Modulation of Galactic Electrons in the Heliosphere During the Unusual Solar Minimum of 2006–2009: A Modeling Approach

Abstract

The last solar minimum activity period, and the consequent minimum modulation conditions for cosmic rays, was unusual. The highest levels of Galactic protons were recorded at Earth in late 2009 in contrast to expectations. A comprehensive model was used to study the proton modulation for the period from 2006 to 2009 in order to determine what basic processes were responsible for solar modulation during this period and why it differs from proton modulation during previous solar minimum modulation periods. This established model is now applied to studying the solar modulation of electron spectra as observed for 80 MeV-30 GeV by the PAMELA space detector from mid-2006 to the end of 2009. Over this period the heliospheric magnetic field had decreased significantly until the end of 2009 while the waviness of the heliospheric current sheet decreased moderately and the observed electron spectra increased by a factor of ∼1.5 at 1.0 GeV to ∼3.5 at 100 MeV. In order to reproduce the modulation evident from seven consecutive semesters, the diffusion coefficients had to increase moderately while maintaining the basic rigidity dependence. It is confirmed that the main diffusion coefficients are independent of rigidity below ∼0.5 GV, while the drift coefficient had to be reduced below this value. The 2006-2009 solar minimum epoch indeed was different than previously observed minima, at least since the beginning of the space exploration era. This period could be called "diffusion-dominated" as was also found for the modulation of protons.

New Evidence for Charge-Sign-Dependent Modulation During the Solar Minimum of 2006 to 2009

“…For both electrons and protons the newly determined local interstellar spectra, see also Potgieter et al (2014a), used as unmodulated input spectra for the model are also shown in the two figures. The different behaviour of electrons in comparison with protons at low rigidities were discussed in detail by Potgieter et al (2014bPotgieter et al ( , 2015 and is not repeated here. In the rest of our work, we focus on rigidities above 0.4 GV, which is the lowest rigidity available for the proton spectra.…”

“…Strauss & Potgieter 2014a). This approach leads to reliable estimates for both the proton and electron LIS (see also Potgieter et al 2015;.…”

“…Observations are overlaid with the corresponding computed spectra (continuous lines) for an A<0 cycle magnetic field polarity Potgieter et al 2015). Colour coding shown in the legend indicates the seven selected time slots for both experimental and computed spectra.…”

New Modeling of Galactic Proton Modulation During the Minimum of Solar Cycle 23/24

“…The numerical model used in this study is further described in detail by Potgieter et al (2014Potgieter et al ( , 2015. The modulation parameters as modeled are discussed below.…”

Modulation of Galactic Cosmic Rays in the Inner Heliosphere, Comparing with PAMELA Measurements

“…Voyager 1 was assumed to have crossed the heliopause (HP) at ∼ 122 AU on August 2012 (Webber & McDonald 2013), cosmic ray spectra in the energy between 5 MeV to 50 MeV in the very local interstellar medium was then reported by Stone et al (2013). The cosmic ray spectra data from PAMELA and Voyager 1 can be used to construct the very local interstellar spectrum (LIS, see e.g., Potgieter et al 2014;Ngobeni & Potgieter 2014;Potgieter et al 2015;Bisschoff & Potgieter 2016). The LIS is important as the input spectrum in the solar modulation study.…”