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The Astrophysical Journal


This paper provides a theory of using Liouville's theorem to map the anisotropy of TeV cosmic rays seen at Earth using the particle distribution function in the local interstellar medium (LISM). The ultimate source of cosmic ray anisotropy is the energy, pitch angle, and spatial dependence of the cosmic ray distribution function in the LISM. Because young nearby cosmic ray sources can make a special contribution to the cosmic ray anisotropy, the anisotropy depends on the source age, distance and magnetic connection, and particle diffusion of these cosmic rays, all of which make the anisotropy sensitive to the particle energy. When mapped through the magnetic and electric field of a magnetohydrodynamic model heliosphere, the large-scale dipolar and bidirectional interstellar anisotropy patterns become distorted if they are seen from Earth, resulting in many small structures in the observations. Best fits to cosmic ray anisotropy measurements have allowed us to estimate the particle density gradient and pitch angle anisotropies in the LISM. It is found that the heliotail, hydrogen deflection plane, and the plane perpendicular to the LISM magnetic field play a special role in distorting cosmic ray anisotropy. These features can lead to an accurate determination of the LISM magnetic field direction and polarity. The effects of solar cycle variation, the Sun's coronal magnetic field, and turbulence in the LISM and heliospheric magnetic fields are minor but clearly visible at a level roughly equal to a fraction of the overall anisotropy amplitude. The heliospheric influence becomes stronger at lower energies. Below 1 TeV, the anisotropy is dominated by small-scale patterns produced by disturbances in the heliosphere.



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