The Effect of a Fisk-Type Heliospheric Magnetic Field on Cosmic-Ray Modulation

Abstract

The Fisk model of the heliospheric magnetic field (HMF) has proved to be quite difficult to implement in three-dimensional numerical modulation codes. We have developed a divergence-free Fisk-Parker hybrid HMF that is easier to implement and that should be a reasonable approximation for the case when field lines open into the heliosphere both in the polar coronal holes and at low latitudes. To study the effects of this hybrid field on galactic cosmic rays, we solve the three-dimensional steady state Parker transport equation numerically, covering the entire model heliosphere. We find that latitudinal cosmic-ray gradients are reduced as expected, but only during epochs when particles are drifting from the polar regions of the heliosphere toward the ecliptic plane. We investigate 26 day recurrent variations of both protons and electrons and find that the amplitude of these variations are directly proportional to the latitudinal intensity gradient, independent of species, in agreement with observational studies. In the absence of drifts in the code, electrons and protons obey different but still linear relationships.

Comparison of different analytic heliospheric magnetic field configurations and their significance for the particle injection at the termination shock

“…The latter is called the modified Fisk field B mF . The Fisk field is used in the hybrid representation by Burger & Hitge (2004), where a Parker-like field dominates in the ecliptic and over the poles, while in between a Fisk-like field contributes most to the HMF.…”

“…The assumption of a constant solar wind speed in this field, was abandoned by , see also Schwadron et al (2008). For a deeper discussion of these HMFs, see Burger & Hitge (2004), Burger (2005), and Burger et al (2008).…”

“…Burlaga et al 2002;Murphy et al 2002;Mursula 2007;Roberts et al 2007;Mordvinov 2008;Ebert et al 2009) and corresponding modeling (e.g. Burger & Hitge 2004;Giacalone & Jokipii 2004;Burger 2005;Schwadron & McComas 2005;Giacalone et al 2006;Ferreira et al 2007;Burger et al 2008) that can be used to analyze the asymmetry of the HMF have not yet convincingly settled the debate over which of the fields is closest to reality. For a more detailed discussion of the difficulties to distinguish between different fields on the basis of in situ measurements of magnetic fields, see the recent paper by Hitge & Burger (2010).…”

Theory of cosmic ray modulation

“…The end result is a field line that moves in heliographic latitude. Over the last ten years, various attempts to incorporate the Fisk field into numerical modulation models have been reported (Kóta & Jokipii 1999;Burger et al 2001;Burger & Hitge 2004). A recent overview of various models for the heliospheric magnetic field, including Fisk-type fields, is given by Burger (2005).…”

MHD simulation of the inner‐heliospheric magnetic field

“…[4] Several authors have suggested modifications of both fields [Jokipii and Kota, 1989;Smith and Bieber, 1991;Schwadron, 2002;Burger and Hitge, 2004;Burger et al, 2008;Schwadron et al, 2008], which have been quantitatively compared in a study by Scherer et al [2010]. Although very useful for many purposes, these analytical representations of the HMF cannot be used to reproduce actual measurements in sufficient detail at any given time in the solar activity cycle.…”