An ab initio approach to modelling time-dependent cosmic-ray modulation in the heliosphere
The ab initio approach to cosmic ray modulation places a strong, primary emphasis on understanding the basic causes of cosmic-ray modulation. This requires knowledge and an understanding of both the large and small-scale structure of the heliosphere. A key part of this is understanding lies in how turbulence inﬂuences cosmic-ray modulation over the solar-cycle. Our understanding of the role of turbulence in cosmic-ray modulation has now reached a level where we can provide some answers to the questions of how various turbulence quantities that govern diﬀusion and drift in the heliosphere inﬂuence cosmic-ray modulation over time scales associated with the solar activity cycle and the solar magnetic cycle. The present study presents a three-dimensional, time-dependent, ab initio cosmic ray modulation model, developing this code from an eﬀective-value steady-state approach to full time-dependence, in the process fully characterising the numerical complexities implicit to this process. In such a model, scattering and drift coeﬃcients are required that depend realistically on turbulence input quantities such as magnetic variances and correlation scales. These are scaled both spatially and temporally following observations of these quantities, and using parametric ﬁts to results computed from state-of-the art two-component turbulence transport models. Large-scale heliospheric quantities such as the solar wind speed, heliospheric magnetic ﬁeld magnitude, and tilt angle are also modelled using observationally-motivated solar cycle and spatial dependences. The time-evolution of the wavy current sheet also plays a key role in the solar-cycle dependent modulation of cosmic rays, and is here for the ﬁrst time implemented with its fully three-dimensional and time-dependent structure in a time-dependent modulation model. The end result of this study is the most realistic solar-cycle dependent three-dimensional cosmic-ray modulation model to date, that is able to self-consistently reproduce the major salient features of the observed cosmic ray intensity temporal proﬁles. A better understanding of the primary drivers of cosmic-ray modulation over decadal time-scales also leads to a better understanding of how intensities could vary over time-scales of centuries, as is here demonstrated. These insights are essential to being able to reliably predict future cosmic ray intensities, as meaningful extrapolations can only be done by modelling the fundamental physics in a self-consistent manner.