Study of the Relationship Between Sunspot Number and the Duration of the ≈ 1.6 – 2.2 Year Period in Neutron Monitor Counting Rates

Neutron monitor counting rates show periodicities in the ≈ 1.6 – 2.2-year range. These periodicities have been associated with a solar origin affecting the cosmic ray propagation conditions through the heliosphere. Our hypothesis is that the periodicities in the ≈ 1.6 – 2.2-years range correspond to a single periodicity that changes its duration over time. López-Comazzi and Blanco ( Astrophys. J. 927 (2), 155, 2022 ) found that the duration of the ≈ 1.6 – 2.2-year period ( τ ) is linearly related to the average sunspot number ( SSN_a ) in each solar cycle. The relationship shows that shorter ≈ 1.6 – 2.2-year periods occur during stronger cycles when SSN_a is higher. Therefore, the duration of this period varies from one solar cycle to another. This study focuses on this relation. For obtaining this relation, the values of the duration of the ≈ 1.6 – 2.2-year period in global neutron monitor counting rates (a virtual station determined by averaging of the different neutron monitor counting rates along the world) along the Solar Cycles 20 – 24 have been used. We extend the sample by adding the duration of the ≈ 1.6 – 2.2-year period in Huancayo neutron monitor counting rates along Solar Cycle 19 to this linear relationship. Once the linear relationship is extended, τ for the current Solar Cycle 25 is computed giving ≈ 2.24 years. Drawing on this more accurate relationship given by SSN_a = (-120 ± 10) τ + (320 ± 20) , we computed τ for the cycles previous to the existence of neutron monitors (Solar Cycles 7 – 18). These ≈ 1.6 – 2.2-year periodicities in neutron monitor counting rates could be produce by variations in the solar magnetic field due to an internal mechanism of the solar dynamo called Rossby waves. Concretely, the harmonic of fast Rossby waves with m=1 and n=8 fit with the detected ≈ 1.6 – 2.2-year periodicity. In addition, the variation of the solar magnetic-field strength from weaker to stronger solar cycles could explain the different periods detected in each cycle. Based on the detected periodicities using the dispersion relation for fast Rossby waves, a solar tachocline magnetic-field strength of ≈ 7 – 25 kG has been estimated.