Heliospheric Modulation of Cosmic‐Ray Positrons and Electrons: Effects of the Heliosheath and the Solar Wind Termination Shock

Abstract

The importance of the solar wind termination shock (TS) and the modulation that may occur in the heliosheath have become most relevant, as emphasized by cosmic-ray observations of the Voyager spacecraft in the distant heliosphere close to the TS. The role of the TS and that of the heliosheath on cosmic-ray electrons and positrons are studied with a numerical model, including global drifts and a Jovian electron source. The consequent chargesign dependence is computed using improved local interstellar spectra and new fundamentally derived diffusion coefficients. The importance of modulation in the heliosheath is studied for the two species, as well as the differences between a model with and one without a TS. We found that the modulation in the heliosheath depends on the particle species, is strongly dependent on the energy of the cosmic rays and the magnetic polarity cycle, and is enhanced by the inclusion of the TS. From the computations it is possible to estimate the ratio of modulation occurring in the heliosheath to the total modulation between the heliopause and Earth. For electrons the factor modulation in the heliosheath becomes comparable to the factor between the TS and Earth at low energies for both polarity epochs. During A > 0 cycles the heliosheath cannot really be considered a modulation ''barrier'' above $150 MeV for electrons, while for positrons this occurs at somewhat higher energies during the A < 0 cycle. The presence of the TS is thus more pronounced for electron modulation during A > 0 polarity cycles but for positron modulation during A < 0 cycles. For positrons, with a completely differently shaped local interstellar spectrum, the modulated spectra have a very mild energy dependence below $300 MeV, even at Earth, in contrast to electrons, protons, and antiprotons. These characteristic spectral features may be helpful for distinguishing between electron and positron spectra when measured near and at Earth. These simulations can be of use for future missions to the outer heliosphere and beyond.

Constraints on cosmic-ray positron excess and average pulsar parameters

“…The top and bottom dot-dashed curves have been determined by Clem et al (2000) assuming the Protheroe model with the inclusion of solar modulation and solar polarity effects. The dotted curve represents the positron fraction estimated by Potgieter & Langner (2004) at solar minimum during a positive polarity period.…”

“…Particle fluxes propagating along the HCS are more modulated with respect to those coming from the poles. Modelizations of electron and positron fluxes for different conditions of solar modulation and solar polarity have been carried out by Potgieter & Langner (2004). However, these authors use ISM electron and positron energy spectra about 30% higher than other authors below 1 GeV, while the e + spectrum becomes lower above 1 GeV.…”

“…However, various estimates of e + and e − secondary fluxes in the ISM differ by more than a factor of two as a function of the energy (see Protheroe 1982;Moskalenko & Strong 1998;Stephens 2001a,b). Moreover, the solar activity and drift of opposite-charge particles in the heliosphere modulate cosmic-ray observations near Earth (Potgieter & Langner 2004), and only an accurate evaluation of the drift process during opposite polarity periods allows us to distinguish among different models of secondary electron and positron calculations. Finally, only a reliable secondary-component evaluation leads to identifying possible extra positron sources.…”

The heliomagnetic and solar-cycle related variations of the cosmic ray flux modeled with the BoPo-hybrid code

“…Jokipii et al 2004) and acceleration at the termination shock (e.g. Potgieter & Langner 2004). A qualitative description of the changes of the gradients are discussed in Jokipii et al (1993), where at low energies, the radial gradient changes abruptly from a lower value inside the shock to a higher value outside, where as at high energies, the higher value of the gradient are inside the shock.…”

Characteristics and Energy Dependence of Recurrent Galactic Cosmic-Ray Flux Depressions and of a Forbush Decrease with LISA Pathfinder

“…Positively charged particles propagate mainly sunward in the ecliptic along the heliospheric current sheet (HCS) during negative solar polarity periods and over the poles during positive polarity epochs. The opposite holds for negatively charged particles (Potgieter & Langner 2004;Ferreira 2005). Particles propagating along the HCS lose more energy than those coming from the poles (Strauss et al 2011).…”