The long-term heliospheric modulation of galactic cosmic rays according to a time-dependent drift model with merged interaction regions

So far, little work has been done to study the effect of merged interaction regions (MIRs) on the long-term modulation of cosmic rays in more comprehensive simulations of the heliosphere. We therefore present calculations for protons with a two-dimensional time-dependent drift model with an emulated wavy heliospheric neutral sheet (HNS) which include MIRs as large, idealized outward propagating regions with regions of enhanced interplanetary magnetic fields (IMF). The discussion features three classes of MIRs: namely global merged interaction regions (GMIRs), corotating merged interaction regions (CMIRs) and local merged interaction regions (LMIRs) according to the classification of Burlaga, McDonald, & Ness (1993). It was found that the recovery rate (tr) from a single GMIR-induced step decrease in the proton intensity is clearly polarity-dependent, being slower during an A < 0 polarity cycle (northern hemispheric IMF directed toward the Sun) than during an A > 0 cycle (northern hemispheric IMF directed away from the Sun). It plays a crucial role in determining the contribution of GMIRs toward long-term cosmic-ray modulation. The recovery rate is charge dependent, that is, faster for electrons than for protons during A < 0 periods and vice versa during A > 0 periods. A simulation of the declining intensity phase of the modulation cycle with a changing wavy HNS and two successive GMIRs revealed that this approach gives a very natural and convincing explanation for the observed step decreases in long-term modulation. A study of the radial and energy dependence of the calculated declining intensity phase of the modulation cycle showed that two successive GMIRs produced a significant part of the total long-term modulation. In fact, the simulated GMIRs dominated long-term modulation for energies above ∼5 GeV and radial distances (r) larger than ∼40 AU. Similar calculations, but for the intensity recovery part of the modulation cycle indicated that: (i) Consecutive GMIRs are more successful in delaying the long-term proton intensity recovery during A < 0 cycles compared to A > 0 cycles and (ii) are less successful in the delay of the recovery of electrons in relation to protons during A < 0 cycles than during A > 0 cycles. It was realized that LMIRs and CMIRs contribute little toward long-term modulation. The CMIRs, in conjunction with rarefaction regions (RRs), only cause minor short-term periodic variations in the cosmic-ray intensity. In conclusion, time-dependent long-term modulation from the viewpoint of a two-dimensional MIR-drift model is basically a process caused by the interplay between a changing wavy HNS and successive outward propagating GMIRs with the HNS dominating the process during periods of low solar activity and the GMIRs in dominance during times of large solar activity.