Global Gradients for Cosmic-Ray Protons in the Heliosphere During the Solar Minimum of Cycle 23/24

Abstract

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.

Multi-point galactic cosmic rays measurements between 1 and 4.5 AU over a full Solar cycle

“…This result agrees well with previous studies (e.g. Vos and Potgieter, 2016;Gieseler and Heber, 2016). The slope during the comet phase was found to be -2.8±0.12 %/AU.…”

“…After that period, the count rate variation and the ratio is in very good agreement with the expectation of a positive radial gradient of about 2.9 %/AU (e.g. Vos and Potgieter, 2016;Gieseler and Heber, 2016).…”

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

“…It is shown that the radial gradients are always positive while the latitudinal gradients are always negative as expected but with less magnitude than that predicted by earlier works (Potgieter et al 2001). Following de Simone et al (2011) and Gieseler & Heber (2016), Vos & Potgieter (2016) also used a numerical model to compute the spatial gradients of protons from 2006 to 2009. They concluded that although the drift effects were weaker than the predictions from those drift-dominated works due to the suppression by the excess diffusion, they still played an important role due to the significant decrease of HMF magnitude until the end of 2009.…”

Propagation of cosmic rays in heliosphere: The HelMod model

“…As discussed in Bobik et al (2012), we used an enhanced K ⊥,θ in the polar regions; this enhancement is an implicit way of reducing drift effects by changing the CR intensity gradients significantly (Potgieter, 2013) in order to reproduce the amplitude and rigidity dependence of the latitudinal gradients of GCR differential intensities for protons (see Sect. 5.4 and, e.g., Vos and Potgieter, 2016). Moving towards the solar maximum the rate of coronal mass ejections (CME) increases leading to a more chaotic structure of the solar magnetic field and to a stronger turbulence regime.…”