University of Tasmania
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The spatial density gradient of galactic cosmic rays and its solar cycle variation observed with the Global Muon Detector Network

journal contribution
posted on 2023-05-18, 05:32 authored by Kozai, M, Munakata, K, Kato, C, Kuwabara, T, Bieber, JW, Evenson, P, Rockenbach, M, Dal Lago, A, Schuch, NJ, Tokumaru, M, Marcus DuldigMarcus Duldig, John Humble, Sabbah, I, Al Jassar, HK, Sharma, MM, Kota, J

We derive the long-term variation of the three-dimensional (3D) anisotropy of approximately 60 GV galactic cosmic rays (GCRs) from the data observed with the Global Muon Detector Network (GMDN) on an hourly basis and compare it with the variation deduced from a conventional analysis of the data recorded by a single muon detector at Nagoya in Japan. The conventional analysis uses a north-south (NS) component responsive to slightly higher rigidity (approximately 80 GV) GCRs and an ecliptic component responsive to the same rigidity as the GMDN. In contrast, the GMDN provides all components at the same rigidity simultaneously. It is confirmed that the temporal variations of the 3D anisotropy vectors including the NS component derived from two analyses are fairly consistent with each other as far as the yearly mean value is concerned. We particularly compare the NS anisotropies deduced from two analyses statistically by analyzing the distributions of the NS anisotropy on hourly and daily bases. It is found that the hourly mean NS anisotropy observed by Nagoya shows a larger spread than the daily mean due to the local time-dependent contribution from the ecliptic anisotropy. The NS anisotropy derived from the GMDN, on the other hand, shows similar distribution on both the daily and hourly bases, indicating that the NS anisotropy is successfully observed by the GMDN, free from the contribution of the ecliptic anisotropy. By analyzing the NS anisotropy deduced from neutron monitor (NM) data responding to lower rigidity (approximately 17 GV) GCRs, we qualitatively confirm the rigidity dependence of the NS anisotropy in which the GMDN has an intermediate rigidity response between NMs and Nagoya. From the 3D anisotropy vector (corrected for the solar wind convection and the Compton-Getting effect arising from the Earth’s orbital motion around the Sun), we deduce the variation of each modulation parameter, i.e., the radial and latitudinal density gradients and the parallel mean free path for the pitch angle scattering of GCRs in the turbulent interplanetary magnetic field. We show the derived density gradient and mean free path varying with the solar activity and magnetic cycles.

DOI for erratum: 10.1186/s40623-016-0417-1


Publication title

Earth, Planets and Space



Article number









School of Natural Sciences


Terra Scientific Publ Co

Place of publication

2003 Sansei Jiyugaoka Haimu, 5-27-19 Okusawa, Setagaya-Ku, Tokyo, Japan, 158-0083

Rights statement

Copyright 2014 The Authors-Licenced under the terms of the Creative Commons Attribution License (, (CC BY 4.0)which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.

Repository Status

  • Open

Socio-economic Objectives

Expanding knowledge in the physical sciences