The effect of the heliospheric current sheet on cosmic-ray modulation

Abstract

The heliospheric current sheet is a dominant feature of the heliosphere. As solar activity increases, the tilt angle of the current sheet increases, and so does the region swept out by this structure, to cover most of the heliosphere during solar maximum conditions. An analysis of neutron monitor data in the form of count rate as function of tilt angle is presented. It is shown that the use of an effective tilt angle from a moving average preceding the time of observation, instead of the tilt angle at the time of observation, yields intensity-tilt loops that are in qualitative agreement with predictions of an idealized drift model. The characteristics of these loops are then a natural consequence of drift patterns during alternate solar magnetic polarity cycles. A detailed theoretical derivation for the drift-velocity field, valid throughout a model heliosphere that includes a wavy current sheet, is provided. A simplified ab initio approach is followed to model long-term cosmic-ray modulation using a steady-state three-dimensional numerical code. A composite slab/2D model is assumed for the structure of the turbulence. The spectra for the components are assumed to have a at energy range and a Kolmogorov inertial range. Standard diffusion coefficients based on these spectra are used. A parameterized construction is used for the problematic drift coefficient, for which a generally accepted theoretical description is still lacking. The spatial dependence of magnetic variances and correlation scales, required as input for the drift- and diffusion coefficients, follows from parametric fits to results from a transport model for composite turbulence and not the model itself, hence the qualification of simplified and not fully ab initio. Effective values are used for all parameters in the modulation model. The unusually high cosmic-ray intensities observed during the 2009 solar minimum follow naturally from the current model for most of the energies considered. Lack of information about the solar-cycle dependence of all the required turbulence quantities at Earth, required such a dependence to be modeled. This was done in terms of the solar-cycle dependence of the magnetic field, for which long-term data exist. Reasonable qualitative agreement with long-term cosmic-ray data is found. Better agreement is found for intensity as function of time at higher model energy, and better agreement with intensity-tilt loops at lower energy. In both cases, the highest model intensity occurs during the 2009 solar minimum. This is the first time that turbulence has been demonstrated as the most likely cause of the higher than usual cosmic-ray intensities during the 2009 solar minimum. It is shown that the temporal dependence of the current diffusion coefficients at Earth is inversely proportional to that of the magnetic field. It is, however, emphasized that this proportionality does not apply to their spatial dependence.