Study of the relationship between Sunspot number and the duration of the $\sim$1.6--2.2-year period in neutron monitor counting rates

Neutron monitor counting rates show, among others, a  $\sim$ 1.6--2.2-year period. This period has been associated with a solar origin affecting the cosmic ray propagation conditions through the heliosphere. The duration of this period varies from one Solar Cycle to another.
\cite{Comazzi_Blanco_2022} found the duration of the $\sim$ 1.6--2.2-year period ($\tau$) is linearly related to the averaged sunspot number ($SSN_a$) in each Solar Cycle.
In this piece of research, we have analyzed this relationship. This equation shows that shorter $\sim$1.6--2.2-year periods occur during stronger cycles when $SSN_a$ is higher. Drawing on this relationship given by $SSN_a = (-130 \pm 10) \: \tau + (330 \pm 30)$, we computed $\tau$ for the cycles previous to the existence of neutron monitors (Solar Cycles 7--19). 
By means of the Huancayo neutron monitor spectrum we checked the validity of this equation along the Solar Cycle 19. 
Once the previous relationship is checked, $\tau$ for the current Solar Cycle 25 is computed giving $\sim$ 2.22 years.

An internal mechanism of the solar dynamo called Rossby waves could produce these variations in the solar magnetic field  and, indirectly, in neutron monitor counting rates.
The harmonic of fast Rossby waves with $m=1$ and $n=8$ fit with the detected periodicity and the variation of the solar magnetic field strength from weaker to stronger Solar Cycles could explain the different periods detected in each cycle.
Finally, a solar magnetic field strength of $\sim$ 7--25 kG in the tachocline have been estimated based on the detected periodicities using the dispersion relation for fast Rossby waves.