A study of the time-dependent modulation of galactic cosmic rays in the heliosphere

Abstract

Time-dependent cosmic ray modulation in the heliosphere is studied by using a two-dimensional time dependent modulation model. To compute realistic cosmic ray modulation a compound approach is used, which combines the effect of the global changes in the heliospheric magnetic field magnitude and the current sheet tilt angle to establish realistic time dependent diffusion and drift coefficients. This approach is refined by scaling down drifts additionally (compared to diffusion) towards solar maximum. The amount of drifts needed in the model to realistically compute 2.5 GV proton and electron and 1.2GV electron and helium intensities, as measured by Ulysses from 1990 to 2004, is established. It is shown that the model produces the correct latitudinal gradients evident from the observations during both the Ulysses fast latitude scan periods. Also, much can be learned on the magnitude of perpendicular diffusion in the polar direction, K┴θ, especially for solar minimum conditions and for polarity cycles when particles drift in from the poles. For these periods K┴θ = 0.12K║ in the polar regions (with K║ the parallel diffusion coefficient)and K┴θ /K║ can vary between 0.01 to even 0.04 in the equatorial regions depending on the enhancement factor toward the poles. The model is also applied to compute radial gradients for 2.5 GV cosmic ray electrons and protons in the inner heliosphere. It is shown that, for solar minimum, and in the equatorial regions, the protons (electrons) have a radial gradient of 1.9 %/AU (2.9 %/AU), increasing for both species to a very fluctuating gradient varying between 3 to 4 %/AU at solar maximum. Furthermore, the model also computes realistic electron to proton and electron to helium ratios when compared to Ulysses observations, and charge-sign dependent modulation is predicted up to the next solar minimum expected in 2007. Lastly the model is also applied to model simultaneously galactic cosmic ray modulation at Earth and along the Voyager 1 trajectory, and results are compared with> 70 MeV count rates from Voyager 1 and IMP8. To produce realistic modulation, this model gives the magnitude of perpendicular diffusion in the radial direction as K┴r/K║= 0.035 and that the modulation boundary seemed to be situated between at 120 AU and 140 AU.