Effects of the solar wind termination shock on charge-sign dependent cosmic ray modulation

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Abstract

The heliospheric modulation of cosmic rays disguises the true spectral form of the local interstellar spectra for all cosmic ray species below ∼10 GeV. Recent modeling of the propagation of cosmic rays through the Galaxy gives the interstellar spectra for electrons, positrons, protons and anti-protons more reliably than before. Using this information together with the latest heliospheric diffusion coefficients, the electron to positron, proton to anti-proton, and electron to proton ratios are computed with a comprehensive numerical diffusive shock and drift modulation model for a simulated heliosphere. The modulation of the mentioned species are surprisingly different which should assist in establishing the amount of drifts present during different modulation epochs, and can be of use for future missions to the outer heliosphere and beyond.

Introduction

Drift models predict a clear charge-sign-dependence for the heliospheric modulation of cosmic ray (CR) electrons and positively charged particles due to the different large-scale gradient, curvature and current sheet drifts these particles experience in the global heliospheric magnetic field (HMF). For example, electrons and anti-protons will drift inwards primarily through the polar regions of the heliosphere during so-called A<0 polarity cycles, that is when the HMF is directed towards the Sun in the northern hemisphere. Positrons and protons, on the other hand, will then drift inwards primarily through the equatorial regions of the heliosphere, encountering the wavy heliospheric current sheet in the process. During the A>0 polarity cycles the drift directions for the differently charged species reverse, so that a clear 22-year cycle is caused (e.g., Burger and Potgieter, 1999).

The electron to positron, anti-proton to proton and electron to proton ratios at different energies and positions in the heliosphere can be computed in great detail if the local interstellar spectra (LIS) of the different CR species were better known (e.g., Potgieter and Burger, 1990; Langner et al., 2001). Recently, new calculations have been published of LIS for CR electrons and positrons that are based on sophisticated models for the propagation of CRs in the Galaxy, and on comparisons with a variety of data sets, including radio synchrotron indices and γ-rays (e.g., Peterson et al., 1999; Strong et al., 2000; Langner et al., 2001). New calculations for proton and anti-proton LIS with the same galactic propagation models were also published by Moskalenko et al. (2001). For a more elaborate discussions, see also Potgieter and Langner (2001) and Potgieter et al. (2001).

The purpose of this study is twofold: (1) To find a set of diffusion coefficients that can be used for most, if not all, CR species for both solar minimum and maximum conditions and for both polarity epochs. (2) To compute the modulation of galactic electrons (e), positrons (e+), protons (p) and anti-protons (p̄) in a simulated heliosphere using these new LIS as initial values in a modulation drift model with a solar wind termination shock (TS) to establish the consequent charge-sign dependence and the affects of the TS on the modulated e/e+, e/p and p̄/p.

Section snippets

Modulation model and parameters

The model calculations were done with a combined diffusive shock acceleration and drift modulation model with two spatial dimensions, that is, neglecting any azimuthal dependence. See Langner et al. (2004) for a detailed description of the model and parameters. The LIS for protons and anti-protons are those of Moskalenko et al. (2001), for positrons; that of Strong et al. (2000) and for electrons that of Langner et al. (2001). The set of diffusion coefficients are the same as given by Langner

Results

Fig. 1, Fig. 2 show the modulation with respect to the proton, anti-proton, electron and positron LIS, respectively, as a function of kinetic energy for 1, 60, 80 and 90 AU in the equatorial plane. This is done for the A>0 and A<0 polarity cycles with a current sheet tilt angle α=10°. Fig. 1, Fig. 2 show the intensities at 0.05, 0.20, 0.50, 1.00 and 5.00 GeV, respectively, as function of radial distance in the equatorial plane. The proton and anti-proton spectra are compatible with various sets

Discussion and conclusions

Newly computed LIS for CR protons, anti-protons, electrons and positrons make it relevant to revisit the computation of the charge-sign dependent effects for these species caused by gradient and curvature drifts in the heliosphere with a comprehensive model including the solar wind TS, the Jovian electron source, and a new set of fundamentally based diffusion coefficients. The purpose of this study was to compute the modulation of p, p̄, e and e+ using the corresponding new LIS, with a TS at

Acknowledgements

We thank Bernd Heber, Horst Fichtner, Adri Burger, Bill Webber and the participants of the Cosmic Ray Workshop in South Africa in March 2002 for many useful discussions and the SA National Research Foundation for partial financial support.

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