Investigation of the transient cosmic ray decreases observed by voyagers in 2007: A numerical approach

Advances in Space Research

Strauss

et al. 2016

A numerical model for the solar modulation of cosmic rays, based on the solution of a set of stochastic differential equations, is used to illustrate the effects of modifying the heliospheric magnetic field, particularly in the polar regions of the heliosphere. To this end, the differences in the modulation brought about by each of three choices for the heliospheric magnetic field, i.e. the unmodified Parker field, the Smith-Bieber modified field, and the Jokipii-Kóta modified field, are studied. It is illustrated that both the Jokipii-Kóta and Smith-Bieber modifications are effective in modifying the Parker field in the polar regions. In addition, it is argued that the modification of Smith and Bieber is based on observational evidence and has a firm physical basis, while these motivations are lacking in the case of the Jokipii-Kóta modification. From a cosmic ray modulation point of view, we found the Smith-Bieber modification to be the most suitable choice for modifying the heliospheric magnetic field. The features and effects of these three modifications are illustrated both qualitatively and quantitatively. It is also shown how the Smith-Bieber modified field can be applied in cosmic ray modulation models to reproduce observational cosmic ray proton spectra from the PAMELA mission during the solar minimum of 2006 -2009. These results are compared with those obtained in previous studies of this unusual solar minimum activity period and found to be in good qualitative agreement.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The effects of magnetic field modifications on the solar modulation of cosmic rays with a SDE-based model

Raath

Advances in Space Research

Strauss

et al. 2016

“…This makes it possible to incorporate detailed descriptions of the heliosphere and heliospheric structures into these models. Examples of such implementations include the work of Strauss et al (2012), where a fully three-dimensional (3D) wavy heliospheric current sheet (HCS) was implemented; Luo et al (2013a), where the re-acceleration of galactic CRs by the solar wind termination shock (TS) was included; Luo et al (2011Luo et al ( , 2013b, where time-varying modulation parameters were implemented; Strauss et al (2013) and Luo et al (2015) also applied this approach to investigate modulation beyond the heliopause. ADI-based models, in comparison, are notoriously unstable when solving differential equations in higher dimensions and the complexity of these models are thus restricted.…”

Section: Introductionmentioning

confidence: 99%

New insights from modeling the neutral heliospheric current sheet

Raath

Strauss

2015

Astrophys Space Sci

Recently, the modulation of cosmic rays in the heliosphere has increasingly been studied by solving the well known transport equation via an approach based on stochastic differential equations. This approach, which is now wellestablished and published, allows for an in depth study of the modulation effects of the wavy heliospheric current sheet, in particular as its waviness increases with solar activity up to extreme maximum conditions. This is possible because of the numerical stability of the approach as well as its ability to trace pseudo-particles so that insightful trajectories of how they respond to the wavy heliospheric current sheet can be computed and displayed. Utilising such a stochastic model, we present valuable new insights into how the geometry of the wavy current sheet can affect the modulation of cosmic rays, especially at the highest levels of solar activity. This enables us to show, from a modeling perspective, why a certain choice for the current sheet profile is more suited than another at these high solar activity levels. We emphasise the importance of an effective tilt angle and illustrate how this concept can be employed effectively in interpreting results pertaining to the wavy current sheet as well as the modulation associated with this important heliospheric structure.

A Study of Electron Forbush Decreases with a 3D SDE Numerical Model

Luo

Zhang

et al. 2018

ApJ

Because of the precise measurements of the cosmic ray electron flux by the PAMELA and AMS02, Electron Forbush decreases (Fds) have recently been observed for the first time. This serves as motivation to perform a numerical study of electron Forbush decreases with an advanced time-dependent, three-dimensional (3D) stochastic differential equation model, developed earlier to study proton Fds. The model includes a realistic interstellar electron spectrum reconstructed from Voyager observations, and diffusion and drift coefficients to reproduce the modulated spectrum observed by PAMELA in 2009. On the basis of this numerical model, electron Fd profiles for a range of rigidities are simulated. In addition, a systematic comparison between electron and proton Fds during different solar polarity epochs is performed. This approach gives insight into the rigidity dependence of the heliospheric diffusion coefficients and of drift effects over two magnetic field polarity cycles. We find that during an A > 0 epoch, the recovery time of a 1 GV proton Fd is remarkably shorter than the 1 GV electrons, whereas the electron Fd display a faster recovery during an A < 0 epoch. This model clear predicts a charge-sign dependent effect in the recovery time of Fds but less so for their magnitude.