The Algorithm of the Two Neutron Monitors for the Analysis of the Rigidity Spectrum Variations of Galactic Cosmic Ray Intensity Flux in Solar Cycle 24
Abstract
:1. Introduction
2. Two-Station Method for Determining Rigidity Spectrum Exponent γ of the GCR Intensity Variation
3. Experimental Results and Discussion
4. Conclusions
- (i)
- Based on the method of two stations for two pair monitors (Oulu–Potchefstroom and Mexico–Apatity), the changes in the RSV exponent γ of the GCR flux in the 24th cycle of solar activity were obtained. In solar activity minima and around the minima, the γ exponent varies in a range γ = 0.6–0.9, while in the SA maxima and in the vicinity, the gamma exponent changes in the range γ = 1.2–1.3;
- (ii)
- The RSV of GCR isotropic flux is soft in the SA maxima and in the vicinity of the SA, while in the SA minima and in the vicinity of the SA, it is hard in the considered period from 2009 to 2019. Thus, the universality of the temporal changes in the RSV of GCR isotropic flux for all 11 cycles of SA from 1965 to 2019 has been confirmed;
- (iii)
- The results obtained indicate the change in the character of the diffusion of GCR during the decreasing and increasing epochs of SA caused by the changes in the structure of HMF turbulences. In the period of increasing SA, the RSV of the GCR flux quickly becomes soft (i.e., the exponent γ quickly reaches its maximum value: γ = 1.3, while in the period of decreasing SA, the rigidity spectrum gradually becomes hard (i.e., the γ gradually changes from 1.29 to 0.64);
- (iv)
- The structural changes in HMF turbulence play a decisive role in the formation of long-term GCR variations in the heliosphere;
- (v)
- The presented two-monitor method is an alternative to the least squares method when there are only a few monitors working stably in a given period. Because of the lack of data, we cannot use the least squares method;
- (vi)
- The two-monitor method and the least squares method give similar results and confirm universal RSV changes in different periods of solar activity.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A. Calculation of Exponent γ by the Least Squares Method
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Year | AP | AO | AP/AO | AM | AA | AM/AA |
---|---|---|---|---|---|---|
2009 | 0 | 0 | --- | 0 | 0 | --- |
2010 | −1.48 ± 0.50 | −2.59 ± 0.11 | 0.57 ± 0.12 | −1.46 ± 0.08 | −3.20 ± 0.06 | 0.45 ± 0.10 |
2011 | −2.81 ± 0.20 | −5.69 ± 0.03 | 0.49 ± 0.07 | −2.52 ± 0.04 | −6.28 ± 0.02 | 0.40 ± 0.07 |
2012 | −3.82 ± 0.10 | −7.85 ± 0.01 | 0.49 ± 0.05 | −3.17 ± 0.02 | −8.59 ± 0.01 | 0.37 ± 0.05 |
2013 | −4.07 ± 0.09 | −8.89 ± 0.01 | 0.46 ± 0.04 | −3.65 ± 0.02 | −9.45 ± 0.01 | 0.39 ± 0.04 |
2014 | −4.75 ± 0.08 | −9.58 ± 0.01 | 0.50 ± 0.04 | −4.19 ± 0.01 | −9.99 ± 0.01 | 0.42 ± 0.04 |
2015 | −4.92 ± 0.06 | −9.65 ± 0.01 | 0.51 ± 0.04 | −4.53 ± 0.01 | −10.2 ± 0.01 | 0.44 ± 0.03 |
2016 | −2.62 ± 0.18 | −4.89 ± 0.03 | 0.54 ± 0.06 | −2.20 ± 0.03 | −5.14 ± 0.02 | 0.43 ± 0.05 |
2017 | −2.62 ± 0.26 | −3.20 ± 0.06 | 0.82 ± 0.07 | −1.12 ± 0.14 | −2.86 ± 0.06 | 0.39 ± 0.10 |
2018 | −1.13 ± 0.62 | −1.89 ± 0.12 | 0.60 ± 0.07 | −0.53 ± 0.36 | −2.02 ± 0.11 | 0.26 ± 0.06 |
2019 | −1.22 ± 2.17 | −1.38 ± 0.22 | 0.89 ± 0.49 | −1.24 ± 0.07 | −1.64 ± 0.16 | 0.76 ± 0.15 |
R = 200 GV | KP | KO | KM | KA | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
γ | min | av | max | min | av | max | min | av | max | min | av | max |
0.0 | 0.8748 | 0.8555 | 0.8362 | 0.8803 | 0.8534 | 0.8264 | 0.8686 | 0.8556 | 0.8426 | 0.8803 | 0.8534 | 0.8264 |
0.5 | 0.6148 | 0.5932 | 0.5716 | 0.8063 | 0.7455 | 0.6846 | 0.5452 | 0.5328 | 0.5203 | 0.8063 | 0.7455 | 0.6846 |
1.0 | 0.4905 | 0.4688 | 0.4471 | 0.9395 | 0.8237 | 0.7078 | 0.3820 | 0.3712 | 0.3603 | 0.9395 | 0.8237 | 0.7078 |
1.5 | 0.4258 | 0.4043 | 0.3828 | 1.3303 | 1.1008 | 0.8713 | 0.2889 | 0.2796 | 0.2702 | 1.3303 | 1.1008 | 0.8713 |
Rmax = 200 GV | KP/KO | KM/KA | ||||
---|---|---|---|---|---|---|
γ | min | av | max | min | av | max |
0.0 | 0.994 | 1.003 | 1.012 | 0.987 | 1.003 | 1.020 |
0.5 | 0.762 | 0.796 | 0.835 | 0.676 | 0.718 | 0.760 |
1.0 | 0.522 | 0.569 | 0.632 | 0.407 | 0.458 | 0.509 |
1.5 | 0.320 | 0.367 | 0.439 | 0.217 | 0.264 | 0.310 |
YEAR | γ(P-O) | γ(M-A) | KO | KP | KA | KM |
---|---|---|---|---|---|---|
2010 | 0.91 ± 0.26 | 0.92 ± 0.20 | 0.90 | 0.50 | 0.91 | 0.39 |
2011 | 1.09 ± 0.16 | 1.04 ± 0.14 | 1.00 | 0.46 | 0.97 | 0.36 |
2012 | 1.12 ± 0.12 | 1.21 ± 0.09 | 1.02 | 0.44 | 0.92 | 0.31 |
2013 | 1.27 ± 0.11 | 1.29 ± 0.08 | 0.78 | 0.40 | 0.78 | 0.29 |
2014 | 1.36 ± 0.11 | 1.21 ± 0.08 | 0.81 | 0.39 | 0.76 | 0.30 |
2015 | 1.32 ± 0.11 | 1.15 ± 0.07 | 0.80 | 0.39 | 0.74 | 0.31 |
2016 | 1.26 ± 0.14 | 1.07 ± 0.11 | 0.94 | 0.42 | 0.85 | 0.34 |
2017 | 1.15 ± 0.16 | 1.06 ± 0.19 | 1.03 | 0.45 | 0.98 | 0.35 |
2018 | 0.99 ± 0.16 | 0.71 ± 0.12 | 0.94 | 0.48 | 0.83 | 0.47 |
2019 | 0.94 ± 1.09 | 0.34 ± 0.28 | 0.92 | 0.49 | 0.80 | 0.65 |
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Iskra, K.; Siluszyk, M.; Wozniak, W. The Algorithm of the Two Neutron Monitors for the Analysis of the Rigidity Spectrum Variations of Galactic Cosmic Ray Intensity Flux in Solar Cycle 24. Universe 2024, 10, 311. https://doi.org/10.3390/universe10080311
Iskra K, Siluszyk M, Wozniak W. The Algorithm of the Two Neutron Monitors for the Analysis of the Rigidity Spectrum Variations of Galactic Cosmic Ray Intensity Flux in Solar Cycle 24. Universe. 2024; 10(8):311. https://doi.org/10.3390/universe10080311
Chicago/Turabian StyleIskra, Krzysztof, Marek Siluszyk, and Witold Wozniak. 2024. "The Algorithm of the Two Neutron Monitors for the Analysis of the Rigidity Spectrum Variations of Galactic Cosmic Ray Intensity Flux in Solar Cycle 24" Universe 10, no. 8: 311. https://doi.org/10.3390/universe10080311