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

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 ener-

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

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].

gies and with a spectral break between 6 and 12 GV for protons.

72 Cosmic Rays

constant ratio of intensities at low rigidities to be between 6.0 and 6.5.

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

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

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 effects are, (1) ionization energy loss in interstellar matter which is Z<sup>2</sup> /β<sup>2</sup> , and (2) fragmentation collisions which are proportional to a A1/3 dependence of these cross sections.

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

LBM diffusion [19, 20], suggests the correct scenario is one in which most of these secondary

secondary nuclei. Their cross sections for production when the primary cosmic ray nuclei interact with atoms of H and He that are part of the interstellar medium are also quite well

With this as a background we show in **Figure 11** the Voyager measurements of the intensities and spectra of these three secondary nuclei. The calculated abundance for each nuclei is based on a LBM where the mean path length, λ = 20.6 β P−0.45 above P = 1.0 GV and a constant path

below 1.0 GV, and with a truncation parameter = 0.04.

These measurements make a convincing argument that the primary cosmic rays have gone

higher energies the measured B/C ratio may be used to determine the amount of matter traversed as a function of energy or rigidity. We have the V1 determination of the B/C ratio with zero solar modulation below ~1.5 GeV/nuc [4] and the AMS-2 determination of the ratio above ~3 GeV/nuc [17]. These measurements are shown in **Figure 12** along with the LBM propagation prediction using the parameters described in the above paragraph. The agreement is within ±10% from the lowest to the highest energies. Since this is a simple pure diffusion model, this high level of agreement at all energies implies that energy gain (reacceleration)

He and the charge B are the most abundant and well measured of the

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of interstellar matter between ~10 and 100 MeV/nuc (~0.3 to 0.9 GV). At

particles are produced during the extended time of a galactic diffusion process.

The isotopes 2

length = 9.0 g/cm2

through ~9 g/cm2

H and 3

known after years of systematic measurement.

**Figure 11.** A comparison of the measurements of 2

at energies from ~20 to 100 MeV/nuc.

7 and 9 g/cm2

H, 3

V1 and the predictions of the LBM for values of P<sup>0</sup> = 0.316, 0.562, 1.0 GV and a constant path length = 9 g/cm2

GV as described in the text. All three secondary isotopes are consistent with the predictions of a path length, λ, between

He and B nuclei intensities measured by the CRS experiment on

below 1.0

**Figure 10.** Observed relative intensities of He, C, O, Mg, Si and Fe nuclei between 100 and 1000 MeV/nuc. These intensities are normalized to the values of j at 1000 MeV/nuc for carbon nuclei. The figure includes lower energy intensities from [3].

In a perfect LBM for propagation in the galaxy where the sources are uniform and the propagation is effectively isotropic, the distribution of matter path length is an exponential at all path lengths with a mean path length which is ~ to the amount of matter traversed, e.g., in g/cm2 . At low energies where this ionization loss is large enough so that the particles cannot reach us from the nearest sources, the path length distribution becomes non-exponential or truncated at small path lengths. We believe that the different shapes of these spectra at the lowest energies are the best signature of this effect. A real example of this and other low energy propagation effects have been hidden from us previously by the solar modulation effects. The impenetrable fog of almost isotropic propagation on the study of the origin and acceleration of these particles and their role in the Universe in general may, in some small way, have been lifted by these new Voyager observations.

#### **6. Secondary cosmic rays and the mean path length in g/cm2 in the galaxy**

Isotopes such as 2 H and 3 He and charges such as Li, Be, B and so called Fe secondaries, Z = 21–23, are believed to have zero abundance in any possible cosmic ray source. They are therefore produced by interactions of primary cosmic rays such as He, C, O, Mg, Si and Fe, to name the most prominent, either by nuclear fragmentations the interstellar medium, or perhaps partly in or near the acceleration region itself. The presence of the radioactive decay secondary isotope 10Be with a half-life of only 1.5 × 10<sup>6</sup> years as compared with the average cosmic ray life-time of 1.5 × 107 years as determined from the observed 10Be abundance using LBM diffusion [19, 20], suggests the correct scenario is one in which most of these secondary particles are produced during the extended time of a galactic diffusion process.

The isotopes 2 H and 3 He and the charge B are the most abundant and well measured of the secondary nuclei. Their cross sections for production when the primary cosmic ray nuclei interact with atoms of H and He that are part of the interstellar medium are also quite well known after years of systematic measurement.

With this as a background we show in **Figure 11** the Voyager measurements of the intensities and spectra of these three secondary nuclei. The calculated abundance for each nuclei is based on a LBM where the mean path length, λ = 20.6 β P−0.45 above P = 1.0 GV and a constant path length = 9.0 g/cm2 below 1.0 GV, and with a truncation parameter = 0.04.

These measurements make a convincing argument that the primary cosmic rays have gone through ~9 g/cm2 of interstellar matter between ~10 and 100 MeV/nuc (~0.3 to 0.9 GV). At higher energies the measured B/C ratio may be used to determine the amount of matter traversed as a function of energy or rigidity. We have the V1 determination of the B/C ratio with zero solar modulation below ~1.5 GeV/nuc [4] and the AMS-2 determination of the ratio above ~3 GeV/nuc [17]. These measurements are shown in **Figure 12** along with the LBM propagation prediction using the parameters described in the above paragraph. The agreement is within ±10% from the lowest to the highest energies. Since this is a simple pure diffusion model, this high level of agreement at all energies implies that energy gain (reacceleration)

In a perfect LBM for propagation in the galaxy where the sources are uniform and the propagation is effectively isotropic, the distribution of matter path length is an exponential at all path lengths with a mean path length which is ~ to the amount of matter traversed, e.g., in

**Figure 10.** Observed relative intensities of He, C, O, Mg, Si and Fe nuclei between 100 and 1000 MeV/nuc. These intensities are normalized to the values of j at 1000 MeV/nuc for carbon nuclei. The figure includes lower energy intensities from [3].

Z = 21–23, are believed to have zero abundance in any possible cosmic ray source. They are therefore produced by interactions of primary cosmic rays such as He, C, O, Mg, Si and Fe, to name the most prominent, either by nuclear fragmentations the interstellar medium, or perhaps partly in or near the acceleration region itself. The presence of the radioactive decay secondary isotope 10Be with a half-life of only 1.5 × 10<sup>6</sup> years as compared with the average cosmic ray life-time of 1.5 × 107 years as determined from the observed 10Be abundance using

way, have been lifted by these new Voyager observations.

H and 3

**6. Secondary cosmic rays and the mean path length in g/cm2**

. At low energies where this ionization loss is large enough so that the particles cannot reach us from the nearest sources, the path length distribution becomes non-exponential or truncated at small path lengths. We believe that the different shapes of these spectra at the lowest energies are the best signature of this effect. A real example of this and other low energy propagation effects have been hidden from us previously by the solar modulation effects. The impenetrable fog of almost isotropic propagation on the study of the origin and acceleration of these particles and their role in the Universe in general may, in some small

He and charges such as Li, Be, B and so called Fe secondaries,

 **in the** 

g/cm2

74 Cosmic Rays

**galaxy**

Isotopes such as 2

**Figure 11.** A comparison of the measurements of 2 H, 3 He and B nuclei intensities measured by the CRS experiment on V1 and the predictions of the LBM for values of P<sup>0</sup> = 0.316, 0.562, 1.0 GV and a constant path length = 9 g/cm2 below 1.0 GV as described in the text. All three secondary isotopes are consistent with the predictions of a path length, λ, between 7 and 9 g/cm2 at energies from ~20 to 100 MeV/nuc.

longer with us. In fact the original "team of three" is without doubt the oldest scientifically productive team in history for a major experiment with an average age of 87.0 years. And Alan Cummings would have been part of the original team, except that he was a graduate student at the time of the 1st proposal. Now he is ready to retire, but, of course, nobody working on Voyager data would even think of that. And Nand Lal, the guru of the data system, has been around almost as long (have you ever tried the Voyager web site, http://voyager. gsfc.nasa.gov). There is no better one for any space experiment. And Bryant Heikkila, my former student, who can provide any data you need usually within 48-72 h real time, including the ~20 h light travel time to Earth. And last but not least, Tina Villa, who made this chapter

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possible.

**Author details**

William R. Webber

**References**

Address all correspondence to: bwebber@nmsu.edu

2010. Astrophysics Journal. 2010;**723**:L1

1968;**154**:1012

Department of Astronomy, New Mexico State University, Las Cruces, NM, USA

the Voyager spacecraft. Astrophysics. InTech; 2012. p. 309

chambers. Journal of Geophysical Research. 2011;**116**:A02104

[1] Webber WR. Energetic charged particles in the heliosphere from 1-120 AU measured by

[2] Stone EC, Cummings AC, McDonald FB, et al. Voyager 1 observes low-energy galactic

[3] Cummings AC, Stone EC, Heikkila BC, et al. Galactic cosmic rays in the local interstellar medium: Voyager 1 observations and model results. Astrophysics Journal. 2016;**831**:19

[4] Webber WR, Lal N, Stone EC, et al. Voyager 1 Measurements Beyond the Heliopause of Galactic Cosmic Ray Helium, Boron, Carbon, Oxygen, Magnesium, Silicon and Iron

[5] Mewaldt RA, Davis AJ, Lave KA, et al. Record-setting cosmic-ray intensities in 2009 and

[6] Lave KA, Wiedenbeck ME, Binns WR, et al. Galactic cosmic-ray energy spectra and composition during the 2009-2010 solar minimum period. Astrophysics Journal. 2013;**770**:117

[7] Usoskin IG, Bazilevskaya GA, Kovaltson GA. Solar modulation parameter for cosmic rays since 1936 reconstructed from ground-based neutron monitors and ionization

[8] Gleeson LJ, Axford WI. Solar modulation of galactic cosmic rays. Astrophysics Journal.

Nuclei with Energies 0.5 to >1.5 GeV/nuc. http://arXiv.org/abs/1712.02818; 2017

cosmic rays in a region depleted of heliospheric ions. Science. 2013;**341**:150

**Figure 12 .** The B/C ratio as a function of energy. The measurements of this ratio below ~2.4 GeV/nuc are from Voyager 1 beyond the heliopause [3, 4]. The higher energy measurements are from AMS-2 [17]. The calculated ratios are from the truncated LBM model described in the text and the GALPROP-DR model [3].

cannot be significant. The effects of truncation of the path length distributions at small path lengths (where the path length becomes ~0.6 g/cm2 at the highest energies) are predicted in this model and are observed in the flattening of the B/C ratio at the highest energies [21].
