Global gradients for cosmic-ray (CR) protons in the heliosphere are computed with a comprehensive modulation model for the recent prolonged solar minimum of Cycle 23/24. Fortunately, the PAMELA (Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics) and Ulysses/KET (Kiel Electron Telescope) instruments simultaneously observed proton intensities for the period between July 2006 and June 2009. This provides a good opportunity to compare the basic features of the model with these observations, including observations from Voyager-1 in the outer heliosphere, beyond 50 AU
. Radial and latitudinal gradients are calculated from measurements, with the latter possible because Ulysses changed its position significantly in the heliocentric meridional plane during this period. The modulation model is set up for the conditions that prevailed during this unusual solar-minimum period to gain insight into the role that particle drifts played in establishing the observed gradients for this period. Four year-end PAMELA proton spectra were reproduced with the model, from 2006 to 2009, followed by corresponding radial profiles that were computed along the Voyager-1 trajectory, and compared to available observations.
It is found that the computed intensity levels are in agreement with solar-minimum observations from Voyager-1 at multiple energies. The model also reproduces the steep intensity increase observed when Voyager-1 crossed the heliopause region. Good agreement is found between computed and observed latitudinal gradients, so that we conclude that the model gives a most reasonable representation of modulation conditions from the Earth to the heliopause for the period from 2006 to 2009. As a characteristic feature of CR drifts, the most negative latitudinal gradient is computed for 2009, with a value of −0.15 %degree−1
around 600 MV. The maximum radial gradient in the inner heliosphere (as covered by Ulysses) also occurs in this range, with the highest value of 4.25 %AU−1 in 2009