Reconstruction of Interstellar Cosmic Ray Anisotropy via Heliospheric Propagation Modeling and SVD Inversion
Ground-based experiments such as the IceCube Neutrino Observatory and the High-Altitude Water Cherenkov Gamma-Ray Observatory detect cosmic-ray anisotropy on Earth, but magnetic deflections within the heliosphere complicate interpretation. Understanding the original spatial distribution of cosmic rays in the interstellar medium requires modeling particle propagation across the heliospheric boundary. We constructed a simulated transport model that backtracks antiprotons from Earth to the interstellar medium and maps spatial transfer probabilities across energies using HEALPix representations. Because our transfer matrices are singular, inversion relies on singular value decom- position regularization. Ground-based observations lose the equatorial North-South anisotropy component, severely degrading interstellar map recovery. We developed a geometric circle-fitting algorithm to estimate and reintroduce the missing component into the observed signals. Our results show that restoring the North-South anisotropy en- ables more accurate recovery of the interstellar dipole structure. Furthermore, Poisson statistical fluctuations on the detected event counts dominate matrix-transformation errors when spread over multiple energies.