The effect of solar cycle dependent heliospheric turbulence on cosmic ray modulation

Abstract

We solve the transport equations for the radial evolution of the turbulence in the solar wind (Zank et al., 1996) numerically to determine the spatial dependence of the turbulence quantities that are used in the diffusion tensor for galactic cosmic rays. The results are used as input for a two-dimensional steady-state transport equation that is also solved numerically to describe the modulation of cosmic-ray protons in the heliosphere. This procedure is carried out for two sets of parameters to model both solar minimum and solar maximum conditions, respectively. Our choice of turbulence parameters leads to a correlation length and variance of the fluctuating field that vary less with latitude during solar maximum conditions than during solar minimum conditions. Better overall agreement with observed cosmic ray data is found for anisotropic perpendicular diffusion, when the meridional component of the perpendicular mean free path has a flatter rigidity dependence than the parallel mean free path at low rigidity. We find somewhat better agreement with cosmic ray data during solar maximum conditions than during solar minimum conditions for the current choice of the diffusion tensor. During solar maximum conditions, drift effects are reduced by using large values for the random motion of the magnetic field lines, but smaller values are needed during times of minimum solar activity to account for larger drift effects, such as larger latitudinal gradients during A > 0 magnetic polarity.