IMPLICATIONS OFVOYAGER 1OBSERVATIONS BEYOND THE HELIOPAUSE FOR THE LOCAL INTERSTELLAR ELECTRON SPECTRUM

Abstract

Cosmic-ray observations made by the Voyager 1 spacecraft outside the dominant modulating influence of the heliosphere finally allow the comparison of computed galactic spectra with experimental data at lower energies. These computed spectra, based on galactic propagation models, can now be compared with observations at low energies by Voyager 1 and at high energies by the PAMELA space detector at Earth. This improves understanding of basic propagation effects and also provides solar modulation studies with reliable input spectra from 1 MeV to 100 GeV. We set out to reproduce the Voyager 1 electron observations in the energy range of 6-60 MeV, as well as the PAMELA electron spectrum above 10 GeV, using the GALPROP code. By varying the source spectrum and galactic diffusion parameters, specifically the rigidity dependence of spatial diffusion, we find local interstellar spectra that agree with both power-law spectra observed by Voyager 1 beyond the heliopause. The local interstellar spectrum between ∼1 MeV and 100 GeV indicates that it is the combination of two power laws, with E −(1.45±0.15) below ∼100 MeV and E −(3.15±0.05) above ∼100 MeV. A gradual turn in the spectral shape matching the power laws is found, between 2.0 ± 0.5) GeV and (100 ± 10) MeV. According to our simplified modeling, this transition is caused primarily by galactic propagation effects. We find that the intensity beyond the heliopause at 10 MeV is (350 ± 50) electrons m −2 s −1 sr −1 MeV −1 , decreasing to (50 ± 5) electrons m −2 s −1 sr −1 MeV −1 at 100 MeV.

A predictive analytic model for the solar modulation of cosmic rays

“…The predictions of these five models are each in good agreement with this measurement. 4 In Appendix A, we show that these models each also provide good fits to the measured CR proton spectrum and boron-to-carbon ratio, as measured at Earth, after applying the model presented in this paper to account for the effects of solar modulation. …”

“…In particular, the best fits were found for f = α(t) n with n 3 − 6, or f [α/(−α + α 0 )] 2 with α 0 ∼ 90 • . As our default model, we adopt f = α(t) 4 . We note that the preference for this parameterization relies strongly on the single data point from BESS 2002 (and to a lesser extent from BESS Polar I), leaving us less confident in this determination.…”

“…Given the rigidity dependence of Φ for qA < 0, we provide its value for three different rigidities. The values of the modulation potential given in parentheses were derived using f ∝ α, which is disfavored by BESS 2002 and BESS Polar I, rather than our default parameterization of f ∝ α 4 . See text for details.…”

New Very Local Interstellar Spectra for Electrons, Positrons, Protons, and Light Cosmic Ray Nuclei

“…With diffusion having the largest effect on the LIS's, changes to the diffusion parameters were also required to reproduce the observations well, instead of just a rough reproduction. Initial studies showed that a GALPROP plain diffusion model was sufficient when studying electrons (as presented by Bisschoff & Potgieter (2014)), protons and Helium LIS's separately. Modelling protons, Helium, Carbon and the B/C ratio simultaneously, as presented by Bisschoff & Potgieter (2016), required the inclusion of reacceleration in galactic space in the plain diffusion model.…”

“…In the past the GALPROP plain diffusion model was sufficient when studying electrons (Bisschoff & Potgieter 2014), protons and Helium LIS's separately. Including Carbon, the B/C ratio and positrons into the study, the constraints placed on the LIS's by observations necessitated also considering reacceleration and convection in galactic space.…”