010, 2011; Moskalenko et al. 2002, 2003, 2017; Ptuskin et al. 2006b; Vladimirov et al. 2011, 2012; Orlando & Strong 2013; Porter et al. 2017, 2019; Jóhannesson et al. 2018, 2019; Génolini et al. 2018).

The combined effects of the intense solar wind and solar magnetic field modify the local interstellar space and develop a bubble-like structure, known as the heliosphere, that surrounds the whole solar system. The heliosphere affects the propagation of CR particles up to ∼50 GV in rigidity and requires a dedicated modeling to understand all factors involved (see the discussion in Boschini et al. 2017). CR propagation in the heliosphere was first studied by Parker (1965), who formulated the transport equation also known as the Parker equation (see, e.g., discussion in Bobik et al. 2012, and references therein):

$$\begin{eqnarray}\begin{array}{rcl}\displaystyle \frac{\partial U}{\partial t} & = & \displaystyle \frac{\partial }{\partial {x}_{i}}\left({K}_{{ij}}^{S}\displaystyle \frac{\partial U}{\partial {x}_{j}}\right)\\ & & +\ \displaystyle \frac{1}{3}\displaystyle \frac{\partial {V}_{\mathrm{sw},i}}{\partial {x}_{i}}\displaystyle \frac{\partial }{\partial T}\left({\alpha }_{\mathrm{rel}}{TU}\right)-\displaystyle \frac{\partial }{\partial {x}_{i}}[({V}_{\mathrm{sw},i}+{v}_{d,i})U],\end{array}\end{eqnarray} \tag{ 2 }$$

where U is the number density of CR species per unit of kinetic energy T, t is the time, V_{sw, i} is the solar wind velocity along the axis x_i, K^S_ij is the symmetric part of the diffusion tensor, v_d,i is the particle magnetic drift velocity (related to the antisymmetric part of the diffusion tensor), and finally ${\alpha }_{\mathrm{rel}}=\tfrac{T+2{m}_{r}{c}^{2}}{T+{m}_{r}{c}^{2}}$, with m_r being the particle rest mass in units of GeV/nucleon. Parker's transport equation describes: (i) the diffusion of CR species due to magnetic irregularities, (ii) the so-called adiabatic-energy changes associated with expansions and compressions of cosmic radiation, (iii) an effective convection resulting from the convection with solar wind (SW, with velocity ${{\boldsymbol{V}}}_{\mathrm{sw}}$), and (iv) the drift effects related to the drift velocity (${{\boldsymbol{v}}}_{d}$).

The influence of heliospheric propagation on the spectra of CR species is called the solar modulation. Its overall effect leads to the suppression of the low-energy part in the spectra of CR species, while the amplitude of the suppression depends on the solar activity, particle charge sign, polarity of the solar magnetic field, and other conditions. In this work, the particle transport within the heliosphere is treated using the HelMod model (Boschini et al. 2019, and reference therein). The HelMod model, now version 4.0, numerically solves the Parker (1965) transport equation using a Monte Carlo approach involving stochastic differential equations (see a discussion in, e.g., Bobik et al. 2012, 2016). The particle transport within the heliosphere is computed from the outer boundary (i.e., the heliopause) down to Earth's orbit. In the latest version the actual dimensions of the heliosphere and its boundaries were taken into account based on Voyager 1 measurements (Boschini et al. 2019).

The heliopause (HP) represents the extreme limit beyond which solar modulation does not affect CR flux. Thus, the CR spectra measured by Voyager 1 outside HP are the truly pristine LIS of CR species.¹² Using Parker's model of the heliosphere (Parker 1961, 1963) combined with Voyager 1 observations, we were able to estimate the time dependence of positions of the termination shock (TS, R_TS) and the HP (R_HP) as (Boschini et al. 2019):

$$\begin{eqnarray}&&{R}_{\mathrm{TS}}={R}_{\mathrm{obs}}{\left(\displaystyle \frac{{\rho }_{\mathrm{obs}}{u}_{\mathrm{obs}}^{2}}{{P}_{\mathrm{ISM}}}\right)}^{\tfrac{1}{2}}{\left[\displaystyle \frac{\gamma +3}{2(\gamma +1)}\right]}^{\tfrac{1}{2}}.\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&\displaystyle \frac{{R}_{\mathrm{HP}}}{{R}_{\mathrm{TS}}^{{\prime} }}=1.58\pm 0.05,\end{eqnarray} \tag{ 4 }$$

where ρ_obs and u_obs are respectively plasma density and plasma velocity measured in situ at distance R_obs, P_ISM is the stagnation pressure discussed in Section 4 of Boschini et al. (2019), and γ = 5/3. ${R}_{\mathrm{TS}}^{{\prime} }$ is defined as the TS position at the time when it was left by the SW stream that is currently reaching the HP (for more details see Boschini et al. 2019); this typically takes about 4 yr, but depends on the SW speed. Therefore, the actual dimensions of the heliosphere used in HelMod-4 evolve with time. The predicted TS distances are in good agreement with those observed: for Voyager 1 (Voyager 2) the detected TS position is 93.8 au (83.6 au) and the predicted position is 91.8 au (86.3 au), i.e., within 3 au (<3.5% error). Regarding the HP, based on the R_HP observed by Voyager 1, the predicted R_HP at the time of the Voyager 2 crossing was 120.7 au, while in reality it is 119 au.

In the present code, particular attention is paid to the quality of description of the high solar activity periods, which is evaluated though a comparison of HelMod calculations and the CR proton data by Alpha Magnetic Spectrometer (AMS-02; Aguilar et al. 2018a), and to transitions from/to solar minima. This was achieved through introduction of a drift suppression factor and particle diffusion parameters, which depend on the level of solar disturbances (see a discussion in Boschini et al. 2019).

In 2011 the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) collaboration reported observation of a new break (hardening) in the spectra of the most abundant CR species, protons and He, above a rigidity of a few hundred GV (Adriani et al. 2011). This publication confirmed the hardening of the CR proton and He spectra found in earlier experiments, ATIC-2 (Wefel et al. 2008; Panov et al. 2009) and CREAM (Ahn et al. 2010; Yoon et al. 2011). Later, the break was also confirmed by the Fermi-LAT (Ackermann et al. 2014) and with much higher precision and statistics by AMS-02 (Aguilar et al. 2015a, 2015b). The break is smooth and observed at the same rigidity ∼300 GV for both species.

The interpretations of the break started to appear soon after the PAMELA publication. Perhaps the first was a paper by Vladimirov et al. (2012), which offered three distinctly different scenarios that can be tested through precise measurements of secondary species, such as secondary nuclei and $\bar{p}$, and anisotropy measurements. The proposed interpretations include (i) the "propagation" (P) scenario, where the observed break is the result of a change in the spectrum of interstellar turbulence that translates into a break in the index of the diffusion coefficient, (ii) the "injection" (I) scenario, where the break is due to the presence of populations of CR sources injecting particles with softer and harder spectra, and (iii) the "local source" scenario, where the local source injects low- (L-) or high-energy (H-scenario) particles with the spectrum that is correspondingly softer or harder than the rest of CRs produced by distant sources.

The P-scenario implies that the break should be observed in spectra of all CR species at about the same rigidity since the interstellar turbulence acts on all particles. Thus, the index of the rigidity dependence of the diffusion coefficient δ has to have a break at the same rigidity, where its values δ₁ below and δ₂ above the break are connected with the observed value of the break Δα in the spectral index of propagated primary species: δ₂ = δ₁ − Δα, where Δα = α₁ − α₂, and α₁ (α₂) is the observed spectral index of primaries below (above) the break. The observed spectrum of secondary species has an index ₁ = α₁ + δ₁ below the break and an index ₂ = α₂ + δ₂ = α₁ + δ₁ − 2Δα above the break. Therefore, the change in the spectral index of secondary species would be Δ = ₁ − ₂ = 2Δα, i.e., twice the value of the break observed in the spectra of primary species. This scenario also predicts an almost flat ratio $\bar{p}/p$ in the reacceleration model. Additionally, the index δ₂ of the rigidity dependence of the diffusion coefficient above the break becomes smaller and thus more consistent with CR anisotropy measurements (see a collection of data in Ptuskin et al. 2006a).

The I-scenario implies that the index of the diffusion coefficient has no break. Therefore, the change in the spectral index of secondary species would be the same as that for primaries: Δ = Δα. The break in the primary and secondary nuclei cancels when we take their ratio as, e.g., the B/C ratio that would be exactly the same if there were no break. In this scenario, the position of the break in the spectra of individual CR species may vary depending on the composition of CR sources injecting particles at low and high energies, while the predicted anisotropy would exceed the actual measurements; see also Malkov et al. (2012).

The local source scenario implies that the local source dominates in some part of the observed spectrum, at low (L-scenario) or high energies (H-scenario). Therefore, the amount of secondaries should drop significantly in the corresponding energy range since the freshly accelerated particles did not have time for fragmentation. A significant contribution of the local source at high energies (H-scenario) would also dramatically increase the CR anisotropy that may be in conflict with observations (Ptuskin et al. 2006a; Sveshnikova et al. 2013).

Vladimirov et al. (2012) concluded that the P-scenario is preferred, but the absence of reliable measurements of secondary species above a few hundred GV at that time did not allow us to distinguish between different options.

Interestingly, soon after that publication, Blasi et al. (2012) proposed a mechanism for the formation of the spectrum of interstellar turbulence. According to this model, the position of the break in the index of the diffusion coefficient corresponds to the case when the diffusive propagation is no longer determined by the self-generated turbulence, but rather by the cascading of externally generated turbulence (for instance, due to supernova bubbles) from large spatial scales to smaller scales. Independently, on the origin of the break in the spectrum of interstellar turbulence, this would also lead to the expression Δ = 2Δα. There are other more recent papers that apply various versions of the P-scenario to the available data (e.g., Génolini et al. 2017; Niu et al. 2019).

A subsequent release of the spectra of other primary and secondary species by AMS-02 was eagerly awaited. First, AMS-02 confirmed a clear distinction in the rigidity dependencies between the groups of mostly primary nuclei, He, C, O (Aguilar et al. 2017), and secondary nuclei, Li, Be, B (Aguilar et al. 2018c), while the nuclei within each group have similar spectra. Nitrogen that is half-primary/half-secondary fell in between (Aguilar et al. 2018b). The spectral index of the primary species, C, O, below/above the break is about α₁/α₂ ≈ 2.65/2.55, while for secondary species it is ₁/₂ ≈ 3.1/2.9. Here the indices below/above the break were taken at ≈50 GV/700 GV, where the solar modulation is negligible. One can see that the change in the spectral index of secondaries Δ ≈ 0.2 is double the change in the spectral index of primaries Δα ≈ 0.1, as predicted in the P-scenario (Vladimirov et al. 2012) long before the data on secondary species became available (Aguilar et al. 2018c). Note that because there are many different types of sources of CR electrons and positrons and due to the large energy losses of these particles, the spectra of electrons and positrons may behave quite differently and they indeed do so (Aguilar et al. 2019a, 2019b).

The results of our calculations in the I-scenario, the LIS of beryllium, boron, and nitrogen, are shown in Figures 3–5 and compared to the available data. A comparison of our calculations with data taken at different levels of solar activity and at different polarities of the solar magnetic field demonstrates overall good agreement, thus supporting our model approach.

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A moderate overprediction of 10%–20% (at 2–10 GV) is observed in the case of beryllium (Figure 4) when compared to AMS-02 data taken during the same period. Some overprediction (∼20%) is also observed when comparing to the Voyager 1 (Figure 3) and ACE/CRIS data (Figure 5), but in the latter cases it is at the level of ≲2σ. The overprediction in beryllium flux below a few GV is most likely connected with errors in the total inelastic cross sections of beryllium isotopes. The cross-section errors are most significant in the case of beryllium, and in particular, in the energy range below 10 GeV/n (see Figure 6 in Génolini et al. 2018).

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Other discrepancies, such as those reported in Figure 5 for beryllium, boron, and nitrogen when comparing to the HEAO-3 data (Engelmann et al. 1990), are an indication of the systematic uncertainties of the instrument. This is demonstrated by the excellent agreement of spectra of boron and nitrogen with AMS-02 data (Aguilar et al. 2018c) in the whole energy range from 2 GV-2 TV.

Our results for the I- and P-scenarios are shown in Figures 6–8. Since the spectral behavior of CR nuclei at low energies is the same in both scenarios (also in plots in our earlier papers Boschini et al. 2017, 2018b), the P-scenario calculations are only shown above ∼100 GV, where the effects of solar modulation can be safely neglected. Figure 6 shows the B/C ratio in the P-scenario together with AMS-02 data taken at different epochs. The flattening above ∼350 GV is clearly seen, but it is very moderate and agrees well with data.

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The spectra of all nuclei species, Be, B, C, N, O, calculated in both scenarios, are shown in Figures 7 and 8. In both cases the agreement with data is good. In the case of the P-scenario we use only the parameters γ_0,1,2 and R_0,1 from Table 1, while the break at ∼350 GV appears due to the break in the diffusion coefficient (Table 2).

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The effect of the local source producing low-energy CRs (L-scenario) on the observed composition of CRs and production of secondaries was studied in Moskalenko et al. (2003) and Vladimirov et al. (2012). In short, tuning to the observed secondary-to-primary ratio, such as B/C, would require a significant decrease in the normalization of the diffusion coefficient in order to compensate for the presence of locally produced primary species, such as C and O. This, in turn, would lead to an increase of the $\bar{p}/p$ ratio. However, a detailed exploration of this scenario is beyond the scope of this work.

A demonstrated good agreement of our model calculations with measurements of CR species in a wide energy range implies that lithium spectrum should also be well reproduced by the same model. However, a comparison of our calculations of secondary lithium with data exhibits a significant excess over the model predictions above a few GV (Figures 9 and 10) even though the propagation parameters are tuned to the B/C ratio. The additional secondary⁷Li cannot come from the decay of ⁷Be isotope in CRs that decay via K-capture. All GALPROP calculations are already run with the processes of electron pickup, stripping, and K-capture included. Therefore, this may indicate that some part of the observed lithium has a different origin.

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Meanwhile, a possibly connected puzzle is a long-standing problem of the origin of lithium observed in today's universe (e.g., Hernanz 2015). While some fraction of lithium was created in the primordial nucleosynthesis, most of the observed lithium is produced through interactions of energetic CR particles with interstellar gas (spallation reactions). On the other hand, the observed stellar lithium abundances indicate that some proportion of lithium is also produced in low-mass stars and nova explosions. Indeed, the alpha-capture reaction of ⁷Be production ³He(α, γ)⁷Be was proposed a while ago (Cameron 1955; Cameron & Fowler 1971). A subsequent decay of ⁷Be with a half-life of 53.22 days yields ⁷Li isotope. To ensure that produced ⁷Li is not destroyed in subsequent nuclear reactions, ⁷Be should be transported into cooler layers where it can decay to ⁷Li, the so-called Cameron–Fowler mechanism.

The production of ⁷Li in the same reactions in novae was first discussed by Arnould & Norgaard (1975) and Starrfield et al. (1978), while the details of the process were established later (Hernanz et al. 1996). The amount of ⁷Li produced by a classical CO nova corresponds to about 10⁻¹⁰ M_⊙–10⁻⁹ M_⊙, although the exact amount depends on many details of the explosion process.

Recent observation of blueshifted absorption lines of partly ionized ⁷Be in the spectrum of a classical nova V339 Del about 40–50 days after the explosion (Tajitsu et al. 2015) is the first observational evidence that the mechanism proposed in 1970s is working indeed (Hernanz 2015). The observed blueshift of the absorption lines corresponds to the velocity of the ejecta reaching 1100–1270 km s⁻¹. Consequent observations of other novae (V1369 Cen, Izzo et al. 2015; V5668 Sgr and V2944 Oph, Tajitsu et al. 2016; ASASSN-16kt [V407 Lupi], Izzo et al. 2018; V838 Her, Selvelli et al. 2018) also reveal the presence of ⁷Be lines in their spectra, indicating that classical novae are the new type of sources of ⁷Li. The total mass of produced ⁷Li in these novae is estimated from 10⁻⁹ M_⊙–6 × 10⁻⁹ M_⊙.

For our case this means that there is a source of primary lithium and that this lithium may be observed in CRs for the first time, thanks to the high statistics and precision achieved by the AMS-02 experiment (Aguilar et al. 2018c). Though the absolute mass of lithium produced by novae is relatively small, the lithium abundance of the ejecta is comparable to that found in CRs given that the total mass of the ejecta is 10⁻⁵ M_⊙–10⁻⁴ M_⊙. Such lithium-enriched ejecta could serve as a source of primary lithium that is subsequently accelerated in nova and SN shocks, thus supplying additional lithium to CRs.

We note that a similar mechanism was proposed by Kawanaka & Yanagita (2018) albeit with the rather extreme assumption that the spectral hardening observed above 300 GV is due to the local SN Ia. In this model most of the protons, He, and lithium above the break are coming from the local source. This is equivalent to the H-scenario originally considered in Vladimirov et al. (2012) and deemed unlikely, since it would lead to a dramatic increase in CR anisotropy at very high energies, contrary to the observations, and a sharp drop in the B/C ratio above the break that is not observed either (see also a discussion in Section 2.3).

Figure 10 shows a fit (I-scenario) where a small amount of primary ⁷Li was injected with parameters given in Table 1, in addition to the secondary lithium. The agreement with the AMS-02 data (Aguilar et al. 2018c) is significantly improved. A small discrepancy around 2 GV is still remaining that may indicate some unknown systematics. A calculation in the P-scenario looks similar and is not shown in this plot.

Our calculations of the lithium spectrum in the P-scenario shown in Figure 8 already contain primary ⁷Li that improves the agreement significantly. In this scenario, the injection spectrum of primary ⁷Li is the same as that in the case of the I-scenario (Table 1), but the parameter γ₃ is not used. This calculation illustrates that the P-scenario is consistent with all data available from AMS-02 and earlier experiments and seems like a natural explanation of the break in the spectra of all CR nuclei species observed at ∼350 GV. Note that the I-scenario provides a similar quality fit, but at the cost of additional parameters.

Another possible reason for this discrepancy is that the lithium production cross sections that we employ in our propagation code are incorrect. However, from the compilation of the production cross sections (Génolini et al. 2018), one can see that the major production channels are fragmentation of carbon and oxygen, ¹²C, ¹⁶O + p → ^6,7Li, that have been each measured in several different experiments. Even though they are not measured perfectly, each of them is contributing 12%–14% and thus a 20% error in one of them would correspond to only 2%–3% of total lithium production. Other production channels are contributing at a level of 1%–2% or less. It is not impossible, but rather unlikely that cross-section errors are all biased on the same side leading to the observed 20% excess.

Finally, one can see that the AMS-02 lithium data show a kink around ∼100 GV (Figure 10), while the error bars there are rather small. Such irregularity and the relatively large scattering of data points above this rigidity may be partially responsible for the excessive hardening of the lithium spectrum above ∼100 GV. Here we have to wait for further data releases, which should indicate if this kink is an instrumental artifact or a real spectral feature and also improve the statistics at high energies. Meanwhile, since the lithium excess is present even at lower energies, ≳4 GV, we believe that the effect is real, though the fitted values may change somewhat when the more accurate data become available.

The ultimate test of the origin of lithium in CRs would be a measurement of its isotopic composition at high energies. The nova origin of primary ⁷Li would lead to the dominance of ⁷Li at high energies, while at low energies the abundances of ⁶Li and ⁷Li are about the same. However, isotopic abundances are very difficult to measure at high energies and would require a large magnetic spectrometer with a superconducting magnet in space. The outlines of such future instruments are currently discussed in the literature (Schael et al. 2019), but building and launching them into space may take a couple of decades. We therefore should concentrate on elimination of other possibilities through new measurements of the production cross sections or reevaluation of the available data.