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