Solar activity undergoes a variation over time scales of several months known as Rieger-type periodicity , which usually occurs near maxima of sunspot cycles .
An early analysis showed that the periodicity appears only in some cycles , and is absent in other cycles .
But the appearance/absence during different cycles has not been explained .
We performed a wavelet analysis of sunspot data from the Greenwich Royal Observatory and the Royal Observatory of Belgium during cycles 14-24 .
We found that the Rieger-type periods occur in all cycles , but they are cycle-dependent : shorter periods occur during stronger cycles .
Our analysis revealed a periodicity of 185-195 days during the weak cycles 14-15 and 24 , and a periodicity of 155-165 days during the stronger cycles 16-23 .
We derived the dispersion relation of the spherical harmonics of the magnetic Rossby waves in the presence of differential rotation and a toroidal magnetic field in the dynamo layer near the base of the convection zone .
This showed that the harmonic of fast Rossby waves with m=1 and n=4 , where m ( n ) indicate the toroidal ( poloidal ) wavenumbers , respectively , perfectly fit with the observed periodicity .
The variation of the toroidal field strength from weaker to stronger cycles may lead to the different periods found in those cycles , which explains the observed enigmatic feature of the Rieger-type periodicity .
Finally , we used the observed periodicity to estimate the dynamo field strength during cycles 14-24 .
Our estimations suggest a field strength of 40 kG for the stronger cycles , and 20 kG for the weaker cycles .