Propagation of cosmic rays in heliosphere: The HelMod model

Abstract

The heliospheric modulation model HelMod is a two dimensional treatment dealing with the helio-colatitude and radial distance from Sun and is employed to solve the transport-equation for the GCR propagation through the heliosphere down to Earth. This work presents the current version 3 of the HelMod model and reviews how main processes involved in GCR propagation were implemented. The treatment includes the so-called particle drift effects -e.g., those resulting, for instance, from the extension of the neutral current sheet inside the heliosphere and from the curvature and gradient of the IMF -, which affect the transport of particles entering the solar cavity as a function of their charge sign. The HelMod model is capable to provide modulated spectra which well agree within the experimental errors with those measured by AMS-01, BESS, PAMELA and AMS-02 during the solar cycles 23 and 24. Furthermore, the counting rate measured by Ulysses at ±80 • of solar latitude and 1 to 5 AU was also found in agreement with that expected by HelMod code version 3.

Solution of Heliospheric Propagation: Unveiling the Local Interstellar Spectra of Cosmic-ray Species

“…It defines the global behavior of the modulation of the particle flux in the heliosphere and its dependence on time reflects the variations of properties of the interplanetary medium (like the actual solar magnetic field transported by SW and its turbulence) during the different phases of solar cycles (e.g., see Equation 4 in Manuel et al 2014). K 0 is expressed in terms of the monthly Smoothed Sunspot Numbers (SSN); such a relationship was demonstrated to be adequate for the description on how the diffusion parameter depends on solar activity and polarity 15 (see also discussion in Section 2.3 of Boschini et al 2017). Therefore, the effective modulation experienced by CRs is related to the solar activity and polarity of the magnetic field.…”

“…The NMCR allows us to account for short-time and large-scale variations occurring during the high solar activity periods, and thus to rescale the diffusion parameter accordingly. However, the usage of NMCR during the low solar activity periods does not result in an appreciable difference, thus we keep using SSN (Boschini et al 2017) as the activity indicator for such periods.…”

High-energy Gamma Rays from the Milky Way: Three-dimensional Spatial Models for the Cosmic-Ray and Radiation Field Densities in the Interstellar Medium

“…Spatial diffusion, convection with the solar wind, drifts, and adiabatic cooling are the main mechanisms that determine transport of CRs to the inner heliosphere. These effects have been incorporated into realistic (time-dependent, three-dimensional) models (e.g., Florinski et al 2003;Langner et al 2006;Potgieter & Langner 2004;Boschini et al 2017). The "forcefield" approximation that is ordinarily used (Gleeson & Axford 1968), instead characterises the modulation effect as it varies over the solar cycle using a single parameter -the "modulation potential".…”

Modulation of Galactic Cosmic Rays in the Inner Heliosphere, Comparing with PAMELA Measurements

“…However, Ndiitwani et al (2013) did not consider the variations of solar wind speed. Recently, Boschini et al (2017) used a 2D heliospheric modulation (HelMod, e.g., Bobik et al 2012Bobik et al , 2013 model to study the modulation of GCR during solar cycles 23 and 24. In their model, the heliosphere was divided into polar and equatorial regions, the modified Parker spiral HMF (Jokipii & Kota 1989) and the Parker spatial HMF (Parker 1958) were used in polar and equatorial regions, respectively.…”

“…They used a parameter K 0 to describe the time dependence of diffusion coefficients. Bobik et al (2012) discussed the relationship between K 0 and the modulation strength given by the force-field model (FFM, see e.g., Gleeson & Axford 1968;Gleeson & Urch 1971), and Boschini et al (2017) derived K 0 using modulation strength data from Usoskin et al (2011). For periods of low solar activity, it was divided into ascending and descending phases for both negative and positive solar magnetic field polarities, and different polynomial equations were used to describe the relationship between K 0 and the sunspot numbers.…”