Rigidity spectrum of cosmic-ray anisotropy observed by Global Muon Detector Network (GMDN)

The anisotropy of galactic cosmic-rays (GCRs) represents their momentum-space distribution in the interplanetary plasma, playing a key role in revealing the solar modulation of GCRs. The Global Muon Detector Network (GMDN) has been a unique means to observe the anisotropy, thanks to its excellent angular resolution, angular acceptance, and statistics. However, quantitative analysis of the rigidity dependence of the anisotropy has been difficult because of the broad rigidity responses of such ground-based cosmic-ray counters. To overcome this situation and derive the rigidity dependence from geomagnetic- and atmospheric-effect differences in the network's directional channels, we have developed a new analysis method based on the Bayesian estimation approach. The Gaussian process is introduced as a prior distribution for Bayesian estimation. It allows us to constrain the smoothness of the rigidity spectrum, which is required to derive the spectrum from the broad rigidity responses, while being tolerant of spectrum shapes without assuming any analytical function for the spectrum. This paper formulates this Bayesian approach and reports preliminary results of its application to a Forbush decrease event.