**4. The galactic hydrogen, helium and heavier nuclei spectra**

As is the case for electrons, the interpretation of the Voyager measured LIS intensities of hydrogen, helium and heavier nuclei at low energies, and with no solar modulation, may be compared with the higher energy measurements from PAMELA or AMS-2 where the modulation becomes small. This provides a fulcrum of ~105 in energy to examine the spectra of the various nuclei. This is best done by examining the intensity ratios such as H/He, He/C, etc., along with the intensities themselves. Most of the measurements are in E/nuc, whereas the source spectra appear to be rigidity spectra so there is always a factor of at least β in converting from one representation to the other.

We begin this section by examining the spectra of H and He nuclei. **Figure 7** shows the ratio of intensities of H and He nuclei measured at Voyager at energies less than a few hundred MeV/nuc [3] and those at AMS-2 [15, 16] at energies from ~1 GeV/nuc up to 1 TeV/nuc. The Voyager measurements are consistent with a constant ratio ~12.5, for H/He from ~10 MeV/nuc to ~350 MeV/nuc. This might suggest very similar H and He spectra in this energy range. The AMS-2 measurements obtain an E/nuc ratio ~16 at ~10 GeV/nuc, decreasing at both high and low energies. The decrease in this ratio at high energies where solar modulation effects are small, indicates different spectra for H and He nuclei, with a spectral index difference of between −0.10 and − 0.12 for either E/nuc or P spectra since at these high energies β→1.0. At lower energies the AMS-2 H/He (E) ratio decreases and reaches a value ~8 at 1 GeV/nuc. This is due to solar modulation effects. So the main goal of this study is to match the nearly constant LIS H/He (E) ratio of 12.5 measured by Voyager below ~300 MeV/nuc to the ratio of 16 measured at ~10–20 GeV/nuc by AMS-2.

These differences in ratios per E/nuc between a few hundred MeV/nuc and a few GeV/nuc immediately suggest a β dependence is involved and therefore when comparing ratios, source spectra as a function of rigidity is the appropriate parameter. We have found this to be the case in most comparisons of spectra of nuclei, particularly with different A/Z. So we now consider how the differences described above could be understood more simply in terms of source rigidity spectra. We assume that the source spectra of H and He nuclei are the same at rigidities below ~10 GV and can be represented by the formula.

$$\text{dj/d} \text{P} \text{-} \text{P}^{\text{-}6} \tag{1}$$

where we let S vary from −2.20 to −2.28 noting that we have already found that lower rigidity electrons are well described with a spectral index ~ − 2.25 below ~10 GV.

The three solid black curves on **Figure 7** show the calculated H/He ratios after propagation in a LBM using source rigidity spectra for protons with S = −2.20, 2.24 and 2.28 all normalized to the Voyager measured value of 12.5 at 100 MeV/nuc. For the calculated curves above ~10 GV, we use a normalization to the AMS-2 measured ratios and with a source spectra index = −2.36 for

separation of leptons and protons could be going on throughout cosmic time, even stronger at earlier times, and as a result influence our interpretation of the expansion of the Universe.

**Figure 7.** Ratios of hydrogen to helium nuclei intensities as a function of E/nuc as measured by Voyager between 10 and

As is the case for electrons, the interpretation of the Voyager measured LIS intensities of hydrogen, helium and heavier nuclei at low energies, and with no solar modulation, may be compared with the higher energy measurements from PAMELA or AMS-2 where the modu-

various nuclei. This is best done by examining the intensity ratios such as H/He, He/C, etc., along with the intensities themselves. Most of the measurements are in E/nuc, whereas the source spectra appear to be rigidity spectra so there is always a factor of at least β in convert-

We begin this section by examining the spectra of H and He nuclei. **Figure 7** shows the ratio of intensities of H and He nuclei measured at Voyager at energies less than a few hundred MeV/nuc [3] and those at AMS-2 [15, 16] at energies from ~1 GeV/nuc up to 1 TeV/nuc. The Voyager measurements are consistent with a constant ratio ~12.5, for H/He from ~10 MeV/nuc to ~350 MeV/nuc. This might suggest very similar H and He spectra in this energy range. The AMS-2 measurements obtain an E/nuc ratio ~16 at ~10 GeV/nuc, decreasing at both high and low energies. The decrease in this ratio at high energies where solar modulation effects are small, indicates different spectra for H and He nuclei, with a spectral index difference of

in energy to examine the spectra of the

**4. The galactic hydrogen, helium and heavier nuclei spectra**

lation becomes small. This provides a fulcrum of ~105

ing from one representation to the other.

350 MeV/nuc and by AMS2 [10, 15] above 1 GeV/nuc.

70 Cosmic Rays

**Figure 8.** The LIS H/He (P) ratio as a function of rigidity. The data above ~8 GV where the solar modulation of this ratio is small is from AMS-2 [16].

protons, keeping the source spectral index at −2.24 for He nuclei. When a solar modulation of 10–20% in the H/He ratio at about 10 GV is included, a spectral index of −2.24 for both H and He nuclei gives the best fit at low energies along with that for a proton index of −2.36 at high energies and with a spectral break between 6 and 12 GV for protons.

~130 at low energies to about 27 at the highest energies. One might think that this observed ratio would be more or less constant if these nuclei had the same spectra, since they have the same A/Z ratio, etc., but it turns out that, when the actual intensities and spectral shapes are obtained from LBM propagation calculations [10], the observed He/C (E) ratios are reproduced with He and C rigidity spectra with a source spectral index ~ − 2.24 for both components, extending throughout the rigidity range from ~100 MV to ~1.0 TV and with a source

Galactic Cosmic Rays from 1 MeV to 1 GeV as Measured by Voyager beyond the Heliopause

http://dx.doi.org/10.5772/intechopen.75877

73

The reason for this is much like the case for electrons and protons, described earlier; it is mostly in the details of the LBM propagation, again in an overall simple LBM but with certain modifications at small matter path lengths, due possibly to the local distribution of the cosmic ray sources themselves. This modification (truncation) is perhaps the only significant departure from the incredible symmetry imposed by the LBM that is yet discerned from the

It has been possible to extend the earlier Voyager intensity and spectral measurements which were generally in the range 10–200 MeV/nuc [3] up to the GeV/nuc range and above [4]. This technique uses the precision measurement of ionization loss for particles that penetrate the 3 element total energy counters. The spectra of He, C, O, Mg, Si and Fe are obtained in this way

Spectra for these nuclei, including the lower energy Voyager measurements [3], are shown in **Figure 10**. The intensities are all normalized at 1.5 GeV/nuc. There is a dramatic charge dependence of the spectral shape that becomes more obvious at the lower energies. It is believed that these different charges have very similar and possibly identical source rigidity spectra. This identity of source spectra has been determined in the above section for He and C nuclei. In spite of the large dependence of the He and C ratio on energy which, changes from a value ~130 at 10 MeV/nuc to 27 at 1 TeV/nuc where AMS-2 measurements are available, the source

Most of the changes in the measured intensity ratios in **Figure 10** are due to the effects of propagation in the galaxy. The curves in **Figure 10** show these effects vividly. There is a Z dependent effect which becomes more prominent at the lower energies. Two sources of these

The ionization energy loss is particularly important at the lower energies because of the 1/β<sup>2</sup> dependence, but even these ionization loss effects cannot account fully for the Z dependent turnovers of the differential spectra at lower energies. These differential spectra are observed to have maxima which systematically increase from ~30 MeV/nuc for He to ~100 MeV/nuc for Fe. The explanation for this large Z dependence in the maximum energies includes ionization

/β<sup>2</sup>

, and (2) fragmenta-

Voyager studies to date. The details of the He/C ratio study are found in [18].

**5. Spectral shapes of different nuclei at low energies**

up to 1.5 GeV/nuc, with an integral intensity at higher energies [4].

effects are, (1) ionization energy loss in interstellar matter which is Z<sup>2</sup>

energy loss but also includes the effect described as truncation (see below).

tion collisions which are proportional to a A1/3 dependence of these cross sections.

spectra of both He and C nuclei are found to be ~P−2.24.

abundance He/C ratio = 23.7.

The resulting H/He source ratio as a function of rigidity is very interesting. For this ratio we use the directly measured AMS-2 H/He (P) ratio above ~8 GV [16] as is shown in **Figure 8**. This ratio is ~3.5 at the highest rigidities increasing to ~6.0 at 8 GV. At lower rigidities the source ratio must become a constant because both H and He nuclei have identical rigidity spectra. This constant value depends on the exact details of the break, but we estimate the constant ratio of intensities at low rigidities to be between 6.0 and 6.5.

This ratio has important implications for the relative H and He abundances in the region where the main cosmic ray acceleration occurs. In terms of nucleons the ratio of 6.5 gives 63% protons and 37% Helium nucleons. The cosmological value in the case of big bang nucleosynthesis is usually taken to be ~76% protons and 24% Helium nucleons. Certainly interesting.

We now turn our attention to the comparison of the He and C spectra, again using a comparison of Voyager data on this ratio [3], which in this case extends up 1.5 GeV/nuc [4] and the AMS-2 data above 10 GeV/nuc [16, 17] where the solar modulation is small. The observed He/C (E) ratio from a few MeV/nuc to ~1 TeV/nuc is shown in **Figure 9**. It is seen to vary from

**Figure 9.** Observations and measurements of the He/C ratio between 3 MeV/nuc and 10<sup>3</sup> GeV/nuc. Errors on individual GeV/nuc voyager measurements are ±5%. Errors on AMS-2 measurements are less than ±2%. Black curve, labeled P0 = 0.562\*, is for a truncated exponential PLD with mean path length = λ = 20.6 β P−0.45 Above P0 = 0.562 and with truncation parameters = 0.04 for He and 0.12 for C. The curve labeled P<sup>0</sup> = 0.562 is for a simple LBM with a PLD = exponential at all path lengths for P0 = 0.562 GV. Dashed blue line is GALPROP calculation of the He/C ratio from [3].

~130 at low energies to about 27 at the highest energies. One might think that this observed ratio would be more or less constant if these nuclei had the same spectra, since they have the same A/Z ratio, etc., but it turns out that, when the actual intensities and spectral shapes are obtained from LBM propagation calculations [10], the observed He/C (E) ratios are reproduced with He and C rigidity spectra with a source spectral index ~ − 2.24 for both components, extending throughout the rigidity range from ~100 MV to ~1.0 TV and with a source abundance He/C ratio = 23.7.

The reason for this is much like the case for electrons and protons, described earlier; it is mostly in the details of the LBM propagation, again in an overall simple LBM but with certain modifications at small matter path lengths, due possibly to the local distribution of the cosmic ray sources themselves. This modification (truncation) is perhaps the only significant departure from the incredible symmetry imposed by the LBM that is yet discerned from the Voyager studies to date. The details of the He/C ratio study are found in [18].
