Long-Term Cosmic Ray Modulation by Heliospheric Pa- rameters: Non-linear Relations

The heliospheric modulation strength is a good parameter for the long-term modulation of cosmic rays in the neutron monitor energy range. Here we study an empirical relation between the modulation strength and the global heliospheric parameters: the heliospheric current sheet tilt angle, the open solar magnetic flux and the global IMF polarity. The suggested relation closely reproduces the measured annual NM count rates. Using the measured IMF parameters and the modulation strength values computed since 1951, this relation allows us to reconstruct the annual tilt angle for about 25 years before the time of direct measurements of the tilt angle. In addition to more sophisticated theoretical models of galactic cosmic ray (GCR) modulation it is also useful to study empirical regression models. Usually such models linearly relate various heliospheric parameters to the GCR intensity at a fixed energy (see, e.g., [2]). Here we try to generalize this approach. A general parameter of the heliospheric modulation of GCR is the modulation strength Φ, which defines the shape of the modulated GCR spectrum for many practical purposes. E.g., for a given value of Φ one can calculate an approximate shape of GCR differential energy spectrum and the expected count rate of a cosmic ray detector [1], [11]. The modulation strength is measured in MV, has the physical meaning of the average rigidity loss of CR particles in the heliosphere and takes the following form [4] Φ = (D − rE)V/(3κo), where D is the distance of heliospheric boundary (termination shock), rE = 1 AU, V is the solar wind velocity and κo is the (rigidity independent part of the) GCR diffusion coefficient. Although defined only in 1D, Φ can also be used in the real conditions as a formal parameter that fits GCR spectra calculated in 1D model to the actual GCR spectrum measured at 1 AU. The values of Φ have been calculated for the last 50 years [11]. However, here we use an updated Φ series (Fig. 1.a) where heavier species of GCR (α−particles) are also taken into account. The value of Φ depends on several global heliospheric parameters as discussed below. In conpp. 3803–3806 c ©2003 by Universal Academy Press, Inc.