Numerical Modeling of Latitudinal Gradients for Galactic Cosmic-Ray Protons during Solar Minima: Comparing with Ulysses Observations

The latitudinal gradients of galactic cosmic-ray (GCR) protons measured by Ulysses during two successive minima provide a unique opportunity to study the modulation effects in polar regions of the heliosphere. In this work, a GCR modulation model based on numerically solving the Parker transport equation is used to study the latitudinal distribution of GCR protons in the inner heliosphere. Modifications of the standard Parker heliospheric magnetic field, the reduction of particle drifts, the latitudinal-dependent magnetic turbulence characteristics, and the anisotropic perpendicular diffusion coefficient are incorporated in the numerical model to investigate the corresponding modulation effects. It is found that the latitudinal-dependent magnetic turbulence magnitude, which makes the parallel diffusion coefficient decrease with the increasing of latitude, is crucial to obtain the negative latitude gradient in the inner heliosphere during the negative-polarity solar cycle. For the A > 0 period, on the other hand, the latitudinal diffusion coefficient in the inner heliosphere and the reduced drift velocity in the polar region are more important, while the anisotropic perpendicular diffusion coefficient at high latitude might be not essential. Finally, the proton latitudinal gradient and the corresponding differential intensity along the trajectory of Ulysses during its first and third fast latitude scans are computed, and the results show good agreement with the spacecraft observations.