The Heliotail Observed in TeV Cosmic Ray Anisotropy

The gyroradius of TeV cosmic rays is comparable to the size of heliosphere. Before they are detected by air shower experiments on the Earth, the trajectories of TeV cosmic rays are deflected by heliospheric magnetic field from its original interstellar pattern and they gain or lose energies in the motional electric field of the heliospheric plama. These propagation mechanisms causes the map of TeV cosmic rays seen at the Earth to look different from the map seen in the local interstellar medium if there were no heliosphere. We have developed a method of using Liouville's theorem to map out cosmic ray anisotropy from the local interstellar medium to the Earth with an assumption that the cosmic rays have a small pitch-angle anisotropy and a small uniform spatial density gradient as expected from diffusive approximation in Galactic propagation. The amount of heliospheric distortion can be determined by tracing the trajectories of cosmic rays propagating through the heliosphere. In this paper, we apply this method to TeV cosmic ray propagation with a MHD-kinetic model of the heliosphere. By fitting observations from Tibet ASγ and IceCube experiments, we are able to determine the cosmic ray distribution in the local interstellar medium. In the meantime, we are able to locate features in the TeV cosmic ray anisotropy that are associated with specific large-scale heliospheric magnetic structure. One of the features indicates that heliotail could be quite long, at least a few thousand AU.