**3. The galactic electron spectrum**

Voyager has now measured the true LIS electron spectrum from ~1 to 60 MeV. When compared with simultaneous measurements of electrons by the PAMELA spacecraft near the Earth they indicate a solar modulation factor ~500 between the LIS spectrum and that measured at the Earth between about 10–100 MeV (**Figure 4**). At higher energies this modulation decreases. It is believed to be only a factor ~3–4 at 1 GeV, decreasing to perhaps 20% at 10–20 GeV where high precision electron measurements are available from both PAMELA and AMS-2 [10, 11].

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the LIM in just 1–26 day interval of ~0.1 AU in radius. Essentially whatever intensities exist in the heliosphere apparently stay in the heliosphere as a result of an almost impenetrable heliopause at these lower energies. As far as energetic particles go, the interstellar medium at

Other features of the heliosphere newly recognized from this study include: (1) The heliosheath is a very interesting and important region both in terms of accelerating protons and also (more weakly) electrons as well as for large solar modulation effects. The solar modulation effects on the intensity in this region range from a factor ~4 for ~1 GV protons to a factor ~100 for 15 MV electrons and then decrease to a factor ~30 for 4 MV electrons and much less for 1 MeV

The massive acceleration of nuclei, e.g., protons and He and O nuclei in the heliosheath, extending down to ~1 MeV and up to ~100 MeV/nuc, which was previously known and believed to be fueled by high ionization potential IS ions, is joined by the newly found accel-

The 11 year and longer solar activity cycles studied now for over 70 years using neutron monitors, balloon and spacecraft borne instruments at higher energies, and so important for geophysical studies [9], are still significant beyond the HTS. Even for protons at 250 MeV the intensity increase in the heliosheath region is a factor ~4; for electrons, this increase due to solar modulation reaches a maximum of a factor ~100 at ~15 MeV. These effects were previ-

And finally the new observations reported here have also extended the V1 measurements of the local interstellar electron spectrum by a factor ~10 lower in energy (e.g., down to 0.5 MeV) as compared with even the initial Voyager measurements of [2] beyond the HP. For protons the minimum energy measured is now ~1.8 MeV, a factor ~2 times lower than the initial measurement for these particles. The intensities obtained at these lowest energies appear to be consistent with a smooth extension of those measured at higher energies as would be expected from propagation calculations. The range of the lowest energy electrons and protons is only ~50 μ of Si. This places severe constraints on the distribution of nearby sources of these particles but illustrates that, even at these lower energies, the spectra are still a compendium of many sources with an individuality obscured by diffusion in the galactic magnetic fields.

Voyager has now measured the true LIS electron spectrum from ~1 to 60 MeV. When compared with simultaneous measurements of electrons by the PAMELA spacecraft near the Earth they indicate a solar modulation factor ~500 between the LIS spectrum and that measured at the Earth between about 10–100 MeV (**Figure 4**). At higher energies this modulation decreases. It is believed to be only a factor ~3–4 at 1 GeV, decreasing to perhaps 20% at 10–20 GeV where high precision electron measurements are available from both PAMELA and AMS-2 [10, 11].

this location has little recognition of the nearby heliosphere.

electrons which appear to be mostly locally produced.

eration of sub-MeV electrons.

**3. The galactic electron spectrum**

ously unrecognized.

66 Cosmic Rays

**Figure 4.** The electron spectrum measured at Voyager using the TET, B stop and A stop telescopes and the measurements of PAMELA and AMS-2 at higher energies. The figure is in a x E<sup>2</sup> format. Note the severe solar modulation of electrons which amounts to a factor ~500 below 100 MeV and is still ~20% between10–20 GeV/nuc. Also note the V1 spectrum which is ~E−1.3 between about 1–60 MeV. The black curve shows a Monte Carlo calculation with an electron source spectrum ~E−2.25 and a path length ~20.6 β P−0.45 above 0.562 GV and with a diffusion coefficient ~P−1.0 below 0.562 GV.

**Figure 4** shows the electron spectrum measured at Voyager and also in the higher energies where solar modulation effects are small. The plot is a x E<sup>2</sup> presentation which shows both low and high energy differences. There is a large gap in the intermediate energy range for LIS electrons from ~100 MeV to several GeV. At energies above a few GeV the electron spectrum measured by PAMELA and AMS-2 steepens rapidly. Part of this increase in spectral index is due to synchrotron and inverse Compton energy loss which are ~E<sup>2</sup> . This high energy region is shown in **Figure 5** in a x E<sup>3</sup> format. The AMS-2 data on electrons [11] is shown along with Monte Carlo propagation calculations of the electron spectrum using various source spectral indices [12, 13].

We have shown from these calculations that, in order to fit both low energy and high energy data, the source spectral exponent for electrons changes from being ~P−2.24 below about 8 GV to one ~P−2.4 at higher energies extending up to ~1 TV [12, 13].

At ~400 MeV, which is ~1.0 GV for protons there are corresponding measurements of the proton and electron intensities at the Earth by PAMELA and also at Voyager. The ratio of Voyager to PAMELA proton intensities at the two locations is ~4.0 which is caused by the amount of solar modulation between the LIS and the Earth at 1 GV. The electron intensity is also measured at this time by PAMELA and at 1 GV it is 2.5 × 10−2 × the proton intensity. We believe from solar modulation theory [8] that at 1 GV the total modulation of electrons and protons should be nearly the same. So the LIS electron intensity at 1 GV could be estimated from this approach to be 1.4–1.6 × 10−1e/m2 ⋅s⋅sr/MeV. This intensity is very close to the value

So in view of the above similarity of rigidity spectra for electrons and protons, the e/H ratio itself as a function of rigidity should be almost constant. This almost constant value of the e/H ratio occurs between 0.5 and 1.0 GV where loss processes for electrons and protons in the galaxy are about equal. This value of the ratio is about 3–10 × 10−2 as shown in **Figure 6**.

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This source ratio of e/H for galactic cosmic rays as a function of rigidity which has previously been hidden from measurements at the Earth and is related to the acceleration of the galactic cosmic rays, now provides a crucial measurement along with the possible spectral break at ~8 GV. If there are no other selection effects, this ratio could indicate the degree of ionization in

And last but certainly not least, still regarding electrons, we should point out that the electron spectrum ~E−1.3 at low energies, just about 1.0 power less than the assumed source spectrum with exponent = −2.25, may have profound significance. Unless the source spectrum has a 2nd break at ~0.3 GV, which seems unlikely, this flattening of the spectrum is caused by a break in the diffusion coefficient which becomes ~P−1.0 below ~0.5 GV. This break has been predicted [14]. As a result the diffusion coefficient becomes large and these lower energy electrons rapidly flow out of the extended disk of the galaxy [12, 13]. This fraction that escape the disk, calculated in a Monte Carlo diffusion model, becomes ~90% below ~100 MeV and is shown as a function of energy in **Figure 7** of [12]. These electrons, with a spectrum ~E−2 above ~1 MeV, flow outward through the halo and into the local intergalactic medium at essentially the speed of light. They populate the region with a negative charge. Because of their relatively low energy they are undetectable by radio emissions and could be considered a form of non-baryonic dark matter and energy. Perhaps more sobering is the thought that this process of charge

**Figure 6.** Ratios of intensity of electrons to protons as a function of energy, e/H (E), measured by voyager and AMS-2 [10, 15] from 2 MeV to ~1 TeV. The estimated LIS value of the ratio at ~1 GeV as described below in the text is also shown.

the acceleration region.

**Figure 5.** The electron spectrum above 1 GeV measured by AMS-2 [11] and PAMELA [10]. The black solid curves are for (1) a source electron spectrum ~E−2.25 at all energies and (2, 3 and 4) for electron source spectra ~E−2.25 below ~6 GeV and P−2.30, P−2.35 and P2.40 respectively above 6 GeV.

at 1 GV obtained in the Monte Carlo diffusion propagation models that fit the LIS at the low Voyager energies and the high energies measured by PAMELA or AMS-2 [12, 13].

In **Figure 6** we show the e/H (E) interstellar ratios of intensities measured at both Voyager and at AMS-2 from a few MeV to 1 TeV. These ratios, in intensity/MeV, range from ~102 at 2 MeV to ~3 × 10−3 at 1 TeV, a difference of 3 × 10<sup>5</sup> and include the ratio between electron and proton intensities of 3.0 × 10−2 at 1 GV estimated above. This difference in low energy and high energy e/H (E) ratios is mainly caused by propagation effects.

At lower rigidities this source ratio as a function of energy increases for a number of reasons. First of all there is the conversion between a differential energy and rigidity which depends on the different β of the particles. Then there is the dependence of the diffusion coefficient on P−1.0 below 0.5 GV which affects only the electrons and decreases the P−2.25 source index to ~P−1.3. And also there is the energy loss by ionization which eventually reduces the source spectral index for protons from a negative one to a positive value. At the higher energies the synchrotron and inverse Compton losses increase the source spectral index of electrons by almost 1.0 power thus reducing the e/H ratio.

Recall that we have assumed for electrons, that to fit the data at both low and high energies up to 1 TeV, source spectra of the form dj/dE ~P−2.24, below ~6–8 GV are needed with the exponent becoming ~2.40 at high rigidities [12, 13]. Very similar rigidity spectra with almost the same exponents and a break at ~6–8 GeV are required to simultaneously fit the Voyager low energy proton data and the high energy AMS-2 proton data, again from ~2 MeV to 1 TeV [15] (see following sections).

So in view of the above similarity of rigidity spectra for electrons and protons, the e/H ratio itself as a function of rigidity should be almost constant. This almost constant value of the e/H ratio occurs between 0.5 and 1.0 GV where loss processes for electrons and protons in the galaxy are about equal. This value of the ratio is about 3–10 × 10−2 as shown in **Figure 6**.

This source ratio of e/H for galactic cosmic rays as a function of rigidity which has previously been hidden from measurements at the Earth and is related to the acceleration of the galactic cosmic rays, now provides a crucial measurement along with the possible spectral break at ~8 GV. If there are no other selection effects, this ratio could indicate the degree of ionization in the acceleration region.

And last but certainly not least, still regarding electrons, we should point out that the electron spectrum ~E−1.3 at low energies, just about 1.0 power less than the assumed source spectrum with exponent = −2.25, may have profound significance. Unless the source spectrum has a 2nd break at ~0.3 GV, which seems unlikely, this flattening of the spectrum is caused by a break in the diffusion coefficient which becomes ~P−1.0 below ~0.5 GV. This break has been predicted [14]. As a result the diffusion coefficient becomes large and these lower energy electrons rapidly flow out of the extended disk of the galaxy [12, 13]. This fraction that escape the disk, calculated in a Monte Carlo diffusion model, becomes ~90% below ~100 MeV and is shown as a function of energy in **Figure 7** of [12]. These electrons, with a spectrum ~E−2 above ~1 MeV, flow outward through the halo and into the local intergalactic medium at essentially the speed of light. They populate the region with a negative charge. Because of their relatively low energy they are undetectable by radio emissions and could be considered a form of non-baryonic dark matter and energy. Perhaps more sobering is the thought that this process of charge

at 1 GV obtained in the Monte Carlo diffusion propagation models that fit the LIS at the low

**Figure 5.** The electron spectrum above 1 GeV measured by AMS-2 [11] and PAMELA [10]. The black solid curves are for (1) a source electron spectrum ~E−2.25 at all energies and (2, 3 and 4) for electron source spectra ~E−2.25 below ~6 GeV and

In **Figure 6** we show the e/H (E) interstellar ratios of intensities measured at both Voyager and

intensities of 3.0 × 10−2 at 1 GV estimated above. This difference in low energy and high energy

At lower rigidities this source ratio as a function of energy increases for a number of reasons. First of all there is the conversion between a differential energy and rigidity which depends on the different β of the particles. Then there is the dependence of the diffusion coefficient on P−1.0 below 0.5 GV which affects only the electrons and decreases the P−2.25 source index to ~P−1.3. And also there is the energy loss by ionization which eventually reduces the source spectral index for protons from a negative one to a positive value. At the higher energies the synchrotron and inverse Compton losses increase the source spectral index of electrons by

Recall that we have assumed for electrons, that to fit the data at both low and high energies up to 1 TeV, source spectra of the form dj/dE ~P−2.24, below ~6–8 GV are needed with the exponent becoming ~2.40 at high rigidities [12, 13]. Very similar rigidity spectra with almost the same exponents and a break at ~6–8 GeV are required to simultaneously fit the Voyager low energy proton data and the high energy AMS-2 proton data, again from ~2 MeV to 1 TeV [15] (see

at 2 MeV

and include the ratio between electron and proton

Voyager energies and the high energies measured by PAMELA or AMS-2 [12, 13].

at AMS-2 from a few MeV to 1 TeV. These ratios, in intensity/MeV, range from ~102

to ~3 × 10−3 at 1 TeV, a difference of 3 × 10<sup>5</sup>

P−2.30, P−2.35 and P2.40 respectively above 6 GeV.

68 Cosmic Rays

almost 1.0 power thus reducing the e/H ratio.

following sections).

e/H (E) ratios is mainly caused by propagation effects.

**Figure 6.** Ratios of intensity of electrons to protons as a function of energy, e/H (E), measured by voyager and AMS-2 [10, 15] from 2 MeV to ~1 TeV. The estimated LIS value of the ratio at ~1 GeV as described below in the text is also shown.

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

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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

dj/dP~P<sup>−</sup><sup>S</sup> (1)

where we let S vary from −2.20 to −2.28 noting that we have already found that lower rigidity

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

**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

measured at ~10–20 GeV/nuc by AMS-2.

is small is from AMS-2 [16].

rigidities below ~10 GV and can be represented by the formula.

electrons are well described with a spectral index ~ − 2.25 below ~10 GV.

**Figure 7.** Ratios of hydrogen to helium nuclei intensities as a function of E/nuc as measured by Voyager between 10 and 350 MeV/nuc and by AMS2 [10, 15] above 1 GeV/nuc.

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.
