Cosmic-Ray North–South Anisotropy: Rigidity Spectrum and Solar Cycle Variations Observed by Ground-based Muon Detectors

Abstract The north–south (NS) anisotropy of galactic cosmic rays (GCRs) is dominated by a diamagnetic drift flow of GCRs in the interplanetary magnetic field (IMF), allowing us to derive key parameters of cosmic-ray propagation, such as the density gradient and diffusion coefficient. We propose a new method to analyze the rigidity spectrum of GCR anisotropy and reveal a solar cycle variation of the NS anisotropy’s spectrum using ground-based muon detectors in Nagoya, Japan, and Hobart, Australia. The physics-based correction method for the atmospheric temperature effect on muons is used to combine the different-site detectors free from local atmospheric effects. NS channel pairs in the multidirectional muon detectors are formed to enhance sensitivity to the NS anisotropy, and in this process, general graph matching in graph theory is introduced to survey optimized pairs. Moreover, Bayesian estimation with the Gaussian process allows us to unfold the rigidity spectrum without supposing any analytical function for the spectral shape. Thanks to these novel approaches, it has been discovered that the rigidity spectrum of the NS anisotropy is dynamically varying with solar activity every year. It is attributed to a rigidity-dependent variation of the radial density gradient of GCRs based on the nature of the diamagnetic drift in the IMF. The diffusion coefficient and mean free path length of GCRs as functions of the rigidity are also derived from the diffusion–convection flow balance. This analysis expands the estimation limit of the mean free path length into the ≤200 GV rigidity region from the <10 GV region achieved by solar energetic particle observations.